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Proceedings of the KAON Factory Workshop Vancouver August 13-14, 1979 Craddock, M. K. (Michael Kevin) 1979

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PROCEEDINGSOF THEKAON FACTORY WORKSHOPVANCOUVER AUGUST 13-14, 1979Editor: M. K. CRADDOCKMESON FACILITY OF:UNIVERSITY OF ALBERTA SIMON FRASER UNIVERSITY UNIVERSITY OF VICTORIAUNIVERSITY OF BRITISH COLUMBIA TRI-79-1TRI-79-1KAONPostal address: TRIUMF4004 Wesbrook Mall Vancouver, B.C. Canada V6T 2A3PROCEEDINGSOF THEFACTORY WORKSHOPVANCOUVER AUGUST 13-14, 1979Editor: M. K. CRADDOCKDecember 1979PREFACEThis volume contains the proceedings of the Kaon Factory Workshop sponsored by TRIUMF and held at the University of British Columbia on August 13-14, 1979, in conjunction with the Eighth International Conference on High Energy Physics and Nuclear Structure (EICOHEPANS). The Organizing Committee for the Workshop consisted ofM.K. Craddock (UBC and TRIUMF)H.W. Fearing (TRIUMF)J.R. Richardson (UCLA and TRIUMF)The purpose of the Workshop was to consider both the physics potential and the practical design of machines to produce intense beams of kaons and antiprotons (the term "kaon factory" in the title being used for succinct­ness rather than exactitude). The improvements in intensity considered to be within the capabilities of present technology ranged from a factor 10 for new beam lines (Brookhaven, KEK) to 100— 1000 for new accelerators and storage rings (CERN, Fermilab, LAMPF, SIN, TRIUMF, and the USSR). The current interest in developing these beams stems in large part from the exciting results recently obtained in experiments on hypernuclei, kaon scattering, exotic atoms and baryonium— indicating that K/pT factories have a potential for uncovering new physics at least as great as that of the existing pion factories.The Workshop sessions, which were held in parallel with EICOHEPANS, excited an encouraging display of interest, being attended by 230 delegates from 18 countries. The programme of the Workshop, listing the papers pre­sented orally, is given on p. 226. In this volume, these papers,together with the contributed papers presented at poster sessions, have been regrouped under more specific topic headings. With the kind co-operation of their authors, relevant papers contributed to EICOHEPANS have also been included. This should provide some picture of current work and remedy one deficiency in these proceedings— the lack of review papers on Workshop- related topics covered by invited papers at EICOHEPANS (and therefore deliberately omitted from the Workshop programme). For the following re­views readers are referred to the Proceedings of EICOHEPANS (editors:D.F. Measday and A.W. Thomas) to be published as a volume of Nuclear Physics:H.-M. Chan BaryoniumC.B. Dover Exotic atoms and hypernucleiB. Povh HypernucleiThe running of the Workshop was enormously simplified by the co-opera­tion of the EICOHEPANS organizers (led by E.G. Auld and D.F. Measday) who allowed us to hold the meetings in parallel and to parasite on many of their services. The Organizing Committee is especially grateful to May McKee, Bonnie Pyplacz and Dorothy Sample of the EICOHEPANS Secretariat, who looked after (among other matters) the registration and accommodation of the delegates. Assistance was also rendered by many of the TRIUMF staff; in particular Richard Woloshyn kindly helped in the selection of papers for oral presentation. Finally, Ada Strathdee has been responsible for the preparation of these proceedings, to which she has applied her usual high standards.M.K. CraddockiiiC O N T E N T SINTRODUCTION 6Opening remarks, J.R. Richardson .....................................  1Invited paper - Nuclear physics with kaons, C.B. Dover ............... 4Invited paper - Report on Los Alamos Kaon Factory Seminar: Physics,R.R. Silbar ......  12PARTICLE PHYSICSInvited paper - Symmetry-violating kaon decays, P. Herczeg .........  20Invited paper - Hyperon physics and chromodynamics, N. Isgur ........  33Invited paper - Physics possibilities with LEAR, a low-energyantiproton facility at CERN, U. Gastaldi and K. Kilian ............ 43The mechanism of baryonium and dibaryon, H. Nakamura ................. 59Unitary symmetry in dibaryon systems, T.N. Yuan, X.T. Chen,Y.G. Li, Y.S. Zhang and W.W. Wang .................................  63Search for narrow baryonium states near the pp threshold, R. Bertini,P. Birien, K. Browne, W. Bruckner, H. Dobbeling, R.W. Frey,D. Garreta, T.J. Ketel, K. Kilian, B. Mayer, B. Pietrzyk, B. Povh,M. Uhrmacher, T. Walcher and R. Walczak ...........................  65A production experiment of strange baryonium at SLAC, M. Cain,R.D. Kass, W. Ko, R.L. Lander, K. Maeshima-Petrini, W.B. Michael,J.S. Pearson, D.E. Pellett, G. Shoemaker, J.R. Smith,M.C.S. Williams and P.M. Yager .....................................  66Quark model description of the radiative decay of the resonanceA3/2-(1520), E.J. Moniz and M. Soyeur .............................  67Heavy quark-antiquark bound states in the framework of quantumchromodynamics, R.D. Viollier and J. Rafelski .....................  70Meson spectra, K.F. Liu and C.W. Wong ................................. 74HADRON-NUCLEUS INTERACTIONSInvited paper - Kaon elastic and inelastic scattering at 800 MeV/c,R.A. Eisenstein ..................................................... 75Invited paper - Kaon-nucleus interactions, F. Tabakin .................  82Neutron density studies through K~*"-nucleus scattering,S.R. Cotanch ........................................................  92Kaon-nucleus interactions in the A (1520) region, G.N. Epstein andE.J. Moniz ..........................................................  97Measurement of ^-nucleus elastic scattering at forward angles: Anexperiment to be done at KEK, I. Endo and Y. Sumi ..................  101vA production in pd reactions below 1 GeV/c, D.W. Smith, B. Billiris,M. Mandelkern, L.R. Price and J. Schultz ..........................  105Inelastic hadron-nucleus interactions at high energies, M.A. Faessler,U. Lynen, J. Niewisch, B. Pietrzyk, B. Povh, H. Schroder,P. Gugelot, T. Siemiarczuk and I.P. Zielinski .....................  109Hadron-nucleus total cross sections in the quark-parton model,B.Z. Kopeliovich and L.I. Lapidus .................................. 110HYPERNUCLEIInvited paper - Physics for a new kaon facility at the AGS, M. May ... IllA-nucleon potential and binding energy of the hypertriton,H. Narumi, K. Ogawa and Y. Sunami .................................  117A qualitative discussion of the A=4 hypernuclear isodoublet,B.F. Gibson and D.R. Lehman ........................................  121The (K- ,Tr“) strangeness exchange reaction on 6Li, 7Li and 9Be,W. Bruckner, M.A. Faessler, T.J. Ketel, K. Kilian, J. Niewisch,B. Pietrzyk, B. Povh, H.G. Ritter, M. Uhrmacher, P. Birien,H. Catz, A. Chaumeaux, J.M. Durand, B. Mayer, R. Bertini,0. Bing and A. Bouyssy .............................................  124Excited states in light hypernuclei from (K- ,tt-) reactions,N. Auerbach and Nguyen Van Giai ....................................  128OPossible observation of a y-transition in ^Li hypernucleus,M. Bedjidian, E. Descroix, J.H. Grossiord, J.R. Pizzi,A. Guichard, M. Gusakow, M. Jacquin, M.J. Kudla, H. Piekarz,J. Piekarz and J. Pniewski .........................................  133Search for E-hypernuclei by means of the strangeness-exchange reactions (K- ,7r~) and (K~,Tr"f), W. Bruckner, M.A. Faessler,T.J. Ketel, K. Kilian, J. Niewisch, B. Pietrzyk, B. Povh,H.G. Ritter, M. Uhrmacher, P. Birien, H. Catz, A. Chaumeaux,J.M. Durand, B. Mayer, R. Bertini, 0. Bing and A. Bouyssy ........  136Quantum chromodynamics and the spin-orbit splitting in nuclei andA- and E-hypernuclei, H.J. Pirner .................................. 140Supermultiplet structure and decay channels of hypernuclear resonances, excited via (K- ,it-) on 6Li target, L. Majling,M. Sotona, J. Zofka, V.N. Fetisov and R.A. Eramzhyan .............. 141Shapes of A < 41 hypernuclei, J. Zofka ................................ 142EXOTIC ATOMSKaonic hydrogen, A. Deloff and J. Law ................................. 143X-ray yields in kaonic hydrogen, E. Borie and M. Leon ................ 147Kaonic hydrogen atom and A(1405), K.S. Kumar and Y. Nogami ..........  150A search for K-p Ay and K~p -> E°y at rest, J.D. Davies, J. Lowe,G.J. Pyle, G.T.A. Squier, C.E. Waltham, C.J. Batty, S.F. Biagi,S.D. Hoath, P. Sharman and A.S. Clough ............................  154viKaonic atom optical potentials with Pauli correlations,I.E. Qureshi and R.C. Barrett ......................................  155X-rays from antiprotons stopped in gaseous H2 and D2 targets,E.G. Auld, K.L. Erdman, B.L. White, J.B. Warren, J.M. Bailey,G.A. Beer, B. Dreher, H. Kalinowsky, R. Landua, E. Klempt,K. Merle, K. Neubecker, W.R. Wodrich, H. Drumm, U. Gastaldi,R.D. Wendling and C. Sabev .........................................  159The atomic bound states of the ppT system, W.B. Kaufmann .............. 160EN effective potentials in E~ atoms, J.A. Johnstone and J. Law ......  164Short range correction to the energy levels, F. Ando ................. 166Data of hadronic atoms: A survey on X-ray energies, linewidthsand intensities, H. Poth ...........................................  170ACCELERATORS AND BEAMSInvited paper - An improved kaon beam and spectrometer for theAGS, E.V. Hungerford III ...........................................  171Invited paper - The Fermilab booster as a kaon factory, B. Brownand C. Hojvat .......................................................  178Invited paper - Possible kaon and antiproton factory designs forTRIUMF, M.K. Craddock, C.J. Kost and J.R. Richardson .............. 185Invited paper - A LAMPF kaon factory, D.E. Nagle .....................  197Future plans for SIN, J.P. Blaser ..................................... 202A cyclotron kaon factory, L.A. Sarkisyan .............................  203Low energy kaon beam with superconducting combined functionmagnets, A. Yamamoto, S. Kurokawa and H. Hirabayashi .............. 212SUMMARYInvited paper - Summary of the Kaon Factory Workshop, E.M. Henley .... 217Programme of the Meeting ..............................................  226List of participants ................................................... 227Author index ...........................................................  232viiOPENING REMARKSJ. Reginald Richardson TRIUMF, Vancouver, B.C., Canada V6T 1W5 and University of California, Los Angeles, CA, U.S.A. 90024I should first point out that in choosing the title "Kaon Factory Workshop" we had no intention of excluding antiproton factories or research with other particles that can be produced by intense proton beams in the energy range 8-30 GeV. Attention should also be called to papers in the main conference (Eighth International Conference on High-Energy Physics and Nuclear Structure) on baryonium, on hypernuclei and the parallel ses­sions on exotic atoms. Ordinarily these subjects would be included in the purview of this workshop, but under the present circumstances participants are referred to the main conference for these topics.The workshop is divided into two sessions on the physics research possibilities separated in time by one session on the possible hardware.We have requested reports on the physics justification for increased in­tensity by groups at Brookhaven, LAMPF and CERN, and also hardware reports from Brookhaven, Fermilab, TRIUMF, LAMPF and the LEAR project at CERN.FOUR QUESTIONSShould a kaon and/or antiproton factory be built? The answers to all four of the following questions should be evaluated before making a formal, serious proposal to construct a kaon/p" factory. By far the most important question is the following:1) Does the potential scientific research resulting from an increase in intensity justify the expenditure of the large amount of effort and money required? (Acquiring some feeling for the answer to this question is the primary reason for this present workshop.) In evaluating this question one wants to know how intense will the new beams be? What will be the factor of increase over present facilities? In order to give an order of magnitude I will say that M. Craddock tomorrow will describe the TRIUMF concepts giving proton beams to produce 500 times the intensity of the kaon beams potentially available from the AGS and 50 times the slow "p beams to be expected from the new LEAR project at CERN. (This is not an advertise­ment !)An additional question which must be answered in the affirmative:2) Is the concept technically feasible? I believe I can anticipate the results of tomorrow's hardware session by saying that all four invited papers will discuss concepts for increased intensity which are technically feasible. On other points it is probably too early to assess comparative merits. Presumably each concept has advantages and disadvantages.The next two questions are so dependent on the time, place and country involved that it is probably not profitable to discuss them here.3) Is the project feasible from the financial point of view?4) Is the project politically feasible? (Both science politics and national politics must be considered.)2Fig. 1. The relative number of antiprotons produced per incident proton as a func­tion of the energy of the incident proton. These data come from the 1963 compila­tion of Barashenkov and Patera. The data have been normalized to a pion produc­tion proportional to Eply/1+. The figures in parentheses give the momentum of the p" beam.Fig. 2. The production cross sections for K- and p" as a function of the incident pro­ton energy. The K~ momentum is 700 MeV/c while the "p momentum is 850 MeV/c. The Argonne data are of crucial importance in determining the shape of the curves. The target was 10 cm of copper in both cases. Note that the cross section for K- produc­tion is approximately 100 times that for p. The ratio K+ /K“ is about 4. D. Berley and L. Teng presented the data in BNL 50579 (1976).3DESIGN ENERGYIn deciding on the design energy of a kaon/p factory it is essential to know the production cross section for the particles of interest as a function of the energy of the incident proton. Unfortunately this infor­mation is somewhat uncertain— even contradictory in some cases. For example, early data on p" production as collated by Barashenkov and Patera1 are shown in Fig. 1. From these data one would conclude that the varia­tion of p” production with energy has a continuously increasing slope in the energy range 5-30 GeV. However, in Fig. 2 I have combined the data provided by D. Berley of Brookhaven and L. Teng of Fermilab to show both p” (850 MeV/c) and K- (700 MeV/c) in the same energy range. 2 It should be noted that the knees in both curves at approximately 10 GeV are primarily due to unpublished Argonne data, and the assessment of the true shape of the curves depends critically on the estimate of the error assigned to these data. It is clear that a critical analysis of all available produc­tion data should be performed before a final decision is made on the most cost-effective maximum energy for the accelerator. New data on the impor­tant energy region 8-20 GeV would be most welcome.WHY HANG A KAON/p" FACTORY ON THE END OF A MESON FACTORY?In many ways the most difficult energy region to traverse with an intense proton beam is that up to 500 MeV. The meson factories have al­ready done this. An accelerator of given aperture has a current limit at inj ection due toSpace charge. The maximum number of protons in one turn is propor- tional to fB2Y 3 (injection).Phase space. The amount of phase space available in admittance is proportional to 82Y2 or S3y 3 depending on the accelerator. (Liouville's theorem can be largely circumvented by stripping H- ions to H+ at injection.)Of less importance is the fact that for a synchrotron the fractional swing of the radio frequency is given by (1/B - 1). One can make the rough guess that the estimated cost of a kaon/p” factory would probably double if an existing meson factory is not used as an injector.REFERENCES1. V.S. Barashenkov and J. Patera, Fortschritte der Physik 11, 469 (1963).2. D. Berley, Brookhaven report BNL 50579 (1976), p. 257.L. Teng, ibid., p. 189.4NUCLEAR PHYSICS WITH KAONS*Carl B. Dover Physics Department Brookhaven National Laboratory Upton, New York 11973ABSTRACTWe review the types of nuclear and elementary particle questions which can be addressed by studying kaon-induced reactions in nuclei.Kaons offer a variety of possibilities for the study of nuclear and hypernuclear structure physics, as well as the interaction of strange baryons (A,E,h) with nucleons. Recently, there has been a surge of inter­est in kaon physics. Pioneering experiments-*- on the (K- ,ir-) strangeness exchange reaction at CERN and, more recently, at Brookhaven , have pro­vided us with a first glimpse of the excited state spectrum of hyper­nuclei. The present state of hypernuclear physics has been summarized at this conference-*- and in several recent review articles . I will, instead, focus attention on future directions in hypernuclear spectroscopy and the role of the K+ as a nuclear probe. We emphasize the unique features of kaons, but also point out the common ground shared with other hadrons in terms of nuclear structure studies.The K+ and K~ differ dramatically in their strong interactions withthe nucleus, particularly in the low and medium energy region(Plab - -*- GeV/c). This is in contrast to ir+ and it-, whose strong inter­actions with N=Z nuclei are the same. This difference points out the role of strangeness S, a conserved quantity for strong interactions. We have S = +1 for K+ and S = -1 for K“ ; the only baryons with |s|=l, stable withrespect to strong interactions, are the A and E with S = -1.The conservation of strangeness leads to very different interactions of K+ and K“ with nucleons, and hence, also with nuclei. The K-N system (S = -1) can fuse to form Y resonances (also S =-1) with a large cross section (a^ox ^ 30mb for 100 £ T^- < 500 MeV) . The Y* resonances, whichare ordinary three quark (Q^) composites, also communicate with the Att and Ett channels, which are energetically accessible even at the K N threshold. The propagation and modification of Y resonances in the nuclear environment is an intriguing problem, analogous to the formation of N resonances by ttN interactions in the nucleus. Like the pion in the resonance region, the K~ is a strongly absorbed particle in nuclei. Its interactions are thus primarily localized in the nuclear periphery.The K~*~N interaction, on the other hand, is relatively weak at low energies (axoT ~ 10mb for 4 800 MeV/c). The Y resonances are notpermissible as "compound states" of the K+N system, because of strange­ness conservation. Only the "exotic" S=+l resonances, called Z5 's, are* Invited talk presented at the TRIUMF Kaon Factory Workshop, Vancouver,B.C., Canada, August 13-14, 1979.** Supported by the U.S. Department of Energy under Contract No. EY-76-C-02-0016.5available. These necessarily have a more complicated quark structure (Q Q) than the Y*'s and occur at higher energy 800 MeV/c). In the absence of any open inelastic channels (charge exchange excluded) below the pion production threshold, the low energy K+N interaction is a rather simple "background" scattering. The associated K+ nuclear mean free path \ = (poxqt) is about 5-7 fm for Pqab £ 800 MeV/c. This implies that low energy K^'s are capable of penetrating the nuclear interior, unlike K~ and tt“. The K+ is the only hadron which exhibits this property of weak nuclear absorption. Loosely speaking, the low energy K might be referred to as an "electron" of strong interaction physics.A basic goal of nuclear and particle physics is the determination of the strong interactions operating between hadrons, in particular baryon- baryon and meson-baryon forces. Conventional nuclear probes, such as protons, alphas, and heavy ions, explore mainly the nucleon-nucleon sec­tor. By means of K+ and K- induced reactions on nuclei, our knowledge of the basic interactions can be extended. For instance, via the (K“ , tt-) reaction, a neutron in the nucleus is changed into a A particle. The level spectrum of the resulting hypernucleus is sensitive to the residual AN interaction.Other properties of the hypernuclear spectrum are also sensitive to the AN force. For instance, the energy splitting of ground state hyper­nuclear doublets registers primarily the spin-spin component of the AN potential^), which is expected to be repulsive. In this case, the A resides in an Sj, shell model orbit, coupled to a nucleon (or a nucleon hole) in orbit J'nZ j]. The doublet consists of states with J = j- \ and parity tt = (-»* f- . The ground state is the natural parity component with tt = (-) . This is opposite to the nuclear case, where the spin-spin force is attractive, and the ground state has an Si, doublet with tt = (-)^+ -^.These very interesting doublet splittings have not yet been measured in hypernuclei.The strength of the spin-orbit component of the AN potential can also be revealed by an analysis of hypernuclear spectra. This involves the comparison of levels which are presumed to be of pure particle-hole type, such as /yPjgs3/2 * NP -^*-3 . . The preliminary conclusion of the CERN group(^) is that the An spin-orbit force is much weaker than that for the NN sys­tem. If this is confirmed, it may cause some revision in our thinking regarding the origin of the spin-orbit force in the NN case, i.e., m meson dominance.The (K,tt) reaction can be used to produce E-hypernuclei via the ele­mentary processes K~p -> tt“E+ , tt+ E- or K n tt- E°. Because of strong E->-A conversion, we do not expect narrow E-states a priori. However, there may be surprises (selection rules) and we should be on the lookout for them. Some preliminary CERN results indicate some structure in the E region with a width of the order of 10 MeV^' , This permits extraction of the E well depth (about 20 MeV).Information on the AA interaction is not accessible in direct two body scattering experiments, but some average features of this interaction can be obtained from an analysis of the binding energies of double hyper­nuclei. Only two events, corresponding to the formation of AA^ He and AnBe, have been seen in K~ emulsion experiments^- . It would be very interesting to extend these results by counter experiments, using the (K-,K+) reaction to form the AA hypernucleus. More intense beams are6required for such experiments. Recently, some quark models have led to predictions of a stable dibaryon with strangeness -2, called the H.The H shares the quantum numbers of the AA system, although it is prej dieted to be bound by roughly 80 MeV with respect to the AA threshold .If such a particle exists, it might possibly be seen in the (K~,K+) reac­tion on nuclei.The interaction of kaons with nuclei may also be useful in shedding light on some aspects of dynamical symmetries and conservation laws. The possibility of "strangeness analogue resonances" (SAR) exists in the A hypernuclei. These are similar in structure to isobaric analogue reso­nances, and involve a coherent linear combination of states, each of which involves a neutron (for the reaction) changed into a A in the sameshell model state. The SAR is characterized by its permutation symmetry;the wave function is antisymmetric with respect to the interchange of the A and any neutron. Although this picture is an idealization, some theo­retical calculations indicate that there is a tendency to develop such collective states, particularly in heavy nuclei. Little is known experi­mentally in this region.In addition to the SAR, other "supersymmetric" configurations could exist in hypernuclei^), in the context of Sakata SU(3) symmetry. These states are predicted to lie well below the analog states (by 10-20 MeV) and correspond to symmetries which cannot be realized in ordinary nuclei because of the Pauli principle. As an example, consider the (lp)^ con­figuration outside the closed Is well. The orbital permutation symmetry for the resulting ground state of ^Be j_s dominantly [41] which also holds for the SAR in ^ Be*. However, other ^Be states exist with higher orbi­tal symmetry [5]. These "supersymmetric" states allow more relative s-state bonds for baryon-baryon interactions than the [41] symmetry, and hence they lie lower than the SAR. If we neglect the spin dependence of NN and AN forces, the ^Be* excitations may be grouped into irreducible SU(6) multiplets, corresponding to SU(3)x SU(2)a . An approximate SU(6) symmetry implies the existence of a number of non-analog states inti­mately related to the SAR and roughly degenerate in energy with it. The strength of the SAR could be distributed over a number of these excita­tions, leading to an interesting fine structure. The search for approxi­mate symmetries in hypernuclear spectroscopy is one of the most exciting prospects in strange particle nuclear physics.Aside from the question of symmetries, the spectroscopy of hyper­nuclei promises to be a rich and rewarding field. The experiments of the CERN groups have provided the first quantitative results on the excited state spectrum of light hypernuclei. These states have been interpreted as relatively pure A particle -n hole structures, analogous to the sim­plest excited configurations in the ordinary nuclear shell model. Other quantities of interest, which will be the focus of later experiments, include spins of excited levels, electric and magnetic multipoles, tran­sition multipoles, lifetimes and disintegration products. Numerous inter­esting questions of spectroscopy arise. For instance, one wouj.^ expect core excited states in hypernuclei' , such as a 1“ state in C com­posed of the 1/2“ excited state of C coupled to a A in the Sj^  orbit.There will also be cases where the A (Si*) + excited core configuration is approximately degenerate with the ground state core plus the A in a higher orbit. There will then be strong configuration mixing; the (K- ,tt-) crosssections to the two diagonalized states will be very sensitive to the details of the mixing. Excitation of giant resonances may also play a role. For example, one could first make a 2° hypernucleus via the pro­cess K n->Tr-Z°; the 1° could then convert to a A by exciting a T = 0 core to the T = 1 giant dipole resonance. Nucleonic decay modes of excited states could also populate interesting two^hole configurations in^the residual nucleus, i.e. K- + ^ C  -* tt- + , followed by /\ C -* + p.Such two hole states can be collective in heavy nuclei.One can also ask what can be learned about the properties of ordi­nary nuclei from a study of hypernuclei' '. For instance, a A coupled to a rotational or vibrational band would lead to a change of the moment of inertia or the effective phonon energy, respectively. In superconduct ing nuclei, the A can influence the energy gap; there could be an anomaly in the binding energy for such nuclei because of the important three body ANN potential. The A also lead!to alterations in electromagnetic proper­ties. For instance, we would expect changes to the quadruple moment of a rotational nucleus due to the additional core polarization induced by theA. This effect, which arises principally from the quadrupole component of the average AN potential, would lead to a change in the effective charge. Similarly, there would be modifications in the magnetic moment. The A would contribute through its spin; the orbital contribution would be zero, since the A always migrates to the Si^  orbit in the ground state. The A contribution is isoscalar, and it will modify only the isoscalar magnetic transitions of the core. Since the AN interaction is attractive the A will cause compression in the core, thereby increasing the Coulomb energy in the system and causing a change in radius. This radius change may be able to shed some light on the problem of nuclear compressibility.The A may also intervene in other areas of nuclear structure. In a mass region close to an oblate-prolate phase transition, the A may influ­ence the value of A at which the transition occurs. One is also invited to consider the possibility of K- - induced nuclear fission. A related problem would be the influence of A on "shape isomers", i.e. low-lying levels that spontaneously fission.K“ absorption on a nucleon in the nucleus can lead to the formation of a Y resonance. The Y*, like an N resonance formed by the absorption of pions,will propagate in the nuclear medium. Its energy and lifetime will be modified in the nucleus, due to Fermi motion, Pauli restrictions, collision damping, etc. These effects show up, for instance, in K and tt- nucleus elastic scattering and total cross sections, from which one can extract an energy shift and broadening of the resonance. It is essential to measure these cross sections in a variety of nuclei, in order to test many-body theories gf resonance propagation in nuclei. A good candidate for study is the Y (1520) resonance at 400 MeV/c. It is a narrow (P ~ 15 MeV) isolated resonance in a relatively high K”N par­tial wave (£=2).In contrast to the K , the K does not form resonances with nucleons at low energy, although there is the still unsettled question of exotic Z* resonances at P]_a^ > 800 MeV/c. Being weakly absorbed, the K+ is a promising probe of nuclear densities(9)} in particular, the neutron den­sity. There is less ambiguity in its reaction mechanism than for strong­ly absorbed particles. The K optical potential is largely determined by the term linear in the density, although higher order corrections have been estimated'9).8The K+ is of some potential use from the point of view of determining quasiparticle properties of single nucleon orbits. Via the (IT1', K+p) reaction, one might investigate the knockout of protons bound well below the Fermi surface, taking advantage of the weak absorption property of the K+. The (K-*-, K+p) reaction exhibits some simplifying features in compari­son to the usual (p, 2p) reaction, i.e. less dominant final state inter­actions^. The problem is again one of available K+ flux; the cross sec­tions are too small for experiments with currently available beams.Recent experiments involving tt~  absorption by deformed nuclei have led to the population of surprisingly high spin (up to 1 2+ or so) members of rotational bands in various residual nuclei. The mechanism for this is not yet well understood. It would be interesting to study the absorp­tion of K~ by the same deformed nuclei in order to compare to the pion results. Note that in K~ absorption, the resulting rotational band is that of the hypernucleus. There may hence be some interesting changes in the behavior of the system in a "backbending" region ( band crossing), if it can be reached via K~ absorption.With incident K+ or K- beams, one can inelastically excite the nu­cleus to various final states-^. The most strongly excited configura­tions are usually the natural parity (l- , 2+ , 3“) collective states, as is true for almost any elementary probe. In particular regions of energy the strong isospin dependence of the elementary K %  interaction can lead to approximate isospin selection rules for inelastic scattering. For instance, K+N non-spin-flip scattering is dominated by T=1 amplitudes below 500 MeV/c; the resulting nuclear transitions on N=Z targets have AT=0. An experimental test would support the results of phase shift analyses of the elementary interaction. The situation is less clear for spin-flip processes. A particularly interesting case involves transi­tions to maximum spin "stretch configurations" of differe^ isospin. An example consists of the T=0, 1  ^ 4~ states an ^ . Thesestates presumably are dominated by a single particle-hole configuration. Cross sections involving spin flip are usually quite small for K"^ 's (< 1 0 yb), and the experiments would be difficult with currently avail­able beams.One aspect which is of crucial importance is the possibility of pro­ducing a A at rest in the nucleus via the (K- , it-) process^3. This zero momentum transfer condition is achieved for an incident K~ momentum of 550 MeV/c. This enables the "walking A" to enjoy a rather large proba­bility of sticking to the nucleus, rather than being directly ejected into the continuum in a quasielastic event. Given a certain beam inten­sity, the (K- , ir-) reaction provides the optimum mechanism for hyper­nucleus production. Other reactions have been proposed, based on the sub­stantially larger beam intensities available for pions, protons, or heavy ions. These include the following:a) tt + (N,Z) -> a(N-1, Z) + K+b) p + (N,Z) -* a (N, Z-l) + p ’ + Kc) p + (N,Z) -> a (N, Z) + K+d) (N,Z) + p -> a (N-1, Z) + n + K+e) 3He + (N,Z)+ A(N+1, Z+l) + K+Reaction a) proceeds via associated production ir n->- AK on one nucleon.At * 1 GeV/c, the momentum transfer at 9 = 0° for the K is about430 MeV/° f°r the two body process. On a nuclear target, this is reduced somewhat, but remains larger than the Fermi momentum. Consequently, most9of the A's will escape quasielastically. Few low-lying, low-spin discrete states will be formed. However, the tt n-»-AK reaction may still be useful for forming certain high spin states at 0°, for which the large momentum transfer is well matched. Detailed estimates remain to be done.Reactions b) and c) also involve a sizable momentum transfer to the A, reaction b) being more favorable in this respect. Theoretical estimates have been made , with sizable cross sections predicted, but extensive searches-^ with the Saturne accelerator at Saclay have not yet seen dis­crete states of hypernuclei produced by process b.Reaction d) involves the production of hypernuclei by bombardment of a hydrogen target with high energy heavy ion beams (several GeV/particle). Mass 16 hypernuclei have actually been produced1  ^ in the LBL Bevatron using a beam of 2.1 GeV/ particle -^0 . Since the hypernuclei are relativistic, they are able to escape from thick production targets, and hence their lifetime can be measured. This information can be compared with theore­tical predictions for the lifetime based on the process AN->NN^ -^ .Process e) is an example of coherent K+ production with energetic light ion beams. There are no theoretical calculations for this reaction. The analogous production of tt°'s from nuclei has been observed with 60-200 MeV ^He beams^. Since the ratio of the He kinetic energy to the Q-value is quite similar for tt° and K+ production, one might expect^1 cross sec­tions of 1 pb/sr for K+Is.For K- physics, the main thrust of the next few years will continue to be concentrated in studies of hypernuclear structure via the (K~, it-) reaction. Measurements of K- and tt- elastic scattering will be necessary supplements, in order to pin down the optical model parameters. To sum­marize, some crucial aspects of hypernuclear structure includea) spin and parity assignments, from (K-, ir“) angular distributions or, in p-shell hypernuclei, from (K~, it- y) experiments,b) electromagnetic properties (static and transition moments), again via the (K- , tt- y) reaction,c) experiments with better energy resolution ( < 1  MeV) with aview towards resolving states of different spin arising from the same par- ticle-hole configuration, ex. (P3/2 P3/2~ ^  ^+ ’ T^ese split­tings will be very revealing of tne AN residual interaction. However, high resolution experiments of this kind require intense beams,d) the detection of core polarized states or weakly excited unnatural parity states, for example a ir = (-)^ + 1  member of the doublets,e) the search for collective strangeness analog resonances in heavy nuclei; the role of symmetries in hypernuclear physics.f) the possibility of narrow structures in the E-analog region; new selection rules; extraction of E well depth and its isospin dependence.For K+ physics, the problems are quite different here. We are studying the nuclear response to a very "gentle" probe. We are not con­cerned with a new spectroscopy but an augmentation of our level of know­ledge of ordinary nuclear structure. Some aspects of K+ physics include:a) extraction of neutron and proton densities from precision K"1" elastic scattering data; comparison with other probes, particularlye", p, tt1,b) inelastic scattering to collective states and also unnatural parity high spin states. Such experiments are feasible with existing beams, although sufficiently accurate elastic scattering data for a meaningful extraction of Pn(r) must await greater intensities.10REFERENCES1. B. Povh, invited talk at 8th Intern. Conf. on High Energy Physics and Nuclear Structure, TRIUMF, Vancouver, Canada, August, 1979; R. E. Chrien et al, BNL preprint (1979).2. B. Povh, in Reports on Progress in Physics 39^ , 824 (1976); Ann. Rev.Nucl. Part. Sci. 26_, 1 (1978).3. D. Walecka, Ann. Phys. (N.Y.) 63_, 219 (1971); see also A. Bambergeret al, Nucl. Phys. B60, 1 (1973) for comments on the spin-spin part of the AH potential.4. W. Bruckner et al, Phys. Lett. 79B, 157 (1978); A. Bouyssy, Phys.Lett. 84B, 41 (1979) .5. R. Bertini, in Proc. 2nd Int. Topical Conference on Meson-Nuclear Physics, Houston, March 1979, AIPCP//54 (AIP, New York, 1979), p. 703. R. Bertini et al, contribution to this conference.6 . M. Danysz et al, Nucl. Phys. 49_, 121 (1963); D. J. Prowse, Phys. Rev.Lett. 17, 782 (1966) .7. R. Jaffe, Phys. Rev. Lett. 38^ , 195 (1977).8 . R. H. Dalitz and A. Gal, Phys. Rev. Lett. 36^ , 362 (1976).9. C. B. Dover and P. J. Moffa, Phys. Rev. C16, 1087 (1977).10. R. H. Dalitz and A. Gal, Ann. Phys. (N.Y.) 116, 167 (1978); A. Gal,J. M. Soper and R. H. Dalitz, Ann. Phys. 66, 63 (1971); 7_2, 445 (1972).11. H. Feshbach, in Proceedings of the Summer Study Meeting on KaonPhysics and Facilities, Brookhaven National Laboratory, June, 1976, p. 391 (BNL-50579).12. R. D. Koshel, P. J. Moffa, and E. F. Redish, Phys. Rev. Lett. 39,1319 (1977).13. H. D. Engelhardt, C. W. Lewis and H. Ullrich, Nucl. Phys. A258, 480(1976) .14. C. B. Dover and G. E. Walker, Phys. Rev. C19, 1393 (1979).15. H. Feshbach and A. K. Kerman, Preludes in Theoretical Physics(Amsterdam, North-Holland, 1965), p. 260.16. V. N. Fetisov, M. I. Kozlov and A. E. Lebedev, Phys. Lett. 38B, 129 (1972) .17. E. Aslanides et al, quoted by T. Bressani and A. Fainberg in ref.(11), p. 137.18. K. J. Nield et al, Phys. Rev. C13, 1263 (1976).19. R. H. Dalitz, Proc. Intern. Conf. on Hyperfragments, St. Cergue,March, 1963 (CERN publ. 64-1, 1964), p. 147; see also ref. (11), p.l.20. N. S. Wall et al, Proc. of Vth Intern. Conf. on High Energy Physics and Nuclear Structure, Uppsala, 1973 (Ed. G. Tibell, North-Holland, 1974), p. 279.21. T. Bressani and A. Fainberg, ref. (11), p. 137.11DISCUSSIONPOVH: Can you tell me why should we look for Y*(1520) behaviour innuclei? What do we learn from these experiments? One should not forget that this type of experiment is hard as it requires kaons below 400 MeV/c.DOVER: We study the many-body dynamics of resonance propagation in nuclei.The Y*(1520) is an attractive case because of its narrow width in free space.BERNSTEIN: I want to express scepticism that neutron densities can beobtained from K+-nucleus scattering since pions at low energies are also weakly interacting and this just leads to a complex reaction mechanism.DOVER: The it- and K+ reaction mechanisms are very different at low ener­gies, even though both may have long mean free paths in nuclei. For ir- , the leading term in the optical potential, proportional to the elementary ttN s-wave amplitude, is very small. Large corrections due to true absorp­tion occur for low-energy tt- . These are not related to the single­particle density in any clear way. For K+, on the other hand, the first- order potential dominates at low energies and there is no true absorption contribution. Thus the optical potential for K+ is closely related to the single-particle density and offers a promising probe for this quantity.BARRETT: Are there any calculations of the K+-nucleon interaction usingthe quark model?BUGG: Yes, they have been done by Hamilton at NortheasternUniversity.DOVER: There are bag model calculations by D. Strottman and also by theNijmegen group of J.J. deSwart on the spectrum of exotic Z* resonances.HUNGERFORD: To provide the underlying basis for K-nucleus elastic and in­elastic scattering, the elementary amplitudes are needed. How well are these known and what experiments are needed to determine these amplitudes?DOVER: The elementary K+ and K- nucleon amplitudes are fairly welldetermined at 800 MeV/c. At lower momentum (<600 MeV/c), the situation is much worse.12REPORT ON THE LOS ALAMOS KAON FACTORY SEMINAR: PHYSICSRichard R, Silbar Theoretical Division, Los Alamos Scientific Laboratory Los Alamos, New Mexico 87545ABSTRACTThe motivations, discussions, and preliminary conclusions of the LASL Kaon Factory Seminar, which met 15 times in the Spring of 1979, are reported. It is technically feasible, but expensive, to build a kaon factory using LAMPF as an injector. Taking advantage of the increased beam intensity, excellent secondary beam lines could be built. While we continue further study of the physics justification for a kaon factory, we also propose to gradually increase LASL parti­cipation in kaon and antiproton physics.INTRODUCTION"A very important factor if one looks forward to a kaon factory," Louis Rosen remarked in a Physics Today article in 1966, is that a linac, such as the then-proposed LAMPF, could increase its energy by adding stages of acceleration. In the time since then, we have been building and learning how to use LAMPF, and this suggestion has lain more or less dormant. This last summer, however, it became clear that the question of a kaon factory was now ripe for consideration. This re­sulted in a report to the LAMPF User's Group Long-Range Planning Committee, 1 which discussed a possible configuration for a kaon factory extension of LAMPF and the kinds of physics questions that could be addressed by such a facility. In this report it was suggested that a working group be formed to study technical and scientific issues in more detail.In the Fall of 1978 we began discussing formation of such a group. We were spurred on in this regard by the realization that people at TRIUMF, our Canadian counterpart, had already presented preliminary design studies of a kaon factory extension for TRIUMF at the Cyclotron Conference in Bloomington, Indiana. 2 Further, in conversations with V. M. Lobashov (Inst, for Nucl. Res., Moscow), it also became apparent that our Soviet colleagues in Krasnaya Pakhra may have intentions of converting as soon as possible the meson factory under construction into a kaon factory. 3 Also, the LAMPF Technical Advisory Panel had urged the LAMPF management to direct some effort to long-range studies along this line. Thus, with the encouragement of Rosen and under the general guidance and prodding of Darragh Nagle (a preliminary organiza­tional meeting was held in his office in December), the Kaon Factory Working Seminar (KFWS) began its meetings on January 8 , 1979.The structure of the KFWS was broken down into two intermeshing subtopics— the physics aspects (organized by R. R. Silbar and J. D. Bowman) and machine/facilities aspects (organized by R. J. Macek andA. A. Browman). LASL divisions participating were MP, T, and, to a lesser extent, CNC, P, and AT. About ten persons were regular13attendees, but up to 20 people were at times present for a particular session. The seminar met 15 times during the Spring of 1979. In many respects it was a learning experience for most, if not all, of us. The last meeting before a long summer break was held in May, but we expect the KFWS to resume meeting in the fall.In this talk I will briefly summarize the physics aspects of our discussions. You will hear tomorrow from Darragh Nagle more detail concerning our machine-related and experimental-facility-related delib­erations. Also, tomorrow afternoon, Peter Herczeg will talk about what might be learned from a kaon factory regarding kaon and hyperon decays. This talk is an outgrowth from one that Herczeg gave in the KFWS in April.The subjects I will discuss today will necessarily be treated somewhat cursorily. You should view what I say more as a report on our seminar's activities than as an in-depth discussion of these physics topics. In fact, most of these subjects will be dealt with in detail by other speakers in this Workshop or in the ICOHEPANS program.I will try to flag the connections to these talks when appropriate.Although the kaon factory I am going to talk about would be a user-oriented facility, with user input at all levels of policy, much of what I will say has a strong LASL-centric flavor. Should Los Alamos get involved in proposing a kaon factory? Does it fit in with our laboratory-wide goals? Is it the natural extension of LAMPF, or is some other direction more appropriate for us to pursue? These questions were always in the back of our minds as we met.To conclude these introductory remarks, let me state the major conclusions of our first half-year of the seminar:1.) It is technically feasible to build a kaon factory using LAMPF as an injector (see Fig. 1). A reasonable energy for such a proton accelerator would be 15 to 30 GeV with a beam current of 100y amps, some 100 times more intensity than is available at the Brook­haven AGS accelerator. The cost of such a machine, together with experimental areas and facilities, is crudely estimated to be $150 M.2.) It looks feasible to build improved beam lines to take advan­tage of the increase in primary beam intensity. Such beams would have both good purity and flux.3.) The largest remaining question is whether the physics to be done with such a kaon factory is worth the cost and effort. We believe a number of the important topics of interest have now been identified, but they need critical study. Bear in mind, however, that some ofthe most interesting experimental programs being carried out at meson factories today were not dreamed of in the original justification.4.) A kaon factory need not necessarily be built at Los Alamos, but there are certain advantages to doing so. LAMPF can be used as an injector and there is a reservoir of experience in dealing with the transport of high-intensity beams and with high-radiation-level target cells. LAMPF itself would continue to be available for pursuit of physics and applications with the 800 MeV beam. At the time the kaon factory would become operative, however, many of the physics acti­vities and experimental facilities would probably be diverted to dealing with kaons and antiprotons.14Fig. 1. A theorist's-eye view of a kaon factory at LAMPF,CHRONOLOGY, SPRING 1979The fifteen sessions of the seminar, in summary, covered the following topics.January 8An organizational meeting, led by R. R. Silbar, which included discussion of competing projects at other national laboratories, review of previous kaon factory studies and workshops on "kaon physics," an example of how increased intensity would help in a 4°Ca(K+ ,K+)h°Ca experiment, and generation of a list of 16 topics that might be studied or discussed in these seminars.January 15Remarks by A. A. Browman on what sort of kaon factory could be built, assuming LAMPF as an injector. As mentioned, this and other such subjects will be discussed in detail by Darragh Nagle. Also,E. W. Hoffman reviewed what is presently achieved in kaon and antiproton secondary beams. The fluxes obtained depend upon primary beam energy, but there are "knees" in the production cross sections for low-energy K-,s around 10 GeV and for p's around 25 GeV. It was emphasized that present-day kaon beams are strongly contaminated by other particles, mostly pions, even after one stage of mass separation. This problem of beam purity is very important and must be faced if the full use of increased primary beam intensity is to be realized. In the course of the seminar we returned to this subject a number of times, as you will see, and we now feel this is a soluble problem.15January 29D. D. Strottman reviewed K+N and K+-nucleus physics. The situation with respect to "exotic" ichsi resonances is experimentally murky, but there are theoretical grounds for believing such resonances exist, in bag models or otherwise. For K^"-nucleus scattering, the weak KT*"N interaction suggests multiple scattering approaches are better founded than for TT-nucleus scattering. Glauber model predictions of elastic and inelastic scattering cross sections were presented.1* The subject of K+-nucleus scattering will be discussed by Eisenstein and Tabakin, the next two speakers, so I will not say more about this.February 5B. F. Gibson reviewed the status of hypernuclei, a form of nuclear matter in which one nucleon is replaced by a A (or E) hyperon. Several possible reactions for producing hypernuclei were discussed; the (K- ,7T-) reaction is currently of most interest. Physics to be learned from hypernuclei includes hypernuclear matter itself, aspects of the hyperon- nucleon interaction, and perhaps properties of ordinary nuclear matter from use of the A as a "test probe" unaffected by the Pauli principle.The reaction mechanism of recoilless A production, in (K- ,tt~), is some­what controversial, but good experiments at the "magic" beam momentumof 500 MeV/c are yet to be done. There are some very recent indications of the existence of E-hypernuclear states. The corresponding "magic" momentum for E-states is 300 MeV/c; presently no channel can provide such low-energy kaons. Hypernuclear physics has been reviewed at the ICOHEPANS session this morning by Povh, and will also be discussed by Dover on Friday afternoon.February 12C. M. Hoffman reviewed the BNL Workshop on the AGS Fixed-Target Research Program, held last November. 5 We have just heard of Brook- haven's plans in this regard from May. We also discussed at this time the CERN program on antiproton physics, which will be described in some detail tomorrow by Gastaldi.February 26R. L. Burman discussed the neutrino facility that will be proposed to take advantage of the proton shortage ring (PSR) at the LAMPF WNR facility. Such a short duty factor use of the PSR is very compatible with the neutron time-of-flight program of solid state investigations.March 19, March 26, and April 2Discussions by R. J. Macek, H. A. Thiessen, and E. Colton (Argonne National Laboratory), respectively, on the design of low-energy separated kaon beams. Based on experience, it is necessary to collimate at a secondary focus to improve the quality of such beams.April 6P. Herczeg reviewed the status of the CP-violation parameters in kaon decays. There is renewed interest in this subject because of gauge theories which have natural CP-violation built in. Of the "classical" suggestions for the origin of CP-violation, the -*■ 2tt parameters, together with the limit on the neutron dipole moment, tend16to rule out all but the "superweak" model. The differences between the Kobayashi-Maskawa gauge model and the superweak theory are small, but might be measurable in the future. As mentioned, Herczeg will expand on this subject in his talk tomorrow.April 16H. A. Thiessen reported on a meeting held at BNL to discuss an improved kaon beam and spectrometer there. (See talks by May and Hungerford at this Workshop.) A. A. Browman then made a number of com­ments on a kaon facility at LAMPF and gave some rough cost estimates.May 14M. M. Sternheim (University of Massachusetts, Amherst) reviewed the physics of kaonic and exotic atoms. This subject will be discussed in the ICOHEPANS program on Friday afternoon by Dover.May 17B. Povh (Max Planck Institute, Heidelberg) spoke informally on a number of subjects of interest to him, mostly in response to questions from the floor. His recent experience in p experiments was emphasized.May 21An informal discussion of where we are and what we should do. R. L. Burman discussed other proposals from other laboratories that are likely to be coming soon before NUSAC for consideration. G. H. Sanders presented, at some length, reasons why we at LAMPF should not build a kaon factory. Arguing from the physics program outlined in the Bowman- Gugelot-Nagle report, he pointed out that other, present-day facilities can satisfy many of the stated needs, at least for the nuclear physics problems posed. He then asked if there is an alternative future project for LAMPF that might be more interesting. One possibility might be a second proton storage ring, possibly with variable energy, for reinjec­tion into Area A. H. A. Thiessen also mentioned some possible smaller projects, such as additional experimental areas for LAMPF.May 29Wrap-up session for Spring, 1979. R. R. Silbar discussed material he sent to P. D. Barnes for the preparation of the NUSAC Facilities Subcommittee report on kaons and antiprotons. This was a somewhat personal distillation of the work of this seminar, particularly as it relates to the formulation of a core program for future work (at LASL, or elsewhere) in this subfield. This material forms the basis of the recommendations given below.SUBJECTS NOT YET DISCUSSEDIn the coming year, after the KFWS resumes, a number of other physics topics will be dealt with more fully. These include:I.) What can be learned in general from rare decays of kaons?(An extensive program investigating rare pion and muon decays has been underway at LAMPF for some time.)172.) What neutrino experiments can only be done with kaon factory beam intensities? What are the requirements imposed on a neutrino experimental facility?3.) How big are the advantages of studying pion-nucleus scattering at energies well above the (3,3) resonance?4.) Are there novel nuclear chemistry experiments to be done at a kaon factory? For kaon-induced reactions, a severe problem could be the pion contamination in the beam.PROPOSED CORE PROGRAM FOR LASL PARTICIPATION IN KAON AND ANTIPROTON PHYSICSThe following is a suggested program, developed together with J. D. Bowman and D. E. Nagle, for building up some LASL momentum in the direction of eventually building a kaon factory extension to LAMPF. The program is not yet official policy of the Los Alamos Scientific Laboratory management, nor is it even universally accepted by all the KFWS participants.Near Term ProjectsThis means activities that would be undertaken in the next five years.1.) It is quite likely that a new low-energy kaon beam will be commissioned and built relatively soon at the Brookhaven AGS. This would presumably optimize flux and purity to the extent possible at given present AGS intensity. It would be reasonable for LASL to par­ticipate in the design, but not the construction, of this new beam.This would naturally fall under activity of group MP-10; in fact,H. A. Thiessen has already been involved in preliminary discussionsof this beam (see seminar precis for April 16). Perhaps as much as0.5 SMY (Staff Member Year) could be invested by LASL in such advisory work.2.) In the next two years it would be useful for LASL to become involved in user-group experiments with kaons and antiprotons at other facilities, such as BNL. Two experiments come to mind in conjunction with further exploratory work on a kaon factory.(a.) The LAMPF tt° spectrometer could be easily transportedto BNL and applied to study the interesting strangeness- changing, charge-exchange reaction (K~,tt°) on nuclei.(b.) Production cross sections of K1 , p (and also tt- ) as afunction of beam energy, laboratory production angle, and atomic number (target) are only roughly known at present. Our present knowledge corresponds to that at LAMPF energies before we carried out the (much- cited) LASL experiment in 1969 to measure tt* production in detail at 730 MeV at the Berkeley 184" Cyclotron.It would be useful for future beam design studies to do the same for K's and p's.18An estimated level of effort for the two experiments would be about 5 SMY's each. Perhaps some of the work can be shared with one or more university user groups.3.) The "preproposal study" of kaon factory physics, as represented by this Seminar, should be continued. The basic question to be answered is whether the higher intensity of a kaon factory is really needed to do interesting nuclear and particle physics with K's and p's. It will soon be necessary, however, for some members of the Seminar, to participate using more than bootlegged time. To this end proposals for LASL Institutional Supporting Research funds have been submitted by bothMP and T divisions, each asking for 1 SMY of support in FT 80. Physics topics to be studied next year should include more detailed investi­gations of some of the subjects already discussed this last spring, as well as the subjects mentioned above as not yet having been touched.We also plan to look into a number of facilities-related questions.4.) It is desirable to increase the participation of other LASL Divisions and the medium energy physics community in these discussions.One way of achieving the latter is to encourage long-term visits by university people on sabbatical leave. The visitor would devote more or less full time to consideration of one of the above-mentioned topics.5.) If the suggested activity in Items 1.) - 4.) generates sufficient enthusiasm and momentum, we would begin to prepare a kaon factory proposal, presumably not unlike the "Blue Book" proposal for LAMPF in 1965. This might already begin three years from now and could involve perhaps 10 SMY of effort and extensive collaboration with the nuclear and high-energy physics communities.Long-Term ProjectsThis refers to activities five to ten years hence and assumes we will have decided that a kaon factory is worth proposing (Item 5. above). The design and proposal would be completed, and enlisting community support would begin. A political question to be answered is whether the expense of such a large project could be shared with some other country, such as Canada. If the project is authorized, many people will be involved in the construction of the ring and experimental facilities for many years. During this time, however, it would be useful for LASL to continue doing kaon and antiproton experiments in the user- group mode at other facilities. One experiment every two years might be a reasonable level of effort. This would be valuable experience that would ease the transition to doing physics at the kaon factory.CONCLUSIONSTo summarize our first semester of study in the KFWS at Los Alamos:1.) A kaon factory at LAMPF is technically feasible, but expensive.2.) There appear to be many interesting physics questions that can be addressed with such a machine.3.) The important task before us is to decide if the physics tobe learned warrants the expense and effort needed to build a kaon factory.As a result of a rather encouraging five months, we at Los Alamos will continue to pursue this line of development. The KFWS will be meeting again in the fall.REFERENCES1. J. D. Bowman, P. C. Gugelot, and D. E. Nagle, Report to the LAMPFUser's Group Long-Range Planning Committee, Sept. 1978.2. J.R. Richardson, Proc. 8th Int. Conf. on Cyclotrons and their Applications, Bloomington, Indiana, Sept. 1978, IEEE Trans NS-26, 2436 (1979); M. K. Craddock, C. J. Kost and J. R. Richardson, ibid., 20653. Yu. G. Basargin, et al. , Sov. Phys. Dokl. 18_, 229 (1973).4. D. D. Strottman, LASL Report LA-UR-79-398 (to be published).5. L. Ahrens, et al., ed., Workshop on the AGS Fixed-Target Research Program, Nov. 1978, Brookhaven Report BNL-50947, UC-34d.20SYMMETRY-VIOLATING KAON DECAYS P. HerczegTheoretical Division, Los Alamos Scientific Laboratory University of California, Los Alamos, New Mexico 87545ABSTRACTThe content of this talk comprises two parts. In the first, an analysis of the muon number violating decay modes of the K-mesons is given. Subsequently, some new developments in the field of CP-violation are reviewed and the question of time-reversal invariance and the status of CPT-invariance are briefly considered.INTRODUCTIONThe system of K-mesons has a remarkable record in the history of modern physics. In 1956, the famous "0-x puzzle" led to the discovery of parity-violation in the weak interactions. Eight years later, observation of the decay Kg -> 2tt destroyed the notion that CP-invariance is an exact symmetry of nature. More recently, the absence of any appreciable strange­ness-changing neutral current interactions, indicated by the strong sup­pression of decays such as Kg -*■ y+y- , demanded in the framework of unified gauge theories the introduction of the charmed quark. 1 Subsequently, the order of magnitude of the charmed quark mass was successfully predicted from the observed Kg-Kg mass difference. 2Instrumental to this role were the relatively large mass of the K- mesons which allows a great variety of decay modes, including some non- leptonic ones, and the existence of two distinct, almost degenerate, neu­tral kaon states. Is it conceivable that studies of K-decays would lead to developments of similar importance in the future? The areas that appear to have the best chance are again those where an apparent symmetry principle would be probed. In this talk, I would like to consider some topics which belong to this domain. This is not to suggest that other aspects of K- decays are of minor importance. Precision measurements of the "classic" kaon (and hyperon) decays, for example, have become especially important at the present time, since new theoretical developments suggest some deviations from the Cabibbo model. 3 Also important are detailed studies of nonleptonic decays, to understand the pattern of violation of the Al = 1/2 rule. Last, but not least, investigations of the "non-exotic" rare decays, such as Kg + y+y", K+ + tt+vv i.. .are of great value since here one probes the effects of the higher order weak and electromagnetic interactions, calculable in principle in renormalizable gauge theories, 14 and also the possible presence, at some level, of strangeness-changing neutral currents.MUON NUMBER VIOLATING KAON DECAYSRecently there has been considerable interest, both experimental and theoretical, in the question of possible muon number violation. This re­flects the realization that in unified gauge theories, it is possible to account for the stringent experimental limits for processes such as y -*■ ey, y“Z -* e“Z, Kg -> ey,.. .without having to require a fundamental law of muon number conservation, and moreover, that these processes could, in21fact, occur with branching ratios which are not far from the present experi­mental upper limits. 5The existing pion factories were essential for obtaining the severe bounds on the branching ratios of strangeness-conserving muon number viola­ting reactions and will continue to be indispensable for improving the attained accuracies. What additional information can one obtain from studies of the strangeness-changing processes? Would a facility capable of improv­ing considerably the existing limits be of great significance? These are the issues I would like to try to explore here. 6Restricting attention to decay modes which do not involve neutrinos and/ or photons, and which contain no more than three particles in the final state, the following muon-number violating, lepton-number conserving decay modes of the charged and neutral kaons are possible:k l e±p+, (la)K S -> e ^ + j (lb)k l-> Tr°e±p :':, (lc)K S p°e±p+, (Id)K± -> 7r+ e±p + . (le)Needless to say, none of these have been seen so far. Experimental upper limits appear to be available only for (la) and (le) . 7Let us consider the decay -> pe (K^ -*■ p+e“ } for definiteness) in some detail. The general form of the amplitude isM(Kl -* p+e-) = A UY5V + B uv , (2)where A,B are complex numbers. Neglecting the electron mass, the decay rate is given byT(KL -> p+e-) = mK (l - m2/m|-)2 ( | a| 2 + } B [ 2) / 8tt (3)= (1.8 x 107)(|A|2 + |B | 2) eV,and the branching ratio relative to KL -> all is (using T (KT -> all)exp= 1.27 x l(T8eV)B(KL -*■ p+e") = T (Kl -* p+e-)/r(KL + all) (4)= (1.4 x 101 5 )(|A|2 + [B [2).nTo elucidate the meaning of the experimental bound,B(Kl + y+e")<2 x 10-9 , (5)we shall have to consider the various ways in which muon number violation could take place. To remain as model-independent as possible, we shall first represent the muon number violating interaction involved by a phenomenological quark-lepton coupling of the form22Leff = " J  C(fVA + fAA W 5p)jA <6>+ (fSP ey + fpp eiy5y)Jp] + H.c.,where f\/A> fAA>«**are parameters characterizing the strength of the corresponding terms relative to 2- 1 / 2 G (G - 10“5mp2) andJA = SY\Y5d + dYxY5s (7)Jp = siYsd + diy5s „ (8)(6) is the most general nonderivative local effective Lagrangian that could contribute to K^^ye. As we shall see, it covers all the cases of interest.The contributions of (6) to A,B areA = (4.2 x 10_7)fM  aA + (2 x 10_6)fPP ap , (9)B =; -(4.2 x 10-7)fyA aA “ (2 x 10-6)ifsp ap (10)where aA>p are defined by<0 |j^[KL (p)> = p-^  mK aA/ /2mK (11)<01 Jp I Kl (p)> = -i m|- ap/ /2mK . (12)The constant aA can be estimated using SU(2) symmetry:<0| J^|kl (P)> = /2 <0| syxy5u|K+> = (EK //2mK) (13) while ap can be related to aA making use of the relation3XJ^ = (ms + md)Jp . (14)One findsaA « 0.48 (15)ap - aAmK/ (ms + md) -1.5 (16)where we have used fj^  - 1.23 1% ®  and ms - 150 MeV, md ~ 7.5 MeV for the quark masses.®For simplicity, we shall consider two special cases for the Lagrangian( 6) :a) fVA = fpp = fSP = 0 ; fM  + 0 ,b) fyA = fAA = fSP = 0; fPP ^ 0 •The experimental bound (5), together with equations (9), (15), and (16)implies thenfor cases (a) and (b), respectively.lfM | ^ 6 x 10-G (17)| fpp | ^ 4 x 10“ 7 (18)23Is there any further significant constraint on f^A, fpp? As we shall see, the answer is in general affirmative, since the interactions which lead to the effective Lagrangian (6) will, as a rule, also contribute to the - Kg mass difference Am = mL - mg, and Am, being second-order weak in magnitude, is extremely sensitive to contributions from strangeness- changing neutral "current" interactions.In the framework of unified gauge theories, -> ye (as well as other AS = 1 muon-number violating processes) could occur via higher-order effects (y,e coupled to intermixing leptons) or at the tree level, provided that there are neutral gauge bosons or neutral Higgs mesons coupled directly to both (ye) and (sd).1®Let us consider these possibilities individually:1) Muon number violation via neutral gauge boson exchange. In a sequen­tial SU(2)l x U(l) gauge theory, flavour-changing neutral gauge boson- fermion couplings are absent. 1 However, such couplings may, in general, be present if SU(2)l x U(l) was part of a larger flavour group. Quark-flavour and lepton-flavour changing transitions will also be present if the usual "vertical" gauge interactions are supplemented by "horizontal ones," which connect the generations, as may be necessary in order that the parameters of the mixing matrix, connecting the mass eigenstates and the gauge-group eigenstates, be calculable. 1 2Let us consider a fermion-gauge boson coupling of the formAfX = g,gYxY5lJ + g" + H.c. (19)with given by eq . (7). The Lagrangian (19) leads to an effective semileptonic interaction (6), with fgp = fpp = fVA = 0 ancl fAA = 8gTg"M^/g2Mx, (g2/8M^ = G//2) , and consequently to KL -*■ ye with a branching ratio (cf.eqs. (3), (9), and (15))B(Kl ye) - (3.7 x 103)(g'g"/g2)2 (my/mx) 4 . (20)The Lagrangian (19) will also give a contributionAmx = 2(g")2Re <K° | (sy'S'gd) (Sy^ygd) |k °>/m | (22)to the Kp, - Kg mass difference Am. There is no reliable method available at present to evaluate the matrix element (22). An estimate, which should be adequate for our purposes, can be obtained using the "vacuum insertion method." 1 3 We findAmX = ~3 fKmK(§"/Mx) 2 (23)- (2.5 x 103)(g"/g)2 (Mw/Mx ) 2 eV .For Amx not to exceed the experimental value Amexp - (3.5 x 10“6) eV, we must haveMx > (2.7 x 104) Mn . (24)As a consequence, for a given g* and g", B(KL -*■ ye) cannot be arbi­trarily large, but must obey11*B(Kl + ye) 5 (7 x 10"15)(g1/g")2 (25)24It follows that g'/g" - 500, B(KL -*■ ye) reaching its experimental upper limit (5) for g* = 500 g" . 15 If we assume (in the spirit of unified gauge theories) that g' - g" - g, thenMx - (2.7 x 10 )M^ , (26)ea a IIfaa! < IQ-8 , (27)andB(Kl + pe) f 7 x 10" 15 . (28)2) Muon number violation via neutral Higgs exchange. If the Higgs sector of the SU(2)l x  U(l) model is extended to include at least two ^  Higgs doublets, muon number may be violated by the Higgs-lepton couplings. The neutral Higgs mesons which mediate y <-*■ e transitions could, in general, be coupled also to AS = 1 quark densities, leading to processes such as Kl ye. Muon number may be violated also by Higgs mesons associated with group structures beyond SU(2)l x  U(l).Let us consider a Higgs-fermion interaction of the formffh = gh(siy5d 4- diy5s)<J>h + g£ eiy5y<j)h . (29)The contribution of (29) to B(Kl ■> ye) and Am is given byB(KL -> ye) = (1.3 x 10It)|fpp| 2 (30)- (1.3 x 101+)(/2 ghg^/Gm^ ) 2andAmh = f (Sh/mh)2mKfK2 tmK/(ms + md)^2* (3DAmexp and eq. (31) implymh > 107g|; GeV (32)so that for a given g^ and g^, we must haveB(Kl -> ye) 1 (1.6 x 10~lt+) (g^/gh) 2 * (3 3)Consequently, the experimental limit (5) requires g^/g^ - 350. As an example, suppose that g^ = 2*/Itmp and g^ = 2^/Lfms/G. It follows thatmh > (6 x 103) GeV (34)B(Kl + ye) < 8 x 10” 1 5 . (35)The choice g^ = 21 /'+my^G, gft = 21 /1+mdv/'G would, instead, lead tomh > 320 GeV (36)B(KL ye) < 3 x 10-12 . (37)25Larger values of BCKL^ye) corresponding to other ratios for the Higgs couplings cannot be, of course, ruled out.3) Muon number violation via intermixing leptons. A prominent example here is the standard sequential six quark-six lepton SU(2)l x  U(l) model, which has so far been remarkably successful in accounting for a wide variety of weak interaction data. Even in the absence of the mechanisms described earlier, muon number will not in general be conserved as long as the neutrinos are not all exactly massless (or degenerate). Neglect­ing muon number violation due to v , v mixing, all muon number violating effects will be proportional to the parameter By where 3 and y measure the amount of the vT mass eigenstate in the gauge-group eigenstates ve and Vy, respectively. * 7 ’ * 8 The -> ye rate in this model has been calculated in ref. 17. With the experimental limits (By) 2 < 2 x 10" 3 I? * * 8 and m^ < 250 MeV*8 one obtainsTB(Kl -* ye) < 5 x 10" * 6 . (38)We are now ready to state our conclusions regarding -»■ ye:a) Above the level of about 10-11+ for the branching ratio, the decay -> ye is not expected to be sensitive to a flavour changing neutral gauge boson coupled to (ye) and (sd) with comparable strength. In con­trast, for a neutral gauge boson coupled to (ye) and to a strangeness- conserving quark density only, the rate for y“Z -> e~Z could be as large as the corresponding experimental limit. 20 Consequently, in the range 1 0 - 1 9 < B(Kl -*■ ye) < 2 x 1 0 -9 the decay Kl -*■ ye probes the presence of other possible sources of muon number violation, b)A branching ratio consider­ably larger than ^ 1 0 - *2 would suggest any of the following possibilities or combinations thereof: the existence of an additional generation ofleptons and quarks2* ; the presence of a neutral Higgs boson22 coupled to (ye) more strongly or to (sd) more weakly than we have assumed above; the existence of a strangeness and muon number changing neutral guage boson with a considerably stronger coupling to (ye) than to (sd).Concerning Kg -*■ ye, no experimental information seems to be available yet. This decay is sensitive to the antisymmetric combination sr-id - d r ( i  = A,P). In general, (ye) may be coupled to a linear combi­nation a(sFd) + b(3rs) with a £ ±1, allowing for both KL a- ye and Kg -*■ ye to occur even in the approximation Kg L = K1j2*We shall turn now to consider briefly K-*- -*■ ir+ye. This decay would be sensitive to an effective interaction analogous to (6) but involving vector, scalar, or tensor23 quark densities. For a vector coupling the branching ratio isB(K+ -* Tr+ye) = r (K+ -> 7r+ye)/r(K+ -* all) = (6.4 x 10“*) f f w  | 2 . (39)Assuming that the contribution to Am of a neutral gauge boson Xy coupled to Jv = syxd + dy^s is comparable to Am^ (eq. 23), one obtainsB(K+ -> Tr+ye) < (8 x lCT17) (g^/gv) 2 to be compared with the experimental limit7B(K+ -*■ Tt+ye)exp < 7 x 10~9 . (41)26For a scalar coupling,BCK4" -* Tr+ye) = 8 |fs s |2 , (^2)and Amexp implies (assuming Amg = Amh),BOT*- + /pe) < 10"1 7 (g^/g'^)2 . (43)For gg/g's = and gg/gg = nip/md’ ^ 2  ^ leads toB(K+ h, 7r+pe) < 6 x 10- 1 8 (44)B(K+ -v ir+ye) < 2 x 10- 1 5  (45)andrespectively.In the standard SU(2)l x  U(l) model with three generations, one would have B(K+ Tr+ye) < 6 x 10“ 1 8 .*7As seen from eqs. (39) - (46), compared to the results for -> ye,IC1" -> ir+ye is much less sensitive to a vector or scalar coupling than Kt ■* ye is to an axial vector or a pseudoscalar one.No experimental limits are available for K ^ g  -*■ TT°ye. Both will occur (as well as id- -> Tr+ye, to which they can be related) if (ye) is coupled to a general combination air^d + bdr^s (i = V,S,T) even in the approximationk s ,l  = k  .CP, T, and CPTAlthough the discovery of CP-violation dates back to 1964, its origin remains an unresolved question. The experimental developments since 1964 can be summarized as follows:21* 1) No CP-violation (or T-violation) was found outside the neutral kaon system; 2) More accurate experimental infor­mation became available on the parameters which describe the observed CP- violation; 3) Sharper limits were set on CP or T-violating amplitudes in various processes. The data are consistent with a theory in which CP- violation arises solely through the mixing of K° and K2, such as a super- weak theory.25 On the theoretical side, the success of unified gauge theo­ries led to investigations of the possible ways in which the observed CP- violation could arise in such a framework.26 The basic mechanisms are CP- violation in the gauge boson—quark couplings and in the interactions of Higgs mesons. Below we shall discuss briefly two models which are of imme­diate experimental interest.1) CP-violation in the gauge boson interactions. The prominent example is again the sequential SH(2) x U(l) model with three generations (the minimal number that could accommodate CP-violation in the fermion-gauge boson couplings) . 27 CP-violation could reside also in the couplings of gauge bosons belonging to a larger flavour group*28In the six quark-six lepton model, the mixing matrix, which relates the quark mass-eigenstates d,s,b to the gauge group eigenstates d'js'jb', con­tains three mixing angles 0j, 02, 63 and a CP-violating phase, 6 :27andImAo/ReAo = fK’F . (50)In eqs. (48) - (50), A0 is the K -* 2tt(I = 0) amplitude,K 1 = s2c2t3 sind/ci, (tp = tan0^) and fReAQ is the fraction of ReA0 due to pegguin diagrams. F ^nd F are functions of mc/mt and K = s2 + s2c2t3COs6/ci. F, in addition, depends on the cutoff mass y in the evaluation of the penguin diagrams. (l-D)Am = Ambox is the usual box-diagram contribution to Am = m^-nig and DAm is the part of Am arising from contributions of low-mass intermediate states (it0 ,13, 2ir ,... ) , which cannot be reliably calculated.For f 0, apart from some new effects in rare kaon decays and in the decays of charmed particles, the model reproduces closely the results of the superweak theory.31 An important result, arrived at in ref. 32 is that for an appreciable value of f (which may be the clue for the understanding of the Al = 1/2 rule), the ratio| e 1 /e | = fF/(l-D)(fF+F) (51)could be as large as the present experimental limit |e’/e|exp - 1/50.24For a given value of other parameters, (51) turns out to be a de­creasing function of K. The maximum allowed value of K, dictated by D, corresponds to the minimum of |e’/e|. Assuming [D| < 2  (suggested by estimates of DAm) and choosing f = 1/2, m2/y2 = 2.25, mt;/mc = 10, the limits |e1 /e| ^ 7.7 x 10-3 or |e’/e| ^ 9 x 10- 3 are obtained, 30 depending on whether the box diagram was calculated by vacuum insertion, or in the bag model . 8 Smaller values of |e’/e| (which would correspond to larger values of one or more of the quantities mt/mc, mc/y, and D, or to a small­er value of f30’32) cannot be, of course, ruled out.In addition to effects in K -> 2tt, deviations from the superweak pre­diction may occur also in some other nonleptonic decays, for example, in K -> 3tt. Predictions of the possible magnitude of such effects are yet to be made . 33 In semileptonic decays no CP-violation is present in lowestwhere = cos 0], s^  - sinThe parameters e and e * involved in the CP-violating observables29n | - e 4- e ' (46)nCo ~ e _ 2e' (47)are predicted in this model to be^®/2|e| = (l-D)(ImA0/ReA0 + K ’F) , (48)v^ 21e 1 | = (1/20) IroA0/ReA0 (49)28order. The electric dipole moment of the neutron Dn is predicted to be of the order of 1 0 -29 to 1 0-30, (to be compared with the present experi­mental limit i Dn| exp < 1.6 x 10~2k (90% C.L.) )31* which presumably would not be attainable even with the next generation of experiments.2) CP-Violation through Higgs boson exchange. If the Higgs sector of the SU(2)l x U(l) model is extended to include at least three doublets (at least two, if the neutral Higgs exchange is allowed to change flavour), the quartic self-interaction of the Higgs bosons may, in general, violate CP . 35 CP will not be then conserved by the scalar propagators and as a result, the exchange of a Higgs boson will induce an effective CP-violating Fermi interaction with strength of order Gmm'/m^ . 36CP-violating effects in this model have been estimated in ref. 37 with the results |e’/e| - 0.02(!) and Dn = -2.8 x 10-25. It should be noted that by increasing the "transition" Higgs mass, Dn could be made correspondingly smaller, but the model could not then account for the ob­served CP-violation. The latter, on the other hand, may be due to other causes. In order that [e T/e|could have a smaller magnitude, further Higgs doublets seem necessary. CP-violating effects are expected also in semi- leptonic reactions, notably a muon polarization Py normal to the decay plane in k£ -* ir_y+v and K+ -* Tr°y+v, corresponding to Im? (the ratio of T-violating and T-invariant form factors) of order 10-3, to be compared with the present experimental limit Im£ = 0.012 ± 0.026.38 Again, smaller values of Im^ cannot be ruled out. In particular, CP-violating effects in Kl 2 tt and in K^may not be related, since in the leptonic couplings a different Higgs meson might be involved. To search for smaller P^,K+ -> Tr°y+v is the better suited, since here the final-state interactions are relatively negligible.In addition to CP-violating quantities such as n+_ and n00> we have also encountered in models described above observables which violate time- reversal invariance. The simultaneous appearance of CP-violation and T- violation is of course a consequence of the CPT theorem, which is satisfied in a local relativistic quantum field theory, such as the models we have considered. Although the success of gauge theories has but strengthened our belief in local quantum field theory as the correct framework to des­cribe the fundamental interactions, it is important to remain open-minded and to be aware of the extent to which consequences such as the CPT theorem have been experimentally tested.As emphasized in ref. 39, the existing bounds on the strength of possi­ble CPT-violating interactions depend on their symmetry properties. The best available limit refers to the case when the CPT-violating interaction is also CP-violating, but conserves parity and strangeness. It is deduced from the limit on the mass difference between K° and K°,Sk e [m (K°) “ m(K°)]/(mL - m s ) . 39 Let us write for the parameter e (in eq.46) e = e + 6 , where e and <5 represent the CPT invariant (T-violating) and CPT-violating (T-invariant) parts, respectively. An evaluation1*0’21* of the Bell-Steinberger unitarity relation, using the present experimental informa­tion yields21* Ree = (1.61 ± 0.25) x 10-3, Ime = (1.40 ± 0.25) x 10-3,ReS = (-0.03 ± 0.27) x 10-3, and Im§ = (-0.23 ± 0.27) x 10-39implying that the observed CP-violation is predominantly due to a T-violating (CPT- invariant) interaction! The constant 6 is related to 6^ as /26 = (1/2)6k + B0 39 where B0 ~[y(K0) - y (K°) ] / [y (K°) + y(Ko)] (y(K°) and y(K°) are the decay width of K° and K0) . 39 Assuming that 60 - =[y(K+) - y(K-)]/[y(K+) + y(K")], one infers from the experimental bound29Ak - 10~ 3 1+1 that |<5^ | - 4 x 10~3. Denoting the strength of the hypotheti­cal CPT-violating interaction by yG (G = Fermi constant), its contribution to ($£ is of order | <SK I - yG/G2 = y/G and consequentlyy 1 (4 x 10_3)G (52)implying that the strength of the CPT-violating interaction must be of the order of the superweak interaction or smaller. The limit could be improved by better information on CP-violating K° decay modes and on (provided that the assumption B0 - AK holds39). If the CPT-violating, CP-violating interaction violates parity or strangeness (or both), the information on its strength is weaker: [<$K [ - yG2/G2 = y < 4 x 10~3. A limit of | y | < 10-3  is obtained from AK (or from A^ < 10- 3 , l+2 for the AS = 0 case) . 39 Thus in this case CPT-violation at the level of a milliweak interaction is still tolerable! The limit could be improved by a more accurate experimen­tal result on AKj7r. For CP-conserving, CPT-violating interactions, the limit from 6^, A^, or A^ depends on the strength of the CP-violating inter­action. In most cases the best limits are obtained instead from direct tests of time-reversal violation. 39CONCLUSIONSThe main subjects of our discussion were muon number violating processes with change of strangeness, and some new developments in the field of CP- violation. Although unified gauge theories provide a number of possible mechanisms for the breakdown of muon number conservation, muon number viola­tion is not obligatory, and its discovery would be an event of great impor­tance. On the basis of our discussion it appears that the chances for muon number violation to be found, with a branching ratio between about 1 0-*1* and the existing experimental limits, are better for the AS = 0 reaction y-Z e-Z than for the AS = 1 processes we considered. Once muon number violation was found, however, studies of the AS = 1 processes would provide new information on the underlying mechanisms. Independently of whether muon number violation is seen or not, improved experimental limits on AS = 1 muon number violating processes would give important constraints, independent of those imposed by the leptonic and the AS = 0 semileptonic reactions, on the possible muon num­ber violating interactions.Unlike muon number violation, the breakdown of CP-symmetry is an esta­blished fact. The aim of the experiments is to identify the interaction re­sponsible for it. The prospect that one may be able to distinguish some of the possible sources of CP-violation from a CP-violating superweak inter­action is a most exciting one, and to improve the accuracy of the relevant experiments is of the greatest importance. Some progress can already be made by the existing machines, 113 but for the final answer we may have to wait for new, high intensity beams of kaons.ACKNOWLEDGEMENTSI wish to thank the Physics Department of the University of Sussex where part of this talk was prepared for their warm hospitality, andC. M. Hoffman for useful conversations.30REFERENCES* Work performed under the auspices of the United States Department of Energy.1. S. L. Glashow, J. Iliopoulos, and L. Maiani, Phys. Rev. D2, 1285 (1970); S. Weinberg, Phys. Rev. D5, 1412 (1972).2. M. K. Gaillard and B. W. Lee, Phys. Rev. D]0, 897 (1974);Phys. Rev. D13, 2674 (1976).3. See, for example, R. E. Shrock and L. L. Wang, Phys. Rev. Lett. 41,1692 (1978), and references quoted therein.4. M. K. Gaillard and B. W. Lee, Phys. Rev. DIO, 897 (1974).5. P. Depommier, inv. talk, 8th Intl. Conf. on High Energy Physics andNuclear Structure, Vancouver 1979; B. Hahn and T. Marti, Lectures at the Erice School on Exotic Atoms, 1979.6. We shall give a more detailed account of the investigation describedin this section, along with a discussion of the lepton-number non­conserving decay modes, in a forthcoming paper.7. Particle Data Group, April 1978 Edition, CERN, 1978.8. R. E. Shrock and S. B. Treiman, Phys. Rev. D19, 2148 (1979).9. S. Weinberg, Transactions of the New York Academy of Sciences, _38, 185(1977)10. Still another possibility may be muon number violation through exchange of leptoquarks (bosons causing quark -«-*■ lepton transitions appearing in theories which unify the strong and the flavour interactions). Although leptoquarks are expected to be in general too heavy to cause detectable effects, it is interesting to note that the corresponding AS = 1 muon number violating effective interaction would not be significantly con­strained by Am, since in lowest order there is no accompanying nonlep- tonic interaction.11. S. L. Glashow and S. Weinberg, Phys. Rev. D15, 1958 (1977).12. F. Wilczek and A. Zee, Phys. Rev. Lett., 4_2, 421 (1979).13. The vacuum insertion "approximation" is discussed in ref. 8, where the bag model is used instead to calculate Am in the standard six quark model, yielding Am^ag - 1/2 Amvac.14. It should be noted that in arriving at the bound (24), we have ignoredthe possibility of cancellations among the various contributions to Am.Thus, B(Kl ye) could, in fact, be larger than the upper limit given in eq. (25).15. A conceivable situation (which does not seem to be however very attrac­tive) that could lead to -> ye with vastly different magnitudes for g* and g" would be the existence of separate horizontal gauge groups for leptons and quarks, with gauge bosons Xl and X*1 which mix with each other.16. J. D. Bjorken and S. Weinberg, Phys. Rev. Lett. B8, 622 (1977).17. T. P. Cheng and L. -F. Li, Phys. Rev. D16, 1565 (1977); B. W. Lee, et al, Phys. Rev. Lett. _38, 937 (1977); B. W. Lee and R. E. Shrock, Phys. Rev. D16, 1444 (1977).18. G. Altarelli, et al, Nucl. Phys. B125, 285 (1977). See also B. Hahn and T. Marti, ref. 5.19. W. Bacino, et al, Phys. Rev. Lett. 42, 749 (1979).20. The rate for coherent y- -*■ e~ conversion in sulfur would, in this case, be Ry°^ - (5 x 103) (M^Mx)^ [we have used the formula of 0 . Shanker, Carnegie-Mellon University preprint, April 1979, with a coupling Lfx = g(ey>y + V>)X^, = l/2(uyx u + dy^d)]. The experi­mental limit on R£g“ (Rye <7 x 10-11, cf. B. Hahn and T. Marti, ref. 5), leads to M^ . > (3 x 103 )MW . If the same boson had an axial-31vector coupling to (sd), KL -> pe would occur with a branching ratio B(Kl -* pe) - (3.7 x 103) (Mw/Mx) . Thus, both processes are about equally sensitive to Mx . But Mx now must obey eq. 26, implying1 9 x 10-15 and B(Kl -* pe) - 7 x 10- 1 5  (we have assumed that all the gauge couplings involved are equal to g).21. Note that if muon number is violated via intermixing leptons, T(Kl -* pe) depends, unlike T(p“Z -* e-Z), also on the quark masses.22. Assuming gd = 21 /t+v/G my, and a AS = 0 quark-Higgs coupling of the form2 1 / V g  (mu uu + md dd)cf>^, the coherent p e capture rate for sulfur is (using the2formula of 0. Shanker, ref. 20) = (2.8 x 102)x[my (mu + mcj)mj1 ] 2 . The experimental limit on RyS implies md > 50 GeV.If the same Higgs meson couples also to (sd) with a couplingg£ = 21/1+/g md , then R 4 x 10_ll+, while B(KL pe) < 3 x 10-12.23. We shall not consider here the tensor coupling case. If muon-numberis violated through higher order effects, the effective interaction may, in general, contain such terms. Another possible source of ten­sor couplings would be the effective interaction resulting from lepto- quark exchange.24. For a review of the experimental situation, see K. Kleiknecht, Ann.Rev. Nucl. Sci., 26, 1 (1976).25. L. Wolfenstein, Phys. Rev. Lett. 33, 562 (1964).26. For recent reviews, see L. Wolfenstein inv. talk, "Neutrino 79" Con­ference, Bergen, 1979; R. N. Mohapatra,inv. talk, 19th Int’l. Conf. on High Energy Physics, Tokyo, 1978.27. M. Kobayashi and K. Maskawa, Progr. Theor. Phys. j49, 652 (1973).28. e.g. Ro N. Mohapatra and J. C. Pati, Phys. Rev. Dll, 566 (1975)R. N. Mohapatra, J. C. Pati and L. Wolfenstein, Phys. Rev. Dll, 3319 (1975).29. L. Wolfenstein in Theory and Phenomenology in Particle Physics(A. Zichichi, ed.), Academic Press (1969), p 218.30. L. Wolfenstein, Carnegie-Mellon Univ. preprint, May 1979, and paper contributed to the "Neutrino 79" Conf., Bergen, 1979.31. Jo Ellis, et al, Nucl. Phys. B109, 213 (1976).32. F. J. Gilman and M. B. Wise, Phys. Lett, (to be published).33. See L. Wolfenstein, ref. 26.34. Ir S. Altarev, et al, Acad. Sci, USSR, Leningrad Nucl. Physicsreport UDK-539-12-I, to be published in Nucl. Phys.35. S. Weinberg, Phys. Rev. Lett. 37_, 657 (1976).36. CP-violation may instead (or in addition) be located in the fermion- Higgs couplings. For models in which CP-invariance is broken sponta­neously, see T. D. Lee, Physics Reports 9, 143 (1974).37. A. A. Anselm and D. K. D'yakonov, Nucl. Phys. B145, 21 (1978).38. M. P. Schmidt, et al, Phys. Rev. Lett. U3_, 556 (1979).39. L. Wolfenstein, et al, Nuovo Cimento, 63A, 269 (1969).40. K. R. Schubert, et al, Phys. Lett. 31B, 662 (1970).41. F. Lobkowicz, et al, Phys. Rev. Lett. 11_, 548 (1966).42. D. S. Avres, Phvs. Rev. Lett. 21. 261 (1968).43. New proposals include: R. C. Larsen, et al, (BNL-Yale, AGS);R. Bernstein, et al, (Fermilab) to measure |n0o/ri+-! to an accuracy of 1%, and R. C. Larsen, et al, (BNL-Yale, AGS), to measure Im$ in K+ -*■ 7r°y+v to an accuracy of 0.002.32DISCUSSIONSOERGEL: What would be the size of the transverse polarization of p's?HERCZEG: In one of the recent proposals to measure the polarization (BNL- Yale proposal, 1978) Im f_/f+ ^  3 x 10-3, implying an average polarization of ~ 6 x 10-1+, is quoted, attributed to Weinberg. In Weinberg's theory CP-violating effects depend on the "transition" mass of the Higgs boson. Consequently, no definite number can be given, but with a too large Higgs mass the theory could not account for the observed CP-violation. On the other hand, that may be due to another cause, which is acting simultane­ously. In such a situation P^ could be much smaller.33HYPERON PHYSICS AND CHROMODYNAMICS*tNathan IsgurDepartment of Physics, University of Toronto, Toronto,Canada M5S 1A7After briefly reviewing QCD and introducing the elements of QCD- based models of hadronic structure, the relevance of hyperon resonance physics to testing such models is discussed.What is QCD?QCD (quantum chromodynamics) is a gauge theory of the strong inter­actions with close analogies to QED (quantum electrodynamics) in which the strong interactions arise from the exchange of photon-like quanta called gluons coupled to quark colours R,Y,B in a way related to the coupling of the photon to electric charge. The main difference between the two theo­ries is that the photon is electrically neutral so that electric charge is conserved in the fermion lines. When a quark emits a gluon, however, it can change its colour and net colour can flow into the emitted gluon, ie., gluons carry colour charge and can in turn emit gluons themselves.This can all be summarized by drawing the basic "vertices" of these theories corresponding to the possible elementary interactions in each the­ory. They areFig.II. The elementary vertices of QCD.*Invited lecture at the Kaon Workshop of the VIII International Conference on High Energy Physics and Nuclear Structure, Vancouver, Canada, August 13-14,1979.+For recent reviews of the topics discussed here see: Nathan Isgur, "Soft QCD", lectures at the XVI International School of Subnuclear Physics,Erice, Italy, 1978; Gabriel Karl in Proceedings of the XIX International Conference on High Energy Physics, Tokyo, 1979, p. 135, edited by S. Homma, M. Kawaguchi, and H. Miyazawa (Phys. Soc. of Japan, Tokyo, 1979).ABSTRACT*Fig. I. The elementary vertices of QED.34It is the self-couplings of the QCD gluons ("a non-abelian gauge the­ory") that give it its special properties. One of the most important is the property of asymptotic freedom. When a photon probes a charged par­ticle it sees only vacuum polarization of fermion pairs:matically becomes a strongly interacting theory as we want - Of coursedown so that the consequences of the theory are extremely difficult to deduce. This, alas, is to be expected of any strong interaction theory; the other side of the coin is in this special case, however, extremely delightful, for as q2 00, a -*■ 0 and we are faced with a regime in which our theory of strong interactions has become perturbative so that rigorous tests may be made.This regime of "hard QCD" is currently being put to the test and it looks very promising. I think there is a good chance that QCD is the cor­rect theory of the strong interaction.Where does this leave the many decades of work that has been done in studying the strong interaction where it is strong? Does it mean that true strong interaction physics will play no role in confirming (if it be true) QCD? And, vice-versa, does it mean that QCD can offer no understand­ing of "truly" strong interactions?It is true that at the moment there is no completely rigorous deri­vation of low energy hadronic properties from QCD —  in fact even quark confinement remains an unproved (even if plausible) conjecture. Neverthe­less, it has been possible to construct models of "soft QCD" which incor­porate the various features that are expected to emerge from the theory.Fig. III. The origin of a(q2) in QED.The pairs tend to shield the charge so thata(q2)t as q2t .In QCD, however, we haveFig. IV. The origin of ag(q2) in QCD.and the extra graphs lead to antishielding so thata (q2)+ as q2l sThis feature of the theory has the consequence that at low q2 QCD auto-this means that at low q2 (large distances)perturbation theory breaks35What is Soft QCD?What are the ingredients of such models? There are several, the most important being:1) colour confinement: It is assumed that the long range proper­ties of the theory may be adequately summarized by some phenomenological confinement mechanism like a bag or a confining potential. From the flux tube model of confinement one guesses that-y -yV ( r 12) = -V(r12)(f) -(f) qq I i I 2t - A *where V(r12) is confining and where q^ -> q. by replacing (— ) . -*(— ). .Note the critical feature that V doesn't depend on the flavour (u,d,s...) of the quark, ie., it is colour that counts. Such a potential leads to the existence of only colour singlets in nature and gives relations between the binding forces in mesons, baryons, baryonia, etc.2) one gluon exchange: With the long range character of the theorydescribed phenomenologically, it is next assumed that at short distances where the theory becomes perturbative one can use one gluon exchange. In this case the short distance forces in QCD are analogous to electromagnetic forces. Aside from the 1/r potential, which becomes entangled with the confinement potential, the most important interaction is the colour hyper- fine interaction/ten- I sor y, inter actionFig. V. The colour hyperfine interaction between two baryonic quarkswhich automatically, for example, makes both p > it and A > N.3) quark masses and pointlike nature: Finally it is assumed thatin the regime of interest the quarks can be treated as approximately pointlike particles carrying their so-called constituent quark masses which are roughly36m, - m - 0.33 GeV d um, - m - 6  MeV d um - 0.55 GeV sm - 1.73 GeV cetc.One immediate consequence is that this assumption allows the prediction of hadronic static magnetic moments and Ml transition moments which are dis­played in Table I .Table I. Static and transition magnetic moments in Soft QCD.Theory Expty +2 . 8 +2.79yP -1.9 -1.91n -0.57* -0.61 ± .03A7^4- +2.7 +2.83 ± .25L-ryz-y" n-1 .1 *-1.4*-1.48-1 . 2 0± .37 ± .06 +n o -0.45* -1.85 ± .75y(Ec1-> A ) 1 . 6 1 . 8  :± 0 .2+y (A -* N) 2 . 2 3.4 ± 0 . 2y(p -> it) 0.72 0.59 ± . 06y (p -> n) 1.5 1 . 6 ± 0 . 2 +y (V +  p) 1.5 1.4 ± .02y(nf -*■ (i3) 0.54 0.42 ± .09+y (go ->■ tt) 2 . 2 2.4 ± 0 . 1y(oi -> n) 0.45 0.35 ± .13+y (<t> -> tt) 0.17 0.15 ± .04y (<f> -* n) 0.76* 0.73 ± .07y (<J> n') 0.67*y (k*.O+ K ) 1 .2* 1 . 0 ± 0 . 2y(K*_ 1- K ) 0.93* < 1 (95% c.l.)t means theory precedes measurement* means a significant test of the reduced moment of s quark37What Do We Learn From KN Resonances?All three of the main ingredients of soft QCD are put to the test in the S = -1 resonances. Let's consider first the question of flavour-inde­pendent confinement. This is the analog of electron-muon universality in that it states that just as all the differences between ,say ,an electronic and muonic atom are due to the difference in the masses of the electron and muon (since the interaction pays attention only to the identical char­ges), all the differences in hadrons containing a strange quark may be attributed to the mass difference m - m, (since the colour charges are equal ) . One immediate consequence is that while in an S = 0 resonance the two normal modesp mode: ^  O O O”I 3 2-A mode:Fig. VI. Schematic of the normal modes of three quarks.have the same frequency, in an S = -1 resonance while w will be unchanged, will be smaller. This effect leads to large splittings in the spectrum and to maximal violations of SU(3) symmetry.How can one test(apart from purely spectroscopically)whether or not a physical resonance is in a p or A normal mode? By studying its decay pattern. In fact it is easy to see that a p-excitation will decouple from KN in the single quark transition approximation:(N)(Y*JVus(ic)= 0 since in N p is de-excited.U d S _Fig. VII. The decoupling of p-excitation from KN.Of course one can be more sophisticated, but this example is representative.38Ingredients #2 and #3 are also put to stringent tests by S = -1 resonances. In S = 0 resonances each quark has the same colour magnetic moment, but in S = -1 the strange quark’s colour magnetic moment should be suppressed in the same proportion as its electromagnetic moment: by ta^/m - 0.6. One example of this is in the ordinary ground state £ and A hyperons:p = uud (1 1 + + Tit - 2't'tl)A° = yy (ud - du)s yy (++ - ii)l£° = y= (ud + du)s yy (+1 + + ill — 2 1 1 1 ) .In the A° the s quark's colour magnetic interaction averages to zero soit drops as far as the nucleon does while the E 's stabilization is sig­nificantly reduced. The result isJ mjZ - A = 4  (1 - — ) (A - N) - 80 MeV 3 msexactly as observed experimentally. Similar effects are predicted to oc­cur in the S = -1 resonances.What is the present experimental and theoretical situation? So far matters look quite good, but the S = -1 resonances are a weak link (see Fig. VIII - XII). All seven of the low-lying negative parity S = 0 reson­ances are now well established and studied and reasonably well understood in these models, but only eight of the fourteen S = -1 negative parity resonances are well known and for most of these branching ratios, etc., are poorly determined. For more excited resonances the situation deter­iorates. (For S = -2 and -3 resonances almost no information exists at all).The prospects for improving our knowledge of these very basic had- ronic states with "official" high energy machines is now poor and tending to get worse as E_~* 00. If a kaon factory can provide any or all of1) a good KN multichannel partial wave analysis through the re­sonance region2) data on S* and 0.* resonances3) improved data for rN multichannel partial wave analyses that can pick out those resonances weakly coupled to the rN channel,it will be certain to enhance our understanding ©f quarks and, in my opin­ion, be likely to provide substantial evidence for QCD-based models of hadronic structure.ACKNOWLEDGEMENTSThe work on baryons in soft QCD described in this lecture was done in collaboration with Gabriel Karl.39Figure VIII: The ground state baryons in Soft OCD.N* V  A*’4' W’K' A* VFigure IX: The S=0 negative parity baryons in Soft QCD40Figure X: The S= -1 negative parity baryons in Soft OCD.Figure XI: The S=0 positive parity baryons in Soft QCD41Figure XII: The S= -1 positive parity baryons in Soft QCD42DISCUSSIONBUGG: There used to be great activity in KN experiments. This has de­creased significantly with the discovery of charm and the operation of charm factories. What can one learn from K factories that one cannot learn from charm factories?ISGUR: There is no great difference in what one can learn in principle,but in practice I doubt, for example, if we will ever know much about any but the lowest lying of the charmed baryons. Incidentally, I don't put much stock in the claims that the theory has become much more rigorous in this sector— I think it's just that temporarily it's become sexier.HARGROVE: Will one be able to derive the soft QCD from the hard QCDeventually?ISGUR: That is possible, but the current models and better data willhelp since it helps to know the answer ahead of time.WATSON: The calculation you made originally used an r2 potential. Howhigh in energy would you need to go, in looking at K“N resonances, before you could start making definite statements about the shape of the con­finement potential?ISGUR: I really don't know. It's an interesting question.BOAL: What q2-dependence of the coupling constant was used in the calcu­lation of the baryon masses?ISGUR: We used a constant as, but we are considering more elaboratestudies in the future.BOAL: What transition moments are significantly different in the QCD ap­proach compared to simple SU(3) predictions?ISGUR: Several are quite sensitive to the suppressed magnetic moment ofthe s quark. For example, the SU(3) limit p^ = -0.93 goes to -0.57, much closer to experiment. Other significant changes are pC^h)* andP (K-°-*K°) .43PHYSICS POSSIBILITIES WITH LEAR,A LOW-ENERGY ANTIPROTON FACILITY AT CERN& ^U. Gastaldi 'Institut fur Physik, Mainz, GermanyK. Kilian*^Max-Planck-Institut fiir Kernphysik, Heidelberg, GermanyABSTRACTA summary is given of the conceptual design characteristics of LEAR (Low-Energy Antiproton Ring), the facility planned at CERN to perform phy­sics at low energy with cooled antiprotons. With respect to present p beams, the LEAR facility will increase low-momentum beam intensities by factors of 1 0 3 to 1 0 6, eliminate beam contaminations, and increase the beam density. Storage-ring operations feasible in later developments may include use of a gas-jet target, injection of H~ ions in order to produce pp atoms in flight, and pp collisions in a minicollider mode.An outline is given of the physics possibilities opened up by the im­pressive improvements in the extracted beams and by the new experimental approaches made possible by the storage-ring operation.*) Visitor at CERN, Geneva, Switzerland.44INTRODUCTIONA new facility for performing experiments with antiprotons at low energy is planned at CERN.The core of the facility will be a small storage ring with accelera­tion capability, called LEAR (Low-Energy Antiproton Ring). LEAR will be installed in the PS South Hall (Fig. 1) and useda) to feed high-intensity (> 1 0 6 p/s), high-duty cycle (y 1 00%) low- energy (0.1 to 2 GeV/c) extracted beams (stretcher-ring operation);b) to perform experiments that use directly the circulating internal beam (storage-ring operation with 109 to 5 x 101 1 stored p).LEAR will receive antiprotons from the Antiproton Accumulator (AA)1, the intense source of antiprotons at present under construction2 for the p-SPS programme. Antiprotons will be transferred to LEAR from the AA through the PS used as a decelerator (antiprotons collected, cooled in phase space, and stacked in the AA at 3.5 GeV/c will be injected in the LEAR at ^ 0.6 GeV/c).Fig. 1 Over-all site layoutThe construction of the facility will be carried out in successive stages. A detailed project proposal for the first stage (stretcher-ring operation) will be worked out and will take into account the constraints45connected with the use of LEAR in the later stages of development (storage- ring operation). These stages include the use of an internal gas-jet target, injection of H ions in order to produce pp atoms in flight, and pp collisions in a minicollider mode. Implementation of ISR-type vacuum and p cooling, that are necessary for the later stages of development, will also improve, by orders of magnitude, the quality of the extracted beam in the low-momentum region.The LEAR facility will meet the increasing demand for good quality low-momentum antiproton beams produced by the focusing of interest on NN physics at low energies. Present-day experiments use antiprotons col­lected by tuning the beam transport line at the required low momentum.The production cross-section for p < 1 GeV/c is orders of magnitude below the maximum —  which is met at p 'u 3.5 GeV/c with 26 GeV/c protons on the p production target (see Fig. 2 taken from CERN/PSCC/79-17) .antiproton momentum GeV/cFig. 2 Momentum spectrum of antiprotons produced at 0° with 23 GeV/c protons on a lead target. The number of p per interacting proton is normalized to 1 msr solid angle and ±1% momentum bite. Below 4 GeV/c the curve is estimated by "kinematic reflection". The crosses are preliminary values obtained on the CERN kz5 beam.46The scheme of the new facility foresees, instead, the collection of anti­protons in the AA always at the maximum of the production cross-section*) and subsequent transfer to the required low momentum via deceleration (in the PS). Before deceleration, antiprotons will be compressed in phase space by application in the AA of stochastic cooling techniques recently tested with success at ICE11. The resulting high density of the initial beam will allow deceleration, without relevant losses, down to all required low momenta5. This combination of cooling (in AA) and de­celeration will improve the present working conditions with extracted beams (beam intensity and density, momentum definition, pion contamina­tion) by several orders of magnitude. Further improvements will result from applying additional cooling in*LEAR. Moreover, new experimental possibilities will be opened up by making direct use of the antiproton beam stored in LEAR.Schemes for a low-energy antiproton facility6 and indications for the physics programme to be performed there7-9 were presented at the 1977 CERN Workshop on Intermediate Energy Physics10. Work of two study groups set up at CERN in 1978 to investigate physics possibilities and machine aspects resulted in an assessment of the physics case1 1 and in the first• ip , , , # #conceptual design of LEAR . The increasing interest m  low-energy anti­proton physics motivated the organization of a dedicated workshop, which was held in March 1979 in Karlsruhe13, and preceded by meetings at CERN of study groups dealing with the physics and machine aspects. Physics interest, detection capabilities, and technical aspects of the LEAR facility were discussed extensively13’19. A second conceptual design taking into account the result of the discussions at the Karlsruhe Work­shop was worked out by the authors of Ref. 12 and included in the report3 to the CERN PSCC by the conveners of the study groups. The principle of constructing the LEAR facility was approved in June 1979. The date for the start of LEAR operations in the stretcher mode will be fixed after the approval of the detailed project proposal. The end of 1982 seems a reasonable estimate.In the following sections we present an outline of the LEAR facility and of the physics programme.THE LOW-ENERGY ANTIPROTON RING (LEAR) FACILITYFigure 3 shows a design layout of LEAR located in the west side of the PS South Hall.Antiprotons collected, cooled in phase space, and stacked in the AA at 3.5 GeV/c 15 will be ejected from the AA in batches, decelerated in the PS down to a fixed momentum of about 0.6 GeV/c (3 - 0.5), and then in­jected into LEAR. Each batch must contain more than 109 p, the lower limit for safe operation of the PS instrumentation.Antiprotons will be transported to LEAR through the building of the old 50 MeV linac. A return loop has been envisaged16 to connect the p transport beam line to the old linac in order to allow p+ and H- injectionsinto LEAR completely decoupled from PS operations.The average amount of antiprotons available for LEAR physics will be £ 106 s- 1 (note that the AA will be able to stack a maximum average of7 x 106 p s-1).*) This is the standard mode of operation of the AA.47Fig. 3 Injection line and LEAR in the PS South HallThis together with the lower limit of 109 p per injection imposes a p beam lifetime £ 1 0 3 s for operations with good duty cycle.LEAR will consist of four laminated magnets and a focusing structure with two quadrupole doublets in each straight section. Design characteris­tics and lattice parameters for the stretcher ring operation are listed in Table I, which is taken from Chapter III of Ref. 3, "The proposed facility".An imaginary transition energy has been chosen to maximize the efficiency of stochastic cooling1 . The return yoke of the bending mag­nets will be inside the ring to allow easy extraction of neutrals (pp48Table I. Stretcher ring lattice with p = 3.6 m bendsMomentum range CircumferenceLength of straight sections Free length (regular lattice) Number of straight sections0 . 1 - 2  GeV/c 6 2 . 8 m  10 m 6 m 4Working pointMaxima of lattice functionsMaxima in bendsAperture of vacuum chamberQh2.67Qh =2.67Qv 1.25 Qv = 2.75- -(A.5)2 = -(3.0):= 6.8 mbh= 8.3 m= 17.8 m = 18.8 ma — 2.5 m a = 2 .A mP P= A . 9 m = 6.6 m= 17.5 m = 12.0 ma = 0.95 m a = 1.6 mP P±70 mm: ±32 mmBeam aperturesMaximum acceptancesaH6 = ±45 nmiaTT = ±45 mm Hpay = ±27 mm E = 250 tt mm -mradriEv = 35 tt mm ’mrad Ap/p = ±1.8%Momentum 2 GeV/c 0.1 GeV/cBending field 18.A kG 0.9 kGIntegrated quadrupole gradient 610 (G/cm)m 31 (G/cm)m(Qh = 2.67; V2.75)atoms and h) produced in the straight sections. The orientation of the ring and the circulation sense of antiprotons will be such as to permit installation in the experimental hall of a long pp atom beam line pro­longing one straight section of the ring. A 20 kV KF system will de­celerate or accelerate the beam stored in LEAR from the fixed transfer momentum of about 0.6 GeV/c to the desired working momentum. The bunch length will be h, 40 m working on the first harmonic. ISR-type vacuum elements have been envisaged since the beginning with a view to operation at very low momentum (8 - 0.1), H_ storage in LEAR, and operation with a low-density polarized jet target.LEAR will be usable in various modes corresponding initially to stages of completion, and alternating later on as required by the experi­mental programme. The modes are:491) Stretcher-ring operation la) above 0.3 GeV/c, lb) down to 0.1 GeV/c.• I o • • •In this mode a slow extraction system located m  straight section LSS2 (Fig. 4) should allow the feeding of an extracted beam with an average intensity up to 1.7 x 106 p s- 1 and a spill time of about one thousand se­conds. Splitting of the beam will allow simultaneous feeding of two ex­periments, and branching with a bending magnet will afford the possibility of having more experiments on the floor in standby position.Fig. 4 PS South Hall2) Storage-ring operations2a) Jet target operation: An atomic H or D jet beam (eventuallypolarized) would cross the stored p beam in a straight section19. The experimental apparatus would be installed around the interaction region in the space not occupied by the jet-target installation. An apparatus located behind the bending magnet downstream from the jet target could exploit the monochromatic n beam of antineutrons forward-produced by charge exchange on protons in the jet20.2b) Overlapping p and H~ beams: An H- beam (from the old linacequipped with an H“ source21) would be stored in LEAR together with the p beam. Both beams (circulating in the same direction) would be held by the same RF system. Protonium atoms (pp Coulomb bound states) formed in flight22 in the straight sections of LEAR would emerge straight out of the bends and i) feed experiments on pp atoms located at the end of a long pp atom beam-line prolonging LSS2 (Fig. 4), ii) feed conventional p beam lines (after stripping of pp atoms with foils inside dipole magnets).502c) pp minicollider: pp frontal collisions with c.m. energies up to4.4 GeV/c2 would be obtainable by injecting protons into LEAR with a second injection located in LSS4. The experimental apparatus would be located around the interaction region in LSS3 (Fig. 4).Operation (la) will be feasible with good duty cycle without addi­tional cooling in LEAR and with vacuum at the 10- 1 0 Torr level. ISR-type vacuum ('V. 10- 1 2 Torr) will be necessary for all other operations, es­pecially (lb), (2a), and (2b).Electron cooling23 is necessary for operating efficiently in the mode (2a) 19 and would boost the performances of all operation modes in­cluding (2c) if relativistic electron cooling should prove to work at LEAR energies29 and should become available.Electromagnetic stripping limits the upper velocity of pp atoms ob­tainable in mode (2b) to M  0.6. Gas, H intrabeam, and p H- beam-beam stripping limit the lifetime of the H- beam, and beam-beam and intrabeam stripping limit the maximum H~ beam intensity compatible with refilling with fresh H~. A luminosity of 1029 Av/c s- cm- is estimated with 109 H- and 109 p stored in LEAR (Av is the p velocity in the H- c.m. sys­tem). This luminosity seems to be obtainable with an H" refilling fre­quency below 0.1 Hz.The luminosity estimated for operation (2c) is ^ 1029 s- 1 cm 2 with 6 x 101 1 p and 6 x 101 1 p+ stored in the ring, and a bunch length of 5 m (60 kV RF system).PHYSICS POSSIBILITIES AT LEARFigure 5 shows the momentum range that can be explored with LEAR used in the beam-stretcher mode and in the jet-target operation. TheFig. 5 Momentum range of LEAR together with some relevant resonances and thresholds. In the hatched region below 200 MeV/c no excitation functions are known. In the lower part, thresholds of experimental importance are indicated.51momentum range of the extracted beam can be lowered to zero by decelera­tion in a degrader, with negligible losses if degradation starts below300 MeV/c. Work at the pp threshold could also be done using the ppatoms produced in flight in the pH- overlapping beam mode. The maximum invariant mass accessible is 2400 MeV/c2 in the stretcher-ring and jet- target operations; it would be possible to raise it to 4400 MeV/c2 in the pp minicollider mode.The external beam intensity in the stretcher-ring operation will be ^ 1 0 6 p s-1, and it will stay constant independently of momentum over all the momentum range covered by LEAR. This is due to the combined action of cooling and deceleration and to the big acceptance of the LEAR ring, and can be understood immediately from inspection of Fig. 2. Gains ex­ceeding a factor of 1 0 3 will be obtainable in the low-energy region, asindicated and explained in Table II.Table II. Gains possible with LEAR versus the present situationMode Parameter Gain CommentBeam purity OO a)All modes Duty cycle a 10 b)Emittance > 10 c)Stop rate in106 d)gas targetsExtracted beam operation:Stop rate in dense targets> 103 e)stop expts.Reduction instop volume for > i o 1* f)dense targetsExtracted beam operation: scattering expts.Beam intensity below 500 MeV/cAccess to100 < p <Ap/p < 1%> 103unexplored region 300 MeV/c withe)g)a) (tt /p)T_ AT, = 0 because no pions from the AA. (tt /p) _ ~ 10-100.LEAR r c present p beamsb) Present PS duty cycle » 0.1; LEAR duty cycle 'v. 1.c) Present low-energy p beams have emittance £ ~ 150 tt mm mrad; AA beamdecelerated to 300 MeV/c will have emittance £ < 15 tt mm mrad.d) Factor of ^  1000 beam intensity. Factor of ^ 1000 shrinkage of rangecurve width owing to lower beam momentum and momentum spread.e) Factor of 'V 1000 beam intensity.f) Factor of 'v 1000 range curve width. Factor of > 10 beam cross-section.g) Almost no data as yet available in the literature because Ap x (p) withpresent beams. In contrast to this, LEAR acts as a monochromator.Table III indicates gains of some new approaches that would be pos­sible with the storage-ring operations in LEAR.52Table III. Gains possible with p beams stored in LEARMode Parameter Gain CommentJet-targetoperation Energy resolutionOptimal use of p > 102a)Polarized jet- target operationEnergy resolution> 102 polarizationa)Energy resolution for pp atom X-ray detection> 103 b)pH- storage ringPopulation of h i gh-J_b aryon ium below NN threshold»  20 c)dominant P-wave annihilation c)pp atom-induced spec­troscopy feasible with sensitivityAE „ ApE PLEARd)Energy resolution e)pp minicollider Direct access to 0-+ (ric) and 0++, 1++, 2++(X) charmonium statesa) Energy resolution is limited only by Ap/p of the circulating beam. With 109 stored articles, Ap/p < 10-5 can be obtained with e~ cooling, while standard spectrometers provide Ap/p ~ 10-3.b) i) By using the Doppler shift of the forward-emitted X-rays by ppatoms formed in flight, ii) by using differential absorbers, andiii) by tuning the Doppler shift by varying the storage energy inLEAR, the accuracy for energy measurements is independent of theX-ray energy and is determined by (Ap/p) 22.LEARc) Atomic cascade develops in vacuum.d) Resonant frequency can be obtained by varying the velocity of thepp atom and employing monochromatic high-power commercial lasers.Static properties of p (y, m) and strong interaction perturbationsto atomic levels can be determined with (Ap/p) accuracy.LEARe) AE/E ~ 10-3 without cooling in LEAR. It could become < 10-1* with relativistic electron cooling.53The physics programme of the low-energy antiproton facility high­lights the study of antinucleon-nucleon interactions. Topics of great interest are antiproton annihilation reactions, baryonium spectroscopy,NN resonances and quasi-nuclear NN bound states, and protonium spectro­scopy.Annihilation reactions explore the interior of the nucleon and cantherefore provide deep insight into the internal structure of the protonand the neutron. In spite of a great amount of work performed at high • •  * 2 5 2 6  • •and intermediate energies » and at rest, the available experimental information is very limited and the dynamics of annihilation reactions is still unknown. The low-energy region that will become fully accessible with LEAR (at present almost no data exist in flight for Plab 0*3 GeV/c) looks the most promising and natural one for the study of annihilation. Indeed, while at high energy annihilation is just a small fraction of NN interactions, at low energy it becomes the dominant component. By lowering the energy, the annihilation cross-sections approach the unitary limit in each partial wave, while phase space for non-annihilation events shrinks; channels such as pion production and charge exchange can be switched off by going below their threshold, high partial waves in the entrance channel are damped, and the identification of the final state becomes easier. At rest, pp annihilation occurs from discrete states of pp atoms that form when stopping antiprotons in a hydrogen target. There it is conceivable in some cases to have complete information on the initial state (angular momentum, even spin perhaps) by choosing adequate conditions of the target and by detecting the X-ray emitted in the atomic transition that populates the initial state of an annihilation reaction. This would permit the study of the dependence of annihilation on angular momentum (S-, P-wave annihilation) and maybe also on total spin, and could contribute strongly to the understanding of the annihila­tion mechanism.Baryonium spectroscopy is at present considered as being one of the most attractive topics. Several different theoretical approaches lead to the expectation 6f states strongly coupled to the baryon-antibaryon system and weakly coupled to ordinary mesonic decay channels27’28.Baryonium states below the threshold of the relevant BB channel should be narrow because the coupling to meson channels is dynamically suppressed, and the allowed decay into BB_is inhibited by energy conservation. Bary­onium states just above the BB threshold could be narrow, because phase space keeps the allowed BB decay small. The experimental signature of a baryonium state, which must be highly elastic and weakly coupled to meson channels at all energies, is therefore expected to be much clearer and more striking at low energy near the hn and pp threshold and at higher energies around the AA and £+E+ thresholds. Indeed most of the baryonium candidates so far observed29 cluster in these regions. However, the ex­perimental situation is in continuous evolution because most of the existing baryonium candidates suffer from poor statistics, and for all candidates the experimental information is not enough to assign quantum numbers. All theoretical approaches have in common the expectation of qqqq states which escape the classification of known hadrons among qq states (mesons) and qqq states (baryons). Confirmation of baryonium54states of this qqqq nature would open up a new domain for spectroscopy. Understanding the origin of the rules which inhibit the mesonic decays would help to piece together a picture of the dynamics of light quarks in ordinary nucleons. Baryonium spectra could be used to test ideas in order to provide basic foundations for a theory of strong interactions2 8 and to show dynamically evidence of colour30.Nuclear physics approaches also lead to the expectation of a variety of resonances and quasi-nuclear bound states in the vicinity of the NN threshold31. These states are seen here as 3-quark 3-antiquark states organized in a NN system, where nucleon and antinucleon maintain their identity (like n and p in a deuteron). They are bound by medium- and long-range nuclear forces in a volume with dimensions of the order of 1 fm. These forces are originated by strongly attractive NN potentials that are derived, in one-boson exchange (OBE) models, from NN potentials by G-parity transformation of the different boson exchange contributions. The contribution of annihilation (which is not present in the NN case) is not known. The influence of annihilation on the structure and even on the existence of the NN states, and the relation between quasi-nuclear NN states and baryonium (qqqq), are subjects that are now being debated and are as yet experimentally unsettled. The observation of NN states and the determination of their quantum numbers could provide deep insight into the nature of OBE potentials (nature and origin of the hard core and of the spin-orbit forces and tensor forces in nuclear physics). Esta­blishing relations between quasi-nuclear states and baryonium states will require bridging the gap between particle and nuclear physics with a deeper understanding of subnuclear processes.Protonium spectroscopy is of interest for two reasons. One is that the X-rays emitted in certain transitions to the low-lying levels of the pp atom can be used to tag initial (atomic) states from which annihilation or transitions to baryonium/quasi-nuclear bound states may occur22’32.The second reason is that measurements of shifts and widths induced by strong interactions on the low-lying (L, S) states of the pp atom (13S1, 1°S0, ...) can monitor the existence of resonances and bound states in the corresponding (L, S) channel in the region quite near to the threshold. This region is the hardest to approach experimentally (low beam rates and poor resolution above threshold, high y background below threshold). Shifts and widening of the Coulomb levels are directly con­nected with the strong pp interactions. Precision measurements, typical of atomic physics, look possible owing to the long lifetime of the anti­proton22, so that pp atoms could be used as a testing ground for strong interaction theories £a working theory must predict shift, total width, and decay and annihilation branching ratios of the (L, S) levels of pro­tonium] .Other fields of interest at low energy are p interactions with• — • 3 2. _  • • • 3 3nuclei: pA exotic atoms and pA annihilationCharmonium spectroscopy is the most attractive topic in the high- energy region accessible with LEAR used as a minicollider. The whole charmonium family can be explored with pp collisions in LEAR used as a pp collider34. Antiproton-proton reactions can form directly all members of the charmonium family £in particular the 0-+(r|c) and the 0++, 1 ++, and 2++(x) states not directly accessible with e+e- machines]. The mass and width of these states can then be measured with a resolution given by the55momentum dispersion of the beams in LEAR. With e+e- machines, these states can be reached only via y transitions from 4> states, with an energy resolution limited by the y detectors.A general overview of the physics possibilities opened up by LEAR in the various energy regions and operation modes was given in topical2 0 3 2  3 % — 3 8 • •summary talks ’ » at the Karlsruhe Workshop and reviewed m  Ref. 3.Table II indicates the big improvements possible with LEAR in terms ofbeam intensity, purity, quality and duty cycle. These gains could solveall present experimental uncertainties connected with low statistics andhigh background. In the following we shall restrict ourselves toenumerating some points where specific experimental approaches offeradditional improvements and qualitatively new physics possibilities.Experiments at thresholdUse of gaseous targets possible because of the extremely narrow range curve width (0.5 mg cm-2 H2 < 10 cm Hj gas NTP). Stark mixing drastically reduced -*■ high population of low n atomic states ->-* emission of detectable Lyman ('v 10 keV) , Balmer (a> 2 keV), ..., X-ray transitions. Use of these atomic transitions to measure strong interaction perturbations (AE, T) of atomic levels and to monitor initial states of subsequent annihilation or transition to quasinuclear bound states (x, y/ir coincidences). pH- parallel beam approach -> beams of pp atoms. Atomic cascade in high vacuum dominance of P-wave annihilation. High-resolution X-ray spectroscopy with differential absorbers and tunable Doppler shift. Induced spectroscopy to study hyperfine splittings conceivable.Experiments above thresholda) External transmission targetAccess to completely unexplored region below 300 MeV/c incident momentum. Possibility of studying pure S-wave interaction at very low energy and onset of higher partial waves with increasing energy, nn threshold (98 MeV/c) can be scanned. Monochromatic n beams possible (np interactions: only 1 = 1  states, no Coulomb distortions).High resolution and high sensitivity for weakly populated narrow states (baryonium!).Excitation functions for channels with branching ratios down to the 10-7 level.b) Internal_jet targetExtreme resolution combined with extreme target efficiency.Polarization experiments with pure polarized atomic beam targets (H2j D2, . . .) .pp collider experimentsAccess to 4.4 GeV/c^ invariant mass states also with quantum numbers ^ 1 (interesting for charmonium family).Extreme mass resolution (depends on phase-space cooling applicable).CONCLUSIONSLEAR is likely to produce important physics results in a very short time after the beginning of operations. Indeed it will be possible to56enter immediately into an unexplored energy region using present-day detectors and taking maximum advantage of the high quality of the LEAR beam.Use of compact sophisticated apparatuses with high detection capa­bility will become possible, due to the restricted volume of the interac­tion region even with gas targets.Development in the detector sector for extracted beam operation can go in parallel with implementation of storage-ring operations, which will permit the most efficient use of the available antiprotons together with the maximum energy resolution.The resolution AE/E of experiments in the jet, pH- parallel beams and pp minicollider mode is determined essentially by the momentum dis­persion Ap/p of the stored beam. Implementation of strong phase-space cooling would permit the measurement of strong interaction effects with high accuracy (Ap/p ~ 10-5 with electron cooling) in all interesting energy regions in an energy domain ranging from protonium to charmonium.ACKNOWLEDGEMENTSA large number of colleagues and friends have contributed actively14 to the elaboration of the physics and machine aspects of the LEAR project. We should like to thank them for many stimulating discussions.REFERENCES AND FOOTNOTES1. Design study of a proton-antiproton colliding beam facility,CERN/PS/AA 78-3 (1978).2. R. Billinge and M.C. Crowley-Milling, The CERN proton-antiproton colliding beam facilities, CERN/PS/AA 79-17 (1979), Invited paper presented at the 1979 Particle Accelerator Conference, San Francisco, 12-14 March, 1979.3. U. Gastaldi, K. Kilian and G. Plass, A low energy antiproton facility at CERN: physics possibilities and technical aspects, CERN/PSCC/79-17 (1979) .4. G. Carron, H. Herr, G. Lebee, H. Koziol, F. Krienen, D. Mohl,G. Petrucci, C. Rubbia, F. Sacherer, G. Sadoulet, G. Stefanini,L. Thorndahl, S. van der Meer and T. Wikberg, Experiments on stochas­tic cooling in ICE (Initial Cooling Experiment), CERN-EP/79-16, Presented at the 1979 Particle Accelerator Conference, San Francisco, 1979.5. Deceleration in the PS of protons from 800 MeV down to 50 MeV kinetic energy is at present routine for proton filling the ICE ring during electron-cooling experiments. See P. Lefevre, Deceleration de800 MeV a 50 MeV dans le PS, CERN/PS/OL/M 79-1 (1979).6 . K. Kilian, U. Gastaldi and D. Mohl, Deceleration of antiprotons forphysics experiments at low energy (a low-energy antiproton factory),in Proc. 10th Int. Conf. on High-Energy Accelerators, Protvino,1977 (IHEP, Serpukhov, 1977), Vol. 2, p. 179.7. P. Dalpiaz, U. Gastaldi, K. Kilian and M. Schneegans, Low-energy antiproton experiments with an "antiproton factory" at CERN, pre­sented at the Intermediate Energy Physics Workshop, CERN, September 1977.578 . U. Gastaldi, A possible new experimental approach to the study of the pp system at low energies, in Exotic Atoms, Proc. 1st Int. School of Physics of Exotic Atoms, Erice, 1977 (eds. G. Fiorentini andG. Torelli) (Servizio Documentazione dei Laboratori di Frascati,Rome, 1977), p. 205.9. P. Dalpiaz, Electromagnetic annihilation in low-energy pp colliding beams, CERN pp Note 06 (1977).10. R. Klaspisch, CERN Workshop on Intermediate Energy Physics:Chairman's report, CERN-PS-CDI-77-50 (1977).11. A. Astbury, P. Dalpiaz, U. Gastaldi, K. Kilian, E. Lohrmann, B. Povh and M.A. Schneegans, Possible experiments with antiprotons at low and intermediate energies, CERN/SCC/78-4 and CERN/PSC/78-8 (1978).12. W. Hardt, L. Hoffmann, P. Lefevre, D. Mohl, G. Plass and D. Simon,Conceptual study of a facility for low-energy antiproton experiments,CERN/PS/DL/Note 79-1 (1979).13. Proceedings of the Joint CERN-KfK Workshop on Physics with Cooled Low-Energetic Antiprotons, Karlsruhe, 1979, KfK 2836 (ed. H. Poth).14. Seventy-six contributions filed as CERN-p LEAR-Notes and listed inRefs. 3 and 13 were discussed within the study groups at CERN andduring the Karlsruhe Workshop.15. H. Koziol, The CERN Antiproton Accumulator, in Ref. 13 (Also CERN/PS/AA/Note 79-2 and CERN-LEAR-Note 52).16. D.J. Simon, A possible scheme to transfer 50 MeV H ions (and pro­tons) from the old PS linac to LEAR, CERN/PS/MU/BL/Note 79-10 (CERN-p LEAR-Note 37).17. D. Mohl, Possibilities and limits with cooling in LEAR, in Ref. 13 (Also CERN/PS/DL/Note 79-5 and CERN-p LEAR-Note 73).18. W. Hardt, Slow ejection based on repetitive unstacking, CERN/PS/DL 79 (CERN-p LEAR-Note 65) 1979 and references quoted therein.19. K. Kilian and D. Mohl, Gas jet target in LEAR, CERN-p LEAR-Note 44 (1979) .20. C. Voci, Antineutrons at LEAR, in Ref. 13.21. C. Hill, H- sources —  a summary, CERN-p LEAR-Note 36 and CERN/PS/LR/Note 79-6 (1979).22. U. Gastaldi, pp experiments at very low energy using cooled anti­protons in Proc. 4th European Antiproton Conf., Barr-Strasbourg, France, 1978 (Editions du CNRS, Paris, 1979) (ed. A. Friedman),Vol. 2, p. 607.23. Novosibirsk VAPP-NAP Group, CERN 77-08 (1977) and references given therein.24. H. Herr and D. Mohl, Relativistic electron cooling in ICE, CERN pp Note 53 (1978) (Also CERN/PS/DL/Note 78-4 and CERN-p LEAR-Note 40).25. J.G. Rushbrooke and B.R. Webber, Phys. Rep. 44_, No. 1 (1978).26. H. Muirhead, Antiproton annihilations, in Proc. 4th European Anti­proton Conf., Barr-Strasbourg, France, 1978 (Editions du CNRS, Paris, 1979) (ed. A. Friedman), Vol. 2, p. 3.27. For reviews see J.L. Rosner, Phys. Rep.11C, 189 (1974).G.C. Rossi and G. Veneziano, Nucl. Phys. B123, 507 (1977).Chan Hong-Mo and H. H^gaasen, Nucl. Phys. B136, 401 (1978).R.L. Jaffe, Phys. Rev. D U ,  1444 (1978).28. G.F. Chew and C. Rosenzweig, Phys. Rep. 41C, No. 5 (1978).29. For a review, see L. Montanet, Proc. 5th Int. Conf. on Experimental Meson Spectroscopy, Boston, 1977 (eds. E. Von Goeler and R. Weinstein) (Northeastern University Press, Boston, 1977 ) , p. 260.5830. Chan Hong-Mo, Baryonium spectroscopy as a test for colour dynamics, in Proc. 4th European Antiproton Conf., Barr-Strasbourg, France,1978 (Editions du CNRS, Paris, 1979) (ed. A. Friedman), Vol. 2, p. 477.31. I.S. Shapiro, Phys. Rep. 35C, 131 (1978), and references quoted therein.R. Vinh Mau, The baryon antibaryon description of baryonium, in Proc. 4th European Antiproton Conf., Barr-Strasbourg, France, 1978 (Editions du CNRS, Paris, 1979), (ed. A. Friedman), Vol. 2, p. 463.C.B. Dover and J. Richard, On the level order of the NN spectrum in potential models, in Proc. 4th European Antiproton Conf., Barr- Strasbourg, France, 1978 (Editions du CNRS, Paris, 1979) (ed.A. Friedman), Vol. 1, p. 43_, and references quoted therein.T.E.O. Ericson, Low-energy NN interactions, in Proc. 3rd European Symposium on Antinucleon-Nucleon Interactions, Stockholm, 1976 (eds. G. Ekspong and S. Nilsson) (Pergamon Press, Oxford, 1977), p . 3.F. Myhrer, Low-energy nucleon-antinucleon interactions, in Proc.2nd Int. Conf. on Nucleon-Nucleon Interactions, Vancouver, June 1977 (Amer. Inst. Phys., New York, 1978), p. 357.32. E. Klempt, Antiprotonic atoms, in Ref. 13.33. J. Rafelski, What can we learn from p-A annihilation in flight?,CERN-p LEAR-Note 03 (1979) .34. P. Dalpiaz, Charmonium and other oniums at minimum energy, in Ref. 13, and references quoted therein.35. M. Schneegans, NN annihilation, in Ref. 13.36. H. Koch, Investigations on baryonium with stopped antiprotons, in Ref. 13.37. B. Povh, Baryonium with antiprotons in flight, in Ref. 13.38. H. Poth, Fundamental properties of antinucleons, in Ref. 13.DISCUSSIONRICHARDSON: Do you plan sometimes to accelerate the cooled p" and if soto what energy?GASTALDI: It will be possible to accelerate antiprotons in LEAR up to2 GeV/c. Up to 2430 MeV invariant masses will then be accessible in ex­periments with extracted beams and internal jet target operation. In the pp minicollider mode invariant masses up to 4400 MeV will become acces­sible. Higher energies could be, of course, reached extracting the p beam from the PS at the required momentum. This last possibility is, however, outside the LEAR scheme and is not planned at present. A review of the possibilities in the energy region between the LEAR energy domain and the one accessible with 'p in ISR can be found in ref. 34.59THE MECHANISM OF BARYONIUM AND DIBARYONH. NakamuraCollege of Science and Engineering, Aoyama Gakuin University, TokyoABSTRACT^ ^  ^The spectra of baryonium (q q ) and dibaryon (q )the basis of the quark shell model (q = d or u). The mula for the excited states of the quark systems which kinds of quarks is derived and applied to the analyses mesons (s's), (s'q), (cc) and (bb).INTRODUCTIONThe synthetical analysis of hadron spectra may be one of the most important and interesting problems in particle physics. In this short note, we try such an analysis on the basis of the quark shell model-*- in which the LS force plays the most important role as in the nuclear shell model. The informations obtained from the analysis^ of baryon (q^) spec­trum are fully used in the present analysis.MASS FORMULAIn this analysis, we assume the qq-independence for the Wigner force, LS force and dipole-dipole interaction, i.e., there is not any difference between quark and antiquark concerning these interactions. We use here­after terminology "quark" including antiquark, so far as they are not spe­cified. The low-lying nonstrange mesonic resonances are considered as (qq} system as in usual model while the high-lying resonances, baryoniums, are described as (q^q^) system with the excitations of quarks from s\/2 shell to Pl/2 or &2>/2 shell* It Is assumed that (q^q^) system does not form any bound state.In mass formula, the term which comes from the Wigner force is a fun­ction of quark number and orbital angular momentum. A simple square-root form is taken for this function corresponding to the linear Regge trajec­tories. We introduce the energy AM(Ni,N2) which is necessary for the fusion of N^-quarks and N2~antiquarks. Then, the mass formula for (qq) excited states is given byM = [(2m ) 2 + i/a' + (n-l)/a" ] 1 / 2 + AM(1,1) + < V >f(s + s ’) (1)O JLowhere 2 represents orbital angular momentum, s^ and s' the spins of quarkand antiquark, respectively, n (= 1 , 2 , ---) the quantum number for radialexcitation with a parameter a", a 1 the slope of the linear Regge traject­ories, mD the effective mass of a quark in hadrons. Taking into account that LS force is of rather short range in general, we adopt the following form.< vLS> = n/(2f + 1 ) (2)where n is a constant. The values of parameters m0 , a 1, a" and p are extracted from the analysis^ of baryon spectrum, i.e.,are analyzed on general mass for- consist of various of the spectra of60m = 0.313 GeV, 1/a' = 0.945 GeV, 1/a" = 1.10 GeV, n = 0.40 GeV. oIn multiquark systems, the excitations of plural quarks can occur. Neglecting the recoils for the excitations, we introduce the excitation energy of the k-th quark as follows.\  - I ® " /  + V - '  + <V -  1 >/' ‘ " ) 1 / 2  - N» 0 + < VLS> y k (3)where the quantities with subscript k represent the quantities of the k-th quark and N (= N]_ + N2) represents total quark number. We assume that a dipole-dipole interaction of long range exists in multiquark systems with N >_ 6 . Then, the mass formula for the excited states of nonstrange mul­tiquark systems is given byM = Nm + AM(N, ,N_) + U  + ? I j, t  (4)o 1 z k fc k>h x nwhere jk = £ k + sk and 4 represents a constant.We adjust free-parameters AM(1,1), AM(3,3) and AM(6,0) to the masses of B(1234), M°(2020) and D(2250), respectively. Taking the optimum value for the remaining free-parameter 4 , we get4 =-0.013GeV, AM(1,1) = 0.078GeV, AM(3,3) =-0.121GeV, AM(6,0) = 0.109GeVThe results are illustrated in figs.l and 2 together with the correspond­ing configurations. In the spectra of (q^q ) and (q6) systems, we assu­med that only the state with the maximum angular momentum in each confi­guration is observable except the states close to NTT (NN) threshold.The physical implications of this rule are discussed in ref.^GENERALIZATIONWe try to apply (l)-(4) to the systems which contain various kinds of quarks. For quark-antiquark two-body systems, it is empirically found that a good fit to data is obtained by the following modification for (1 ).M = [m2 + xi/a' + x(n-l)/a" ] 1>/2 + AM(1,1) + < ^ g ^ C s  + s')/x (5)2/3where m = m^ + mj , x = [ W  (2m0) ] • The subscripts i and j representthe species of quark, i.e., i, j = d, u, s, c, b, ---. The implicationsof this modification will be discussed elsewhere. The optimum values offree-parameters nu are given bym, = m , m = 0.400 GeV, m = 1.504 GeV, m, = 4.662 GeV. d,u o s c bThe results are illustrated in figs.3-5. The generalization of (3) and (4) is easily carried out by the use of total quark number N, total quark mass m (= X Njmi) and factor x = [W(Nm0)] .  Generally'speaking, the spectra of hadrons are reproduced excellently by the present model.REFERENCES1. H.Nakamura, K.Arita and K.Mori, Lett, al Nuovo Cimento,21,337 (1978)2. H.Nakamura, K.Arita, K.Mori and H.Noya, to be published613-3,FXG.l Predictions of the meson (qq) and baryonium (q q ) spectra62FIG.2 Predictions of the dibaryon spectrum D(M)FIG.4 Predictions of the (cc) spectrumFIG.3 Predictions of the (ss) and (sq) spectraFIG.5 Predictions of the (b¥) spectrum63SU(6) UNITARY SYMMETRY IN DIBARYON SYSTEMSYuan Tu-nan and Chen Xiao-tian University of Science and Technology of China,Hofei Anhwei, People's Republic of ChinaLi Yang-guo, Zhang Yu-shun and Wang Wei-wei Institute of High Energy Physics, Academia Sinica,Peking, People's Republic of ChinaIf SU(6) unitary symmetry exists in dibaryon systems, the 36 states of the dibaryon systems can form nine exotic nuclei. The 21 totally sym­metric states with the same J (total angular momentum) and the same L (orbital angular momentum) are as follows:[PN]It2 J+1 [PA] [NA] {PP}* {PN}*3l2 J+1{NN}* {PA}* {NA}* > > *Q 1 1 0 2 1 0 1 0 0t 3 0 % -% 1 0 - 1 % -% 0T 0 h % 1 1 1 % h 0Y 2 l 1 2 2 2 1 l 0S 0 0 0 1 1 1 1 l 1The 15 totally symmetric states with the same J and the same L are afollows:{PP}Itl 2J+1{PN} {NN} {PA}3l 2J+1{NA} {AA} [PN]* [PA]* [NA]*Q 2 1 0 1 0 0 1 1 0t 3 1 0 - 1 % -% 0 0 % -%T 1 1 1 % % 0 0 % %Y 2 2 2 1 1 0 2 1 1S 0 0 0 0 0 0 1 1 1In the above tables, items with stars show isospin triplets. Items without stars show isospin singlets.The mass formula with the same irreducible representation is:M = M + aY + B[T(T+l) - j  Y2] + cS(S+l).The mass relations of the 15 states of the SU(6) are:S=0: Mq = M{ m } , M {pp} = M {m} = M {pN}, M{pp} + M{M} = 2m{pA}.s=1: M{PA} = m {n a }’ m [p a ] = m [n a ]*The mass relations of 21 states of the SU(6) are:S=0: Mo = -M{pA} + M{m} + M{pA}, M{pp} = M{pN} = M{NN},M{PP} + M{AA} = 2m{PA} •s=1: m {p a } = m {n a }’ m [p a ] = M [NA] •A comparison of the theoretical value with experiments is shown in the following table (unity: GeV):64pp PN PA AA3d2 2.14 2 . 13F3 2 . 2 2(input)2.26 2.256 (experimental value) 2.278 (theoretical value)2.336(input)2.50 2.50From the above table it can be found that we have regarded the ex­perimental energy level 2.256 GeV, belonging to the PA, as the {PA}* state; the experimental energy level 2.22 GeV, belonging to the PP, as {PP}* state; and the level 2.336 GeV, belonging to the AA, as {AA}* state. In this case we can get the energy level 2.278 GeV belonging to the {PA}* by calculation. This value agrees with the experiment well, so we predict that the orbital angular momentum of the {AA}* energy level is L=3.Data from Ref. 1 (see the following table) show the PP energy level is the same as PN energy level (S=0). This gives full support to the theory of SU(6) unitary symmetry in the dibaryon systems (unity: GeV):PP isospin mass mass isospin PNxD2 1 2.14 2 . 1 1 *d2COCO 1 2 . 2 2 2.26 1 GO GO1 2.50 2.50 1 ^ 4REFERENCE1. Y. Nambu, 19th Int. Conf. on High Energy Physics, Tokyo, August 1978 (Physical Society of Japan, Tokyo, 1979), p. 971.65SEARCH FOR NARROW BARYONIUM STATES NEAR THE pp THRESHOLDHeidelberg1 -Saclay2-Strasbourg3 Collaboration R. Bertini, 3 P. Birien, 2 K. Browne, 1 W. Bruckner, 1 H. Dobbeling, 1 R.W. Frey, 1 D. Garreta, 2 T.J. Ketel, 1 K. Kilian, 1 B. Mayer, 2B. Pietrzyk, 1 B. Povh , 1 M. Uhrmacher, 1 T. Walcher, 1 and R. Walczak1A systematic search for narrow baryonium states (X) in the mass region between 1.4 and 2 GeV is performed at the PS at CERN, using the reactions pp tt-X and pd -*■ pX with incoming p" momentum between 0.65 and 1.3 GeV/c.In this momentum region the two reactions populate preferentially baryonium states as compared to the normal mesonic resonances. In addition high-intensity and high-purity antiproton beams can be produced at these momenta with conventional means.The two reactions are measured in a typical missing-mass mode, using a newly designed intensive antiproton beam in conjunction with the large- acceptance Saclay spectrometer SPES II. The momentum of the incoming antiprotons is measured in the last stage of the beam and the momentum of the reaction products in the SPES II. The overall resolution of the experiment is 2 MeV.Result of these measurements will be presented at the Conference.66A PRODUCTION EXPERIMENT OF STRANGE BARYONIUM AT SLACM. Cain, R.D. Kass, W. Ko, R.L. Lander, K. Maeshima-Petrini,W.B. Michael, J.S. Pearson, D.E. Pellett, G. Shoemaker,J.R. Smith, M.C.S. Williams and P.M. Yager University of California, Davis, CA, U.S.A. 95616An experiment is in progress at SLAC to search for the manifestly exotic state with baryon number 0 , strangeness + 1 and charge - 1 , which decays preferentially into an antihyperon-baryon pair. If it exists, such a state can belong to either a qqqq SU(3) decuplet or a 27-plet.The reaction is pn -* ^ X - . The forward K£ trigger for the bubble chamber is provided by a hadron calorimeter, 2 m downstream. This hadron calorimeter, made of 1750 acrylic scintillator strips and 122 wave bars, provides an angular resolution of better than 8 mrad.67QUARK MODEL DESCRIPTION OF THE RADIATIVE DECAY OF THE RESONANCE A3/2-(1520)*E.J. Moniz and M. Soyeur+Center for Theoretical Physics, M.I.T., Cambridge, MA, USA 02139ABSTRACTThe radiative decay widths of the A3/2"(1520) resonance and of the lower mass strange resonances are calculated in the spherical cavity ap­proximation to the MIT bag model. The sensitivity of the results to the octet admixture in the A (1520) wave function is discussed.I. INTRODUCTIONWith the operation of kaon factories, it may become possible to per­form precise experiments in the kaon energy region corresponding to the ex­citation of the A(1520) resonance. This resonance, the first above kaon- nucleon threshold, has a very narrow width (16 MeV) and dominates the low energy K“-proton cross-section. Consequently, it is very attractive for studying both hadron structure and the dynamics of hadron resonances in nuclei.We have calculated in the MIT bag model the radiative widths for the decay of the A(1520) to the subthreshold A- and E-states; the radiative decay scheme is indicated in Fig. 1. We assume that the y-decays occur by a single quark transition. Photon emission can be calculated relatively unambiguously and so we can hope to learn about the quark wave functions. While we focus here on this question only, these y-decays may ultimately prove useful for studying isobar propagation in the nuclear medium.In Sec. II, we discuss the quark wave functions for the relevant strange baryons. Our discussion is given in the framework of the static spherical cavity approximation to the MIT bag model.The radiative transitions indicated in Fig. 1 are discussed in Sec. III.II. MIT BAG MODEL WAVE FUNCTIONS FOR THE LOW-LYING STRANGE BARYONSAll of the uncharged baryons indicated in Fig. 1 are made up of one down, one up and one strange quark. The positive parity states are described in the usual way as containing all three quarks in the si/2 orbit. 2 The A(1116) and E°(1193) belong to the ground state octet while the E°(1385) belongs to the ground state decuplet. The negative parity states are described by a single quark L = 1 excitation, P 1 /2 for the A(1405)3 and P 3/2 for the A(1520) Their wave functions, expressed as superpositions of flavor SU(3) multiplets, are determined essentially by the quark kinetic energies, the strange quark mass (of the order of 300 MeV) and the lowest order colored-gluon exchange .2-i+ We allow for small (degenerate) up and down quark masses of the order of a few MeV.*This work is supported in part through funds provided by the US DOE under contract EY-76-C-02-3069 .^Permanent address: CEN de Saclay, Service de Physique Theorique, B.P. #2, F-91190, Gif-sur-Yvette, France.68A (1520)Fig. 1. Radiative decay scheme of the A (1520).The A(1405) is particularly simple since the kinetic energy is signi­ficantly lower when the massive strange quark is promoted to the P 1 /2  orbit. 3 Thus, the wave function contains a P 1 /2 strange quark and two s\/2 light quarks coupled to a singlet. With this model, any radiative transition involving the A(1405) goes by a strange quark transition.The A(1520) has two main components, the singlet (1,3/2“} and the octet (8 ,3/2”(S=0)} with the two s^/2 quarks coupled to zero. The admix­ture of these is fixed primarily by gluon exchange, and DeGrand14 gives the coefficient ag = 0.85 for the singlet and ciq = -0.51 for the octet (we use Lichtenberg5 sign conventions and ignore the contributions from two other octet configurations which represent less than two per cent of the wave function). The SU(6)y admixtures6 are quite similar with the singlet state having an amplitude about ten per cent larger.III. RESULTS AND DISCUSSIONGiven the quark wave functions described above, construction of the current and evaluation of the radiative widths are rather straightforward.We summarize our main qualitative results as follows:1. The rates for the transitions A(1520) -* E°(1385), A(1405) -* E°(1385) and A(1405) -> E°(1193) are zero in this model.2. The y-width for A(1520) -*■ A(1405) is less than a keV while that for A(1520) -> A(1116) is a few keV. However, these are very sensitive to the octet admixture since the strange quark transition amplitude is propor­tional to (ag+/2 aq). This quantity is nearly zero in our model.69Consequently, much larger experimental widths might point to a significant­ly different octet admixture.3. The y-width for A(1520) -* E°(1193) is about 100 keV. The transition goes by the light quarks and the amplitude is proportional to (ag - a0//2).4. The E (1193) -> A(1116) radiative width has been measured to be (11.5±2.6) keV. Our calculated width for that transition is about a third of the experimental value. All of the absolute widths depend sensitively on the bag parameters such as the radius, which we have taken as 1 fm. A very recent redetermination7 of these parameters indicates that all the widths may be scaled up.A more detailed discussion of our calculations and results will be pub­lished elsewhere.We thank John Donoghue and Barry Holstein for help and advice in the course of this work.REFERENCES1. A. Chodos, R.L. Jaffe, K. Johnson, C. Thorn and V. Weisskopf, Phys.Rev. D9, 3471 (1974).2. T. DeGrand, R.L. Jaffe, K. Johnson and J. Kiskis, Phys. Rev. D12, 2060 (1975).3. T.A. DeGrand and R.L. Jaffe, Ann. Phys. 100, 425 (1976).4. T.A. DeGrand, Ann. Phys. 101, 496 (1976).5. D.B. Lichtenberg, Unitary Symmetry and Elementary Particles, second edition (Academic, New York, 1978).6 . D. Faiman and D.E. Plane, Nucl. Phys. B50, 379 (1972);M. Jones, R.H. Dalitz and R.R. Horgan, Nucl. Phys. B129, 45 (1977).7. J.F. Donoghue and K. Johnson, MIT preprint CTP//802, July 1979.DISCUSSIONISGUR: Are your A3/2-(1520) mixing angles consistent with the phenomeno­logical analyses?SOYEUR: Yes, even though they usually give a somewhat larger admixture ofsinglet state.70HEAVY QUARK-ANTIQUARK BOUND STATES *IN THE FRAMEWORK OF QUANTUM CHROMODYNAMICS+R.D. Viollier Center for Theoretical Physics Laboratory for Nuclear Science and Department of Physics Massachusetts Institute of Technology Cambridge, Massachusetts 02139J. Rafelski CERN, Geneva, SwitzerlandABSTRACTBased on the first order running coupling constant a^ ( q 2 ) we derive in the static limit a quark-antiquark potential.The tachyon pole in a^Cq2 ) leads to a partially confining po­tential, while the smooth remainder gives rise to a Coulomb­like interaction. We impose linear confinement by extrapola­ting the confining potential linearly for distances r>r .Thus, aside from the quark masses, m c and m ^ , our model con­tains two free parameters: (i)the renormalization mass A, and(ii)the extrapolation radius r . With A=441 MeV, r =.378fm, m =1.525 GeV, and m^=4.929 GeV, we reproduce the observed or- tfiocharmonium and orthobottomium spectrum very well. This can be viewed as evidence for the validity of the framework of quantum chromodynamics.INTRODUCTIONTwo families of heavy quark-antiquark bound states, the J/i(iE(cc) and the T=(bb) resonances, have been discovered.There is a strong theoretical prediction that at least one more family 1 may exist which has a new type of heavy quark t as fundamental building blocks. The spectroscopic properties of these heavy quarkonium states represent a sensitive test for quantum chromodynamics (QCD ) , 2 the currently accepted gauge theory of strong interactions. In contrast to the light quarks (u,d,s), the nonrelativistic heavy quarks (c,b,t) directly probe the static quark-antiquark potential.THE QUARK-ANTIQUARK POTENTIALThe quark-antiquark potential that describes one gluon-This work is supported in part through funds provided by the US DEPARTMENT OF ENERGY(DOE), contract EY - 76-C-02-3069.also CERN, Geneva, Switzerland71exchange with the vacuum polarization corrections arising from virtual gluon and quark pairs is given by the Fourier transform of the Coulomb propagatora n (q2 )— --------  q 2dq (1 )„ 2 q rdressed with the running coupling constant 3( 2 s 1 A 2 , 1  / 1 A 2 . .aA J B f 1 o g q 2 / A 2 B f (q2 -A2 ) B f \ Qg £ 2 " q 2_A 2 ; .Here A denotes the renormalization mass, and B^ isB f»(ll-2/3f)/4TT (3)where the first term represents the gluon contribution and f stands for the number of (massless) quark flavors contributing to the polarizability of the vacuum.The pole term in Eq. (2) leads to a partially confining vector potentialit t \ 8 1 • 2 Ar ...Uo (r)- T T f r Sln ~2 (4)while the smooth remainder gives rise to a Coulomb like inter­actionU l ^  3B,r-tr ,6 _ 1  “  (5)(log ^ 2) 2+ir2The potential (4) is apparently incorrect for large values of r where, according to lattice gauge theories4 , it should rise linearly. However, there is reason to believe its structure at short distances. In this spirit, we impose linear confine­ment by extrapolating U (r) linearly for distances r>ro oU (r) r<ro —  oU (r)= 4 (6 )U (r )+U'(r ) (r-r ) r>ro o o o o oThe extrapolation radius r is a phenomenological parameter to be determined from the experimental data.NUMERICAL RESULTSWe solve the Schrodinger equation for charmonium and bot-72tomium using the potential U (r)+U1 (r) (Fig. 1). For charm­onium, the three free parameters of the model, A, r , and m ,are determined by fitting the IS, 2S, and IP levels to theexperimental 1 3S (3.097), 2 3S (3.686), and to the center of gravity of the 1 1 3P Q x 2 levels at 3.523 G e V 5 , respective­ly. The fit parameters A = 441 MeV, r = .378 fm, and m =1.525 GeV, are compatible with what one may expect fromother sources. For the bottomium spectrum we use the same values of A and r . The only free parameter left, the bot­tom quark mass m ^ , is adjusted to the experimental 1 3S j (9.46) level of bottomium6yielding m^ = 4.929 GeV.In Fig. 2 we show the charmonium spectrum. The excel­lent agreement between theory and experiment is largely due to the fact that the three lowest levels have been fitted.qThus the only independent tests of the model are the 3 Sj (4.040) level which is unreliable, since it is far above charm threshold, and the 1 3D 1 (3.772) level which cannot be compared directly to the calculated center of gravity ofthe 1 3D levels.1,2,3The real test of quantum chromodynamics comes with the bottomium spectrum shown in Fig. 3. Our calculations agree very well with the observed bottomium spectrum and thus con­firm the reliability of the first order QCD potential. Here the experimental 2 3 S j (10.02)and 3 3S 1(10.38) levels are b e ­low bottom threshold and represent therefore a conclusive test of our model which includes both concepts, asymptotic freedom and linear confinement.REFERENCES1. See e . g . : Y. Hara, Rapporteur talk XIX Int. Conf. on HighEnergy Physics, Tokyo, August 1978.2. See e.g.: W. Bardeen, H. Fritzsch and M. Gell-Mann, inScale and Conformal Symmetry and Hadron Physics (ed.R. Gatto, New York, 1973).3. H.D. Politzer, Phys. Rev. Letters 30_ (1973) 1346.D.J. Gross and F. Wilczek, Phys. Rev. D 8  ^ (1973) 3633 ;Phys. Rev. Letters 3_0 (1973) 1434.4. J. Kogut and L. Susskind, Phys. Rev. D£ (1974) 3501; D l l ,(1975) 395. K. Wilson, Phys. Rev. D IO (1974) 2445.5. N. Bar ash-S chmid t ejt a l . , Phys. Letters 7 5B (1978).R. Brandelik e_t aJ. , Phys. Letters 7 6B (1978) 361.P.A. Rapidis e_t a_l. , Phys. Rev. Letters _ 3 (1977) 526 ;3_9 (1977) 974E.6 . Ch. Berger e_t al. , Phys. Letters 76B (1978) 243.C.W. Darden ejt a_l. , Phys. Letters 7 6B (1978) 246.S.W. Herb e_t a_l. , Phys. Rev. Letters 39j (1977) 252 .W.R. Innis e_t_ aJL. , Phys. Rev. Letters 3_9j (1977) 1240.J.K. Bienlein £tj aJL. , DESY Report (1978).73Fig. 1. The quark-antiquark potential.Fig. 2. The charmonium spectrum. Fig. 3. The bottomium spectrum.74MESON SPECTRA*K.F. Liu and C.W. Wong University of California, Los Angeles, CA, U.S.A. 90024Nuclear physics at intermediate energies may involve certain aspects of the internal structure of mesons, including their spatial extensions and internal compositions. As a first step in providing an overall per­spective on low-lying mesons of different flavor families, we discuss their descriptions as quark-antiquark (QQ), quark-antiquark-gluon (QQg) and "four-quark-bag" states of the constituent quark-gluon model of hadrons.The QQ states of p /tt to T families are identified and fitted by a nonrelativistic, spin-dependent QQ potential with potential strengths which are "asymptotically free". The u,d quark mass is chosen by fitting the proton charge radius. 1 Model meson masses agree well with observed masses, including the isospin-averaged tt-ti mass. The experimental pion charge radius (0.56 ± 0.04 fm) is reproduced.A number of other mesons are known which are probably not QQ states. The most famous are the three puzzling mesons, X(2.83), x(3.45) and X(3.59), in the charmonium region. From the calculated masses and esti­mated properties of QQg states, we argue that these are primarily the ccg, jPC = 0++, 1++ and 2"*-1" states, respectively. They may also contain — 30% admixtures of a combination of the cc 3Pj states and the ccqq bag states of De Rujula and Jaffe. 2 (Mesons with predominantly ccqq structure probably have higher masses.2) On the other hand, both Q(Jg and four-quark bag states may appear close together in the lighter mesons, e.g. as e (0.7), k (1.2) and k'(1.43).1. J.F. Rondinone and C.W. Wong, 1978, unpublished;J.F. Rondinone, Ph.D. Thesis, UCLA, 1978, unpublished.2. A. De Rujula and R.L. Jaffe, in Proc. Fifth International Conference on Experimental Meson Spectroscopy, 1977, ed. E. Von Goeler andR. Weinstein (Northeastern Univ. Press, Boston, 1977), p. 83.*Work supported in part by the National Science Foundation.75KAON ELASTIC AND INELASTIC SCATTERING AT 800 MeV/c*R.A. Eisenstein Carnegie-Mellon University, Pittsburgh, PA 15213ABSTRACT+Data recently acquired at Brookhaven for K elastic and inelastic scattering from 12C and lt0Ca targets are compared to calculations based on simple first-order theories of the scattering process.INTRODUCTIONThe interaction of intermediate energy projectiles with nuclei has long been hoped to be a fertile testing ground for our theories of nuclear structure and dynamics. In the case of meson-nuclear processes, these hopes are often based on special properties of the elementary amplitude which we hope will manifest themselves in the A-body problem in such a way as to illuminate facets of nuclear structure or dynamics which we hope to understand. Such features might include resonance structure in one or more elementary partial waves, large isospin selec­tivity, or, as in the case of kaons, a new degree of freedom (strange­ness) . The latter case, when a new quantum number has been introduced into the nuclear system, is especially provocative since we are altering the nucleus in a profound but intelligible fashion. The usefulness of this approach can be seen in the discussions of the (K",ir_) reaction presented in this conference by Drs. Povh and May.In what follows, I will outline briefly our current understanding of the simplest kaon-nucleus interactions: elastic and inelastic scat­tering. Of special interest are new high quality data obtained at the Brookhaven kaon spectrometer for 800 MeV/c, with which the theory can be compared. The improvement of the scattering theory is important not only for its own sake, but also because it is an important input to the calculation of processes like the (K“,ir-) reaction.THEORYThe kaons form four members of the octet of pseudoscalar mesons shown in figure 1. The K(K) system forms an isodoublet of strangeness + 1 (-1 ), while the pions and the eta are the non-strange members of the group. Thus, while the K* are antiparticles, they are not members of the same isodoublet and so their strong interactions cannot be linked by isospin invariance. An examination of the total K* - N cross sections shows this clearly (see pp. 40-41 of ref. 1). Below 1 GeV/c, the K“(S = -1) cross section shows the existence of many narrow resonances, both in the 1 = 0  (A) and 1 = 1  (£) channels. The approximate cross section at 800 MeV/c is ,v 42 mb/sr for the 1 = 0 (K“ -N) channel.*Work supported in part by the USDOE.76Fig. 1. The octet of pseudoscalar mesons.On the other hand, the K+ (S = 1) data are smoothly varying, ap­parently without resonance structure in this momentum range. The lack of resonance structure is due to the non-existence of any hadrons with strangeness +1. Figure 2 shows a more detailed view of the K+ + p total cross section over the momentum range 0 - 1200 MeV/c compared to a cal­culation by Martin.2 As the energy increases, each partial wave enters gradually and without fanfare. Of interest to us is the fact that at 800 MeV/c the total cross section is ^ 13 mb/sr for K+ , and that partial waves up to at least 1 = 2 are required to describe the data.We are thus dealing with a situation quite different from the ones existing for proton or pion scattering-. In the medium energy range, the proton-nucleon amplitudes are non-resonant (so far) but fairly large (35 mb/sr at 800 MeV) and contain important spin-dependent pieces. The pion cross-section is dominated by the (3,3) resonance which is quite broad (r % 100 MeV) and very large (^ 200 mb/sr at 275 MeV/c in ir+ - p). For both of these probes, there are no open channels other than charge exchange below the tt production threshold. In contrast, the K" - N system has many narrow resonances (T ^ 15 - 30 MeV) and there are open channels down to the K~ - N threshold. The cross sections are moderatelyFig. 2. The total K+ + p cross section as a function of lab momentum.large. Therefore, we expect that the K~-nucleus cross section will reflect these features: the interactionwill be strong and the ampli­tude complicated. On the other hand, the K+-nucleus cross sections should be fairly weak and the ampli­tudes reasonably simple. In fact, we expect the K+-nucleus interaction to be the weakest of any strongly interacting probe, and the resulting mean free path to be large. We note with relief that there is no true absorption of the K+ to complicate things, in distinction to the case for low energy it scattering.77In order to construct a K-nucleus theory, a prescription must be used for extrapolation from the two-body system (KN) to the A-body system. Due to the paucity of experimental data, comparatively little effort has been made toward the building of a sophisticated theory.All calculations2-6 of which I am aware use first order multiple scat­tering theory (a la Rayleigh-Lax) in which the factorization approxi­mation has been invoked. With such a form, the optical potential becomes proportional to the product of the two body amplitude t(k,k') and the nuclear density p (q). In the calculations by Rosenthal and Tabakin5 (RT) shown below, the kaon amplitudes were taken from Martin7 or the BGRT collaboration® in the case of K+ or from Gopal, 9 et al. in the case of K”. The nuclear densities were taken from electron scat­tering data.In their calculations, RT have made use of both co-ordinate10 and momentum space1 1 formulations. The latter treatment provides a convenient means of studying potentially important effects such as off- shell behavior, the angle transformation and Fernd motion. 1 2 The Kisslinger potential,13 2EV(r) = -Ak2bop(r) + A bj V-pV was used in the co-ordinate space calculations, with appropriate kaon values for the parameters b0 and b; . A more detailed description of these matters can be found in refs. 2-6 .EXPERIMENTThe data were all accumulated at the Brookhaven Kaon spectrometer by the members of the CMU-Houston-BNL collaboration. 14 The spectro­meter is described fully in the contribution of E. Hungerford to the workshop. I note in passing some of the relevant parameters: at themomentum used for the experiment (800 MeV/c) the optimal resolution achieved with target out was 1.5 MeV; spectrometer solid angle 'v 11 msr, angular acceptance ± 3-4°, momentum spread ± 4%. The channel plus spectrometer is about 24 meters in length, and there were approximately 20,000 K” on target per 3 x 101 2 protons incident in the production spot. The 12C targets used ranged in thickness from 1.5 to 4.5 g/cm2, while the 40Ca target was 1.8 g/cm. 2 The data have been normalized to the ^ p  cross sections, measured using a CH2 target. The data are pre­liminary, awaiting a full Monte Carlo study of the spectrometer. Ap­proximately 550 hours of beam time were required for data collection, in the ratio 3/2 for Ca/C. Figure 3 shows the data from all runs at 20° for K~ on 1 2 C. The resolution is about 2 MeV; the ground state,2+ at 4.44 MeV and 3" at 9.6 MeV are clearly visible.COMPARISON TO THEORYThe data obtained during the experiment are shown in figs. 4-9. Generally speaking the elastic angular distributions are diffractive in shape, each displaying a minimum at about 27 degrees. The K- data are roughly 10 times larger than those for K+ on the same target. The Coulomb interaction is not important past 'v 10 degrees in Ca and is un­important over the entire C data range.Looking at the RT calculations (figs. 4-9) we note that those for K are in significantly better agreement with the data than are those for K-. This could be interpreted as support for the arguments given78above regarding our expectations for the calculations of elastic scattering.Although the calculations are described in detail in ref.5, certain interesting features should be pointed out here. For the K” - * C calculations (fig.4), the momentum space calcu­lations (using KPIT) show a wide variation depending on whether the angle transformation is in­cluded. It is interesting that the inclusion of the transform depresses the cross section at back angles, opposite to what happens in the tt case. The dif­ference between the KPIT calcu­lation with no transform and the co-ordinate space calculation (KPIRK, also with no transform) is due to the fact that d-waves tered K" projectiles from a iZC target, in the KN t-matrix have been in- The two prominent inelastic states be- eluded as an additional contri- low 10 MeV are easily resolved. bution to the bg term in KPIRK,but not at all in KPIT. (See refs. 4 and 5 for more details of the calculations.) None of the fits is very satisfactory.In the K+ - 12C case, the situation is very interesting. All cal­culations shown in figure 5 use the coordinate space treatment of KPIRK, but with different choices for the calculation of bg and b^. The angle transform has not been included. In the two calculations using Martin amplitudes, the one which includes d- and f-wave contributions to bg is in much closer agreement with the data than the other, which includes only s- and p-waves. We note that the BGRT prediction, even with s-f waves included, is in very poor agreement with the data. It is en­couraging that the data are apparently able to discriminate between the calculations and potentially choose between alternate phase shift sets.Similar conclusions can be made for the Ca case. Figures 6 and 7 show only the KPIRK calculations for the Gopal and Martin amplitudes, with the effective bg including s, d, and f waves in the K+ case. The K+ calculations agree very well with the data.Turning finally to the inelastic scattering results (figs. 8 and 9) we find a less clear situation. The data are compared to a standard1 5 DWIA calculation (DWPI), using a collective form factor for the inelas­tic transition. The standard procedure is to use incoming and outgoing waves determined by the elastic scattering and a deformation parameter 3 determined with other probes (82 = 0.56). In the K” case, the overall shape is reproduced well, but the magnitude is not. This is probably so because the elastic channel description used (see fig. 4, KPIRK calcu­lation) does not describe the elastic data well. In the K+ case, the situation is reversed. This behavior is not understood at present; since the data and the theory are both in preliminary form, further conclusions will have to wait.E n e r g y ,  MeV ( A r b i t r a r y  Z e r o )  Fig. 3. The energy spectrum of scat-79Figs. 4 detailsand 5. - 12C elastic data and calculations. See text forBoth data and calculations are preliminary.Figs. 6 and 7. Same as fig. 4 but for 1+0Ca target.80Figs. 8 and 9. Ki - 12C inelastic data and calculations. See text for details. Both data and calculations are preliminary.What seems clear, however, is that scattering is potentially a useful new tool for exploring our understanding of strong interaction scattering from many-body systems. More experimental and theoretical work should be done on this interesting new part of medium energy physics.ACKNOWLEDGEMENTSI would like to express my thanks to the other members of the CMU- Houston-BNL collaboration, and to Al Rosenthal and Frank Tabakin, for many pleasant and instructive hours discussing these data and their interpretation.REFERENCES1. C. Bricman, et al., "Review of Particle Properties", Physics Letters 75B (1978).2. C. Dover, "Proceedings of the Summer Study Meeting on Kaon Physics and Facilities", H. Palevsky, editor, Brookhaven publication BNL- 50579.3. C. Dover and P. Moffa, Phys. Rev. C16 (1977) 1087.4. C. Dover and G. Walker, Phys. Rev. C19 (1979) 1393.5. A. Rosenthal and F. Tabakin, preprint and private communication.6. S. Cotanch and F. Tabakin, Phys. Rev. C15 (1977) 1379.7. B. Martin, Nucl. Phys. B94 (1975) 413.818 . G. Giacomelli, et al. , Nuc. Phys. B71 (1974) 138 and B20 (1970) 301.9. G. Gopal, et al., Nuc. Phys. B119 (1977) 362.10. R. Eisenstein and G. Miller, Comp. Phys. Comm. 8 (1974) 130.11. R. Eisenstein and F. Tabakin, Comp. Phys. Comm. 12_ (1976) 237.12. See, for example, the contribution of F. Tabakin to this conference.13. L. Kisslinger, Phys. Rev. 98 (1955) 761.14. From CMU: D. Marlow, P. Barnes, N. Colella, S. Dytman, R. Eisenstein,F. Takeutchi, W. Wharton. From Houston: S. Bart, R. Hackenberg,D. Hancock, E. Hungerford, B. Mayes, L. Pinsky, T. Williams. From BNL: R. Chrien, M. May, H. Palevsky, R. Sutter.15. R. A. Eisenstein and G. A. Miller, Comp. Phys. Comm. 11_ (1976) 95.DISCUSSIONCOTANCH: The K+ calculations are predictions not adjusted fits to thedata. As such the very good K+ agreement between theory and experimentshould be compared to the pioneer work of pions.BUGG: The latest K^p -»■ K°p data strongly suggest the existence of an 1=0P 1 /2 resonance at about 1 GeV/c. When Fermi motion is built in, this resonance may make nuclei less transparent to K+ than several speakers have claimed.DOVER: The cross sections do rise rapidly above 800 MeV/c due to theZ* resonances. However, this should have a relatively small (but calcu­lable) effect on the mean free path of low-energy K+,s.82KAON-NUCLEUS INTERACTIONS*F. TabakinUniversity of Pittsburgh, Pittsburgh, PA 15260ABSTRACTThe K -nucleon resonances are discussed. Then K -nucleus optical potential parameters are deduced from the recent Alston-Garnjost et. al.K -N amplitudes by use of a simple, standard impulse approximation approach. The role of the resonances_ and of nucleon motion are_ investigated to see how the various K -N resonances affect the K -nucleus absorption and_the associated cross-sections. The absorption induced+ by the basic K -N resonances is seen to be much larger than for the K case, but not as large or dramatically energy-dependent as for pions. Nucleon motion is found to be very significant especially near the narrow resonances. Illustrative results are presented which demonstrate that close scrutiny, theoretically and experimentally, will be required to reliably extract information about Y*-dynamics.INTRODUCTIONThe great thing about the K+-meson is that, while it does interact strongly with the nucleus, it is not strongly absorbed nor does it have lots of narrow, inelastic, and overlapping resonances which complicate the extraction of nuclear information. The great thing about the K -meson is that it does have lots of narrow, inelastic and often overlapping resonances, which makes it a dynamically rich, challenging particle and not just a weakly absorbed, rather bland probe. The K offers us the possibility of entering into the world of A and £ or, in short, of Y*-hypernucleus physics.K~-NUCLE0N AMPLITUDEClearly for kaons, we have it both ways: with and without strongabsorption, with and without rich resonance structure. Indeed, K—  particles are similar in their both being pseudoscalar mesons of the same mass, but they are not members of the same isospin doublet, as we see in Fig. 1N PFig. 1. The 0 meson and 1/2 baryon octets.*Work supported in part by NSF.83From the above, we see that the K gives its strangeness -1 to a nucleon when absorbed, and a Z or A baryon state is thereby reached.In addition to the ground state Z and A, there are excited states above the baryon octet shown in Fig. 1 which are denoted generically as resonances, with isosinglet Y = A* and isotriplets+Y^ = Z being organized into SU(3) multiplets. In contrast the K meson cannot excite nucleon isobars since none are available with strangeness + 1 .There is^however some speculation^that above of 1*0 GeV/c such so-called Z resonances might exist. +A review of recent advances in elastic and inelastic K nucleus ^experiments has been presented by R.A. Eisenstein ; from S.R. Cotanch we will learn more about the K* meson. Therefore, in this talk only the K case will be discussed, with emphasis on the role of K resonances and on the effect of nucleon motion in determining the energy variation of kaon cross-sections and of kaon-nucleus absorption.The first step in describing the K -nucleus interaction is to examine the K -nucleon amplitude, which is presented in Fig. 2, as Argand diagrams for the recent Alston-Gamjost et al. and Gopal et al.^ amplitudes.4 5Fig. 2. The Alston-Gamjost et al. (solid) and Gopal et al.(dashed) K -nucleon amplitudes, T . The inserted circleshows how to read the n„ and 5 values.X/ X/84The existence of resonances is ascertained by these authors, ’ not merely by detecting peaks in cross-sections, but by the rapid counter-clockwise variation of the amplitudes with energy, which are fit by resonance forms with proper threshold, penetration, and background behavior. That arduous task yields the resonances or spectrum of Y* states displayed in Figs. 3A and 3B.4 5(A) (B)* 4 5Fig 3.The Y spectrum (A) Alston-Gamjost et al. ; (B) Gopal et al.The length of each horizontal line in Fig. 3 represents the elasticity of each state (length ^ Pg/P* where r , T are the elastic and total widths and is the background absorption parameter). For many cases that length is short, corresponding to many open channels, i.e. to quite an inelastic resonance. The vertical lines give the width (T) of each level, which is often quite small especially compared to the broad 3-3 (elastic) resonance found for pions. Thus the Y spectrum is that of inelastic, narrow and often overlapping resonances (Fig. 3). The right hand scale gives PLAB, from which it is clear that in addition to the ground state A(1116) and 1(1190), there are two subthreshold resonances, the A*(1405) and £*(1385). These subthreshold resonances dominate the dynamics of K and 1 atoms, and, as we shall see, also dominate the optical potential in the lower positive momentum region. For P = 0.394 GeV/c above threshold (r^ s > 1.432) we see (Fig. 3) the A(1520), which appears as a narrow, isolated D-wave resonance (also called the D (1520)). As P^^jj is increased, a complicated variety of resonances enter and a corresponding intricate variation of the optical potential with energy is to be expected. The recent impressive CMU experiments at 800 MeV/c are in the region of overlapping resonances.OPTICAL POTENTIAL PARAMETERSIn the nucleus, the K is taken in the impulse approximation (IA) to strike a typical nucleon in level a. This simple picture involves ^n initial nucleus (n) which yields up the nucleon a to be excited to a Y by the incident K“ . The process can be pictured as:85—  *Fig. 4. The K excitation of Y in nuclei.The final state is shown here to be^a residual nucleus n ' and a K ; of course,_one could proceed via the_Y _£o other final states such as in the n(K ,TT )n n(K ,K )n', n(K , K ) n ' > n(K >y)n! _ reactions. The broad range or’possibilities has been discussed by C ’Dover. The above picture also suggests that doorway isobar model ideas^ could play a significant role in describing the dynamics, provided one includes the nucleon motion and the full array of resonance characteristics.Certainly, one must ultimately include the interaction of the Y* with the nA ^ intermediate nucleus; therein lies some hope of learning about Y*-nucleus dynamics.At this stage, however, it is reasonable to examine some simple IA formulations to describe the optical potential. Several papers have appeared recently using such an a p p r o a c h . -phe optical potential in the IA factorized case is of the form( k '  |V|k)  % "tvy.p" ( k 2 b +  b. lc • P  +  b „ k V 2P .  +  . . . ) p ( k ' - k ) ,  ( 1 )1 1 UN o o 1 L Iwhere the potential parameters are related to the basic K - N amplitudes byb£ = 1 Jo (2I"'4 1} (£ F- + (Z + 1} Fi) ’ (2)— 9 — 1 — 1Here E, = k k (k/A) , F = (S - l)/2i,and I is the isospinlabel. For _^simglicity, the "t" in (1) was taken to be(k^ b' + bj £ • k' + b^ Q + b' q ), which enables us to relate the b^of (2; to the b^ parameters of a coordinate space potential that has been used in a slightly modified version of PIRK-*-^  to generate the results presented here:-2E V(r) = (k2 b^ p(r) - b ^  V p V - bj V2p + b^ V4P) . (3)We refer to the above V as the momentum-dependent (MD) form.From the isovector and spin-dependent parts of t , one can also define energy-dependent parameters which enter into the excitation processes in inelastic DWIA calculations (see refs. 8 and 9). Here, thefocus is on the b^, b^, and b^ parameters and the N=Z case of CFor the purpose of gaining insight into the sensitivity of calculated cross-sections to the optical potential, three ways to treat V are considered. First, the momentum dependence in (1) is ignored and86In that case the b p(r), where b is a simple sum of the2 2 »2 4the substitutions k • k' + kM  k k -*■ k„ are used instead of the -»■->» -*■ -> 0 , 0replacement k • k p ->■ -VpV etc. used to get (2j_.potential becomes - 2 EV(r) = k|"b^'s. Calculations done that way are labelled by b(IA).The second case consists of using (2) directly, which we label as (MD) for momentum dependence included. Thirdly, a simple procedure for averaging the b parameters over the nucleon motion is introduced and denoted by (FA) for Fermi-averaged. The Fermi averaging procedurehere is simply to fold the b 's, and b, over a distribution of theThis function P.2N5 as a function of the nucleon momentum P_T.Nnucleon momentum in the nucleus. given inNFig. 5. Distribution of nucleon momentum vs P^(GeV/c).In addition, a procedure developed by A. Rosenthal^ was used to include the effect of having the nucleon momentum vector P^ distributed over angles other than those parallel to the incident kaon. The scheme is basically to perform the integral<b >a fa W  d ' 'N t£(PK ’ V ’ (4)Detailswherein a Lorentz transformation to the two-body C.M. is invoked,of that procedure will be presented elsewhere.-*■-*-The above steps represent a reasonable, albeit oversimplified treatment, which obviously needs to be improved, and can be. Indeed, by use of the developments in pion scattering using momentum space methods, a much improved calculation can be done.^ Nevertheless, as a first examination, the present averaging method suffices to teach us how the nucleon motion, even at skewed angles, can influence the basic optical potential.In Fig. 6 , the variation of b^, b^ and (Eqn. 2) are presented, along_with the values found after averaging over nucleon momentum (Eqn. 4) (The b is a simple sum of the b's.) The arrows indicate where the resonances of Fig. 3 show up in b. In these curves the Alston-Gamjost et. al.^ amplitudes were used. Note that the scales for b^, b^ and \>2 differ. It is b^ that dominates (due to the subthreshold A and £resonances), even over the isolated D _ (1520). After averaging, thecurves become quite a bit smoother, ana much of the underlying resonance behavior is lost. Of coarse, this result is self-evident from comparing the range of nucleon momentum P^, in Fig. 5, to the narrow widths (Fig. 3) which correspond to a small or comparable range of P ,_. One needs to simply overlay Fig. 5, with the b^'s of Fig. 6 to seenow the averaging modulates the P dependence of the b's. A narrow inelastic resonance is easily lost when averaged over the natural motion ofBO I BO R87nucleons in nuclei. Despite that fact, some residual information remains after averaging and the question becomes how to detect the remaining resonance effects.Fig. 6 . The dependence of the optical potential parametersb (F ) on kaon lab momentum. The solid curve is for(IA), the dashed includes the Fermi averaging as inEqn. 4. The notation b^R , b ^  refers to i = 0,1,2 and real and imaginary.CROSS-SECTIONS AND ABSORPTIONThe effect of nucleon motion will certainly be to reduce the energy dependence of the cross section, as is indicated by comparing the potential parameters b^(IA) to b^(FA) of Fig. 6 . How much energy dependence occurs in cross-sections even before that reduction due to nucleon motion is introduced? To answer that question the total cross-section for K - C ^  is presented in Fig. 7 along with the 1967 dataof D.V. Bugg et. al.^3 xhe peak in a near = -95 GeV/c is inreasonable agreement with that data (nucleon motion will probably broaden and possibly lower the calculated result). At lower momenta, the large Im bQ associated with the subthreshold resonances (Fig. 6) causes a to88increase as shown in Fig. 7 A by a dashed curve. (That low region is probably beyond experimental verification, except by kaonic atom studies, because of the kaon decay.)La bora to ry  Momentum (G eV /c )Fig. 7. The total and_elastic differential cross sectionsfor the case b(LA) and no Fermi averaging. Data is from Bugg et al.The overall variation of the elastic differential cross-section for K -C-*- , again in the b(IA) case, is given in Fig. 7B, for laboratory energies ranging from 118 to 718 MeV (some of the corresponding values are given in parentheses). The variation of a(9) with (P ) given in Fig. 7B is unremarkable; one has a mild variation with simple diffractive behavior indicative of a smooth variation of absorp­tion with energy. No dramatic resonance effects associated with sudden increases in absorption are manifest in a (9). The corresponding absorption coefficient n = |S | = exp(2i6 ) versus L is displayed in Fig. 8 , for the b(IA) case of Fig. 7.Fig. 8 . The absorption coefficient |S^| versus L for K -C at laboratory kinetic energies T of 118 to 718 MeV. Dashed curves show the associated Im(S ).-Lj89The absorption for lower L's is seen to decrease with the increasing kinetic energy T R , then increases somewhat in the T 418 MeV (.767 Gev/c) to 618 MeV (.996 GeV/c) region, xne change in absorption is mild and consistent with the variation of a (9) with energy seen in Fig. 7. The origin of this variation of absorption with energy is clearly seen in Fig. 6 ; at lower ?TAR the Im b dominates due to the subthreshold resonance over the contribution due Ho the 0^(1520) resonance. The Im b 0 then decreases, but as the series of D resonances appear at P _ v 0.77 to 1.0 GeV/c the net absorption experiences an increase. However, as seen from the scales in Fig. 6 , that increase is mild.In contrast, the a(9) and | S^J for pions display quite dramatic changes in absorption as one proceeds through the broad and elastic 3-3 resonance. At resonanc^ pions for L = 0 have j S | - 0.1; whereas, for K_ |Sq| - .25 and for K |Sq | - .65 are typical values. Hence the K is absorbed by nuclei more than a K+ , but not as much as a pion.To detect the effects of the underlying K -N resonance and the associated absorption, one clearly needs to scrutinize closely the energy dependence of a (9) and S . For example, the S 's in the region of the isolated Dn _(1520) resonance for K“-C are given in Fig. 9.Here for energies below (118 MeV), near (138 MeV) and above (158 MeV) that resonance, one detects for L < 8 some alterations in S which arise in part from the resonance. Also shown in Fig. 9 is the efrect ofusing the momentum dependent form (Eqn. 3) with Fermi averaging (Eqn. 4) (solid), and without Fermi averaging (dotted). The b (IA) case is the long-dashed, and when nucleon motion is included the result is b(FA) shown by the short-dashed curve. The forL < 4 are quite affected by thesechanges in V. A resonance effect is seen here with the changing appreciably, although the effect of nucleon motion is to modulate that variation (i.e. as one views the dotted (no nucleon motion) and then the solid (with nucleon motion). Nucleon motion also plays a role when the b approximation is used with the effect being largest at and below the Dgg* Also the introduction of the momentum dependence takes us from the smoother b results (dashed)to the varying behavior (solid and dotted) induced by the gradientoperators in Eqn. 3. It is this level of detail that will be required to learn about the resonance in nuclei; clearly both nucleon motion and momentum dependence must be included carefully.Closer scrutiny of the differential cross-section is also requiredto see the effect of the basic K--N resonances. Therefore, the a (9) ratio to Rutherford is presented in Fig. 10A for the b(IA) case. There is some change as one passes through the DQ_(1520) region, in particular the minima move in and deepen. That kind of behavior needs to be evaluated and measured carefully before Y*-nucleus dynamics can be extracted.Fig. 9. j S j  versus L near the L A(1520).907 - 1 2  L. Kisslinger in a recent preprint also examined a (6) for K -Celastic scattering. The cross-sections he obtained in the Dn~(1520)region are shown in Fig. 10B taken from his paper in which tne isobardoorway model is applied to kaons. The curves on the right areobtained by adjusting the width and shift of the resonance to fit thedata of Melkanoff et. a l . ^  The broadening of the D (1520) by 30% inthe nucleus, and the binding shift of AE v 10 MeV(resonance being less bound than a nucleon), illustrate the kind of Y* dynamics that can be extracted from the energy dependence of the cross- sections. Other resonances and the K -atom case were also studied by Kisslinger.9 ( AE* 10)-  12 —Fig. 10. Cross-sections for K -C in the b(IA) case (a) and(B) the isobar doorway model results of Kisslinger.^CONCLUSIONThe extraction of Y dynamics from K -nucleus cross-sections will require a close examination of the energy dependence of the differential cross-section and its associated absorption. Since the K -N resonances are inelastic, narrow, and often overlap, that difficult task will require precision calculations of nucleon motion and momentum-dependence effects inter alia,before one can reliably extract the Y -nucleus dynamics from data. Once we can include such effects, which is more difficult for K than for pions, one might be able to closely scrutinize the energy dependence of a (Q) and of processes which depend on the K~-nucleusabsorption, and learn about Y -hypemuclei.ACKNOWLEDGMENTSThis talk is based on work done together with A. Rosenthal, whose help is greatly appreciated. I also wish to thank R.A. Eisenstein,L. Kisslinger and S.R. Cotanch for information and insights they kindly provided.91REFERENCES1. R.L. Kelly, Invited Talk presented at Meeting on Exotic Resonances Hiroshima University (1978) and R.A. Arndt et al., Phys. Rev. D18, 3278 (1978).2. R.A. Eisenstein, "Experimental Elastic and Inelastic Kaon Scattering" (proceedings of this workshop).3. S.R. Cotanch, "Experimental Elastic and Inelastic Kaon Scattering" (proceedings of this workshop).4. M. Alston-Gamjost et al., Phys. Rev. D18, 182 (1978).5. G.P. Gopal et al., N.P. B119, 362 (1977).6 . C. Dover, "Introduction - Kaon - Nucleus Interactions" (proceedings of this workshop).7. L.S. Kisslinger, "K -Nucleus Scattering in the Isobar-Doorway Model" (CMU preprint, Aug, 1979).8 . C.B. Dover and G.E. Walker, Phys. Rev. C19, 1393 (1979).9. S.R. Cotanch and F. Tabakin, Phys. Rev. C15, 1379 (1977).10. R.A. Eisenstein and G.A. Miller, Comp. Phys. Commun. j?, 130 (1974).11. A. Rosenthal (private communication and to be published).12. Chi-Shiang Wu, Phys. Lett. 82B, 337 (1979).13. D.V. Bugg et al., Phys. Rev. 168, 1466 (1967).14. M. Melkanoff et al., Phys. Rev. Lett. 4_, 183 (1960).DISCUSSIONEPSTEIN: The narrow A (1520) width doesn't always get washed out bynuclear Fermi motion. In (K- ,tt-), for example, the narrow width has a dramatic effect even with Fermi motion in the calculation.AHMAD: Impulse approximation and Fermi averaging are almost a contradic­tion in terms. If Fermi averaging is so important, the natural place to look for it is second order KMT.TABAKIN: We have done a rather simplified treatment of Fermi averagingfor the stated purpose of exploring the potential significance of nucleon motion. We take the t-matrix's dependence on the nucleon momentum vector and average over it, using the P(k^ j) weighting. To do correct Fermi ave­raging, we should use the full off shell, nonstatic theories developed by various people for pions. My only point is simply that for kaons the in­clusion of Fermi motion is crucial, even more so than for pions.ENDO: You don't have a Y*(1520) peak in a^?TABAKIN: That is correct. Note that the parameter b2 is given on adifferent scale in the figure, and it is only a part of the dominant b0 parameter. Thus the b2 part doesn't stand out as you might expect.92NEUTRON DENSITY STUDIES THROUGH K+-NUCLEUS SCATTERING*Stephen R. Cotanch North Carolina State University, Raleigh, N.C., U.S.A.ABSTRACTThe neutron nuclear structure (ground state) probing capability of the K+ meson is examined theoretically through elastic scattering calcu­lations for ^®Ca and Ca. The study focuses on cross section sensi­tivity to existing uncertainties in the kaon-nucleon (KN) interaction and target neutron distribution. The sensitivity to these two uncertain­ties is assessed by performing calculations using Martin vs. BGRT KN phase shifts and Hartree-Fock vs. empirical neutron densities. Results predict sizeable (1 00%) changes in the absolute elastic cross section that is predominantly attributable to the uncertainties in the KN inter­action. However, for the relative cross section difference between iso­topes variations in the neutron density and the KN interaction produce roughly equal effects.INTRODUCTIONAs evidenced by this and previous workshops the intensity of inter­est in kaon physics continues to develop. Hopefully this will foster a similar increase in intensity of kaon beams as well as an opportunity to add an exciting new dimension to physics. In this talk, I will not address the interesting novel features such as strangeness transfer and hypernuclei (K- mesons). Rather, I will discuss the nuclear structure probing capability of the weakly interacting K+ meson. Specifically, this work addresses the feasibility of obtaining new and complementary information about the neutron density through K"*”-nucleus elastic scattering. The results of this theoretical study suggest that with perhaps only a slight enhancement in our knowledge of the KN interaction, additional and improved neutron density information can be extracted.In particular, uncertainties in isotope rms radii differences could be further reduced, which in turn would have an important impact on funda­mental topics such as nuclear matter, neutron core compressibility^ and the status of the neutron skin.MODEL AND CALCULATION DETAILSThe essential aspects of the factorized multiple scattering impulse approximation calculation are outlined in ref. 2. In the present study the prescription for the optical potential, U -> Atp, was generalized to allow for separate proton and neutron densities and interactions.Hence, for a target nucleus having A = Z + NU = Zt„ p + Nt., p , (1)Kp p Kn n*Work supported in part by U.S.D.O.E.93where , t are the elementary kaon scattering transition amplitudes for the proton and neutron and p  , p  are the proton, neutron ground state densities. For numericalPconvenience, as detailed in ref. 2, eq. (1) was manipulated into Kisslinger potential form with separate proton and neutron bQ and coefficients. Two distinct sets of coefficients, corresponding to Martin^ and BGRT^ empirical KN amplitudes, have been generated to test cross section sensitivity.To investigate scattering sensitivity to the neutron density the following procedure was adopted. The target density was specified by using electron scattering^ results to determine p  and then using high energy proton elastic scattering analysis^ to fix^p (using the same p  ) .  Kaon scattering sensitivity to the neutron density was then deduced by*5 repeating the elastic calculations but now using a theoretical neutron density generated from realistic Hartree-Fock calculations?.RESULTS40Table I lists the proton and neutron b coefficients for Ca, using Martin and BGRT amplitudes, at kinetic lab energies of 84, 250, and 446 MeV.Table I. b coefficients in(fm) 8 for 4^Ca,ELAB Proton Neutron(MeV) Martin BGRT Martin BGRT84 -1.29+i.41 -1.23+1.37 -.74+1.21 .43+1.20250 - .35+1.21 - .33+1.17 -.22+i . 1 1 ,02+i.15446 - .15+1.13 - .14+1.10 -.11+i.07 , 00+i.13The interesting point is that the different amplitudes give similar pro­ton parameters but quite different neutron coefficients. These sizeable differences in the neutron part of the optical potential reflect the large uncertainty in the I (isospin) = 0 component of the KN interaction. Clearly, further and more accurate K-deuteron elastic analysis is necessary to reduce this significant variation.In Table II the appropriate neutron rms radii are listed along with the important isotopic difference, A = n r (48) - r (40). n nTable II. Neutron rms radii in fm.40Ca 48Ca AnEmpirical 3.45 3.63 .18Hartree-Fock 3.37 3.68 .31Of special interest is to determine the accuracy of kaon elastic94scattering necessary to meaningfully extract A . Figures 1 and 2 repre­sent the differential cross section (ratio to Rutherford) calculations for ^ C a  and ^8Ca respectively. Notice that the uncertainty in the KN<j (6 )/ctr9c. rn.Fig. 1. Absolute effects from varying the KN inter­action and the ^ C a  neutron density.ginteraction dominates (about a 50 to 100% effect!). As predicted , ini­tial analyses of absolute cross sections will mainly provide informationabout the KN force and little about p . However, if we measure and cal-nculate the relative isotopic cross section difference defined byD(0) = a4Q(0) - a4g(0), (2)°4O(0) + °48(6)then it may still be possible to learn more about p . Figure 3 shows the behavior of D(9) for the three labeled curves in Figs. 1 and 2. Interestingly, the effects from varying p , such that A changes by .13 fm, are now of the same order as effects introduced by changing the in­teraction. As discussed in ref. 5, the experimental error in D(0) is ingeneral much smaller than the error in o(0) and furthermore D(0) is much more sensitive to structure details of the target. Calcula­tions of D(0) at other energies (not shown) reveals similar results and will be discussedQfurther elsewhere.yFig. 3. Relative effects from varying the KN interaction and the target neutron density using the cross sections plotted in Figs. 1 and 2.Fig. 2. Same as Fig. 1 for 48Ca.95CONCLUSIONAlthough the current large uncertainty in the KN interaction pre­cludes extracting structure information from an absolute cross section analysis, the outlook for measuring isotopic difference effects is prom­ising. If absolute scattering cross sections could be measured to within say 20%, a rough optical model analysis could significantly reduce the current uncertainty in the KN interaction. The quantity D(0) would then be experimentally determined to well within 10% and calculations of D(0) would be predominantly sensitive to rms variations in the neutron density. Obviously if more precise absolute measurements could be performed, ex­tremely accurate determinations of An would be possible.REFERENCES1. S. Shlomo, R. Schaeffer, Phys. Lett. 83B, 5 (1979).2. S. R. Cotanch, Nucl. Phys. A308, 253 (1978).3. B. R. Martin, Nucl. Phys. B94, 413 (1975).4. G. Giacomelli et^  a_l. , Nucl. Phys. B71, 138 (1974).5. R. F. Frosch et al., Phys. Rev. 174, 1380 (1968).6. A. Chaumeaux, V. Layly, and R. Schaeffer, Ann. Phys. (N.Y.) 116, 247 (1978).7. J. W. Negele, Phys. Rev. Cl, 1260 (1970).8 . C. B. Dover, P. J. Moffa, Phys. Rev. C16, 1087 (1977).9. S. R. Cotanch, to be published.96DISCUSSIONSILBAR: Can the 1=0 KN amplitudes really be determined from K+d scatter­ing to be useful for K+-nucleus scattering analyses?COTANCH: The K+d information would indeed be quite useful. In addition,K+-nucleus experiments themselves would help reduce the current uncertain­ty in the 1=0 K~*~N amplitudes. Polarization measurements, however, would probably be the best way of improving our knowledge of the 1=0 amplitudes, and I understand such experiments are in progress.BUGG: 1) Experiments are in progress measuring polarization in K+n + K +nand K+n+K^p. One can expect these will significantly improve 1=0 KN phase shifts.2) Applying analyticity to the KN amplitudes would make them signi­ficantly more reliable.3) If a kaon factory is built, the KN experiments can be repeated at least a factor 10 better.SAKITT: I would like to point out that the differences observed betweenthe BGRT and Martin curves stem from the uncertainty in the KN 1=0 phase shifts. The data are considerably worse than what one is used to from TT-nucleon or nucleon-nucleon data. With the exception of the three experi­ments in progress (ours, D. Bugg's and the one at KEK) almost no polariza­tion data exist. Improved polarization data should help reduce the uncertainties in the 1=0 KN phase shifts.DOVER: One must re-emphasize the need for good 1=0 K+N phase shifts atlow energy before any significant constraints on neutron densities can be obtained.97KAON-NUCLEUS INTERACTIONS IN THE A(1520) REGION*G. N. Epstein and E. J. Moniz Center for Theoretical Physics, M.I.T., Cambridge, MA 02139ABSTRACTKaon-nucleus interactions in the energy region dominated by A(1520,in the nuclear medium. In this paper we present some simple calculations aimed at extracting some of the features of the physics in this regime.The A(1520) is the first KN resonance above threshold and has the following properties:occurs in the K p channel. _The production cross section is reasonable. It is the narrowest of all KN, TTN resonances. Its narrow width is cer­tainly due in part to the fact that it is a D-wave and the KN system atthe centrifugal barrier inhibits the decay.To produce A* off a stationary proton requires a K beam momentum of about 400 MeV/c which is substantially lower than present typical beam momenta (> 700 MeV/c). To get down to 400 MeV/c is a non-trivial experi­mental problem. (For later reference we observe that recoilless I produc­tion in K p Ett occurs for 290 MeV/c kaon beam momentum.)If we consider free space propagation of a resonance we can write the propagator G(s) as3/2 ) formation are very interesting for the study of isobar propagationINTRODUCTIONQuantum numbers:Width:Production cross section:1 = 0 ;  JP = 3/2 ; £ = 2 (D-wave)r = (16 ± 2) MeV O = 84 mbDecays: A(1520)KN 46% Ett 42% Atttt 1 0%The following remarks are appropriate. A* production (A* = A(1520))1520 MeV does not have much kinetic energy so thatPROPAGATION(1 )where s = invariant energy variable; s = E 2; F, = resonance mass; F =R R R Rresonance width. But s = E2-p2, so we can Fourier transform G(s) to ob­tainG(r) e ar/r ( 2)where*Work supported in part through funds provided by the US DOE under con­tract EY-76-C-02-3069.98a = /ERrR/2 (1 -i)i.e., the characteristic propagation distance (d ) isRdR ‘ / T N 7 ~R ' (3)For A(1232): d& n, 0.7 fm (rA ^ 120 MeV)For A(1520): d % 3.2 fmIt is clear that if one wants to study resonance propagation the A* is the best candidate.Inside a nucleus d will be modified from its free space value due to the presence of other nucleons. In particular the processes inFig. 1 will occur.Fig. 1. Additional A* damping processes in a nucleus.We use an effective Lagrangian approach to estimate these. The A*Ett and A*NK coupling constants are fixed by the A* partial widths and the KNA, KN£ couplings are taken from the analysis of Nagels et al . 1 _Mono- pole vertex form factors are employed with mass 1 GeV/c2 for the K and 700 MeV/c2 for the tt. If we take the A* to have a momentum appropriate to its production off a stationary nucleon in a kaon beam of 400 MeV/c we find thata(A*N -* £N) ^ 7 mba(A*N ^  AN) ^ 4 mb (4)Such processes would then reduce the value of from the free spacevalue of 3.2 fm to about 2 fm in a typical nucleus. The dampingwould be less if we took into account Pauli blocking.In short, the simple processes considered here should not drastically reduce the A* propagation. However, to study A* propagation in a more realistic fashion it is necessary to make a coupled channel isobar model. Such work is in progress. However, it is interesting to see what happensif the A* remains narrow in the nucleus. To this end we have calculatedthe quasi-free (K , tt- ) spectrum.THE QUASI FREE (K,Tf) SPECTRUMWe use a Fermi gas model for the nucleus (which has Z protons) and consider only single scatters so that the only input information we need99Fig. 2. The quasifree (K,tt) spectrum.100is the K p -* Ett differential cross section. The quantity calculated isd 2cr/dft dE for forward pions. The standard variables are oj = E -E andTT TT K TTq = p^-p^. For quasi-free kinematicsM -M„ „ 2 k q“ * V Mp + 2& M - i  + 1 st + H r  (5)p i E Ewhere k is the struck nucleon initial momentum and the K beam is directed along the z-axis.We calculate the pion spectrum for two cases: (i) F = 160 MeV cor­responding to a broad resonance or very slow energy dependence in the KN Ett cross section; (ii) T = 16 MeV corresponding to the narrow A* resonance. The results for 4 different beam momenta are shown in Figs. 2(a) and (b). The spike spectrum at p = 300 MeV/c in both cases is due to recoilless E production. It is  ^clear that the spectrum for the narrow width A* is dramatically different from the standard parabolic shape. Note that its peak moves faster to higher U) as p increases.This is because for p above resonance the only nucleons "seen" by theKbeam are those "running away," i.e., with positive k and hence larger oo. Such behaviour is entirely due to the selectivity Z of the reaction which stems from the narrowness of the A*.This simple example serves to highlight the possibility that the narrow A* may give rise to interesting new behaviour in physical process­es. Of course more detailed studies are in progress.REFERENCES1. M. M. Nagels, T. A. Rijken, and J. J. de Swart, Phys. Rev. D 15,2547 (1977).101MEASUREMENT OF K — NUCLEUS ELASTIC SCATTERING AT FORWARD ANGLES   AN EXPERIMENT TO BE DONE AT KEK ----I. Endo and Y. Sumi Department of Physics, Hiroshima University, Hiroshima 730, JapanABSTRACTA measurement of elastic K -nucleus scattering is going to be made by the Hiroshima University group at the low-energy separated beam site, K3, of KEK, Tsukuba, Japan.By detecting forward scattered kaons at lab angles less than 200 mr and lab momenta below 1 GeV/c, we will systematically study the energy dependence of forward differential cross sections da/dt, together with the ratio a=Ref(0)/Imf(0) determined from the Coulomb interference for the forward elastic amplitude f(0) and K~-nuclear total cross sectionsINTRODUCTIONThe 12 GeV proton synchrotron of KEK, Tsukuba, Japan came to opera­tion in 1977 and the low energy separated beam channel, K3, has been de­livering p and kaons since January, 1979. This beam channel was designed to yield high intensity kaons whose energy resolution is good enough to be used in a nuclear physics experiment. JAs it has often been pointed out, kaon-nucleus scattering data are quite scarce and any type of new experiments will offer useful infor­mation. We have proposed, as a first step in kaon-nuclear researches, an experiment on elastic scattering of K+ and K~ on several selected nuclei at extremely forward angles. The project has been conditionally approved by the PAC of KEK. Here we describe the motivation and the details of the experimental method.MOTIVATIONSSetting aside the general arguments how kaons are different from pions and nucleons and what an important role they will play as a new type of probe for studying nuclei and so on, here we restrict ourselves to the characteristic features of the forward scattering.The greatest advantage from the experimental point of view is that the cross section for the coherent elastic scattering at forward angles is bigger than that for any other particular reaction channel, so that a systematic survey over wide energy range and on varieties of nuclear species is possible within a reasonable run time.Moreover, by suitably arranging the detector system, we can at the same time determine the total cross section and the ratio, a, of the real to imaginary part of the forward scattering amplitude f(0). The latter quantity will be deduced by observing the differential cross section da/dt around 30 - 100 mr where the Coulomb-nuclear interference shows up. In other words, this experiment will offer the complete knowledge on f(0) through the following relations:102a = 4/tT Imf(O) ,Ref(0) Imf(O) 'Fig .1In Fig. 1, the available experimental data of for K+ and K" carbon scattering2-* are compared with the Glauber model calculation by Fukuma and Endo3). The agreement of the predicted values, with theexperimental data is excellent even at low energies. A remarkable feature of the model is that the imaginary part of the K+C amplitude be­comes dominated by a double scattering term below 400 MeV/c, because the elementary amplitudes for K+p and K+n are almost real at low energies. This makes a ™  behave differently from the impulse approximated cross section c+ (l) as indicated with a dotted line in Fig. 1.On the other hand, the energy dependence of the evaluated K~C ampli­tude is very similar to that of the impulse approximated one, though the magnitude is appreciably reduced. It will be interesting to experi­mentally observe how the dips and bumps due to Y* resonances appear in the K”-nucleus data, because it may eventually lead to some knowledge of the nuclear interaction of Y*.The experimental data on forward scattering amplitude are also useful for obtaining the effective coupling constant of kaons to the nuc­leus and may give a glimpse into the unphysical region of the K-nuclear system through the forward dispersion relation as tried by Arai et al.4)103EXPERIMENTAL METHODFollowing requirements are to be fulfilled:1) The angular acceptance of the spectrometer should cover O<0<2OO mr2) Angular resolution; 60<1O mr.3) Energy resolution; AE<2 MeV,4) Capability of kaon identification in the incident beam of tt/ K =  10 -5) The total length of the detector system should be as short as possible to minimize the kaon decay.6) Data-taking system should work under the high particle rate of 106/s.7) In addition to the ordinary fast logics dealing with the counter signals, another intelligent device is needed which processes the MWPC information to judge if the event falls in the angular region of interest before the raw data are sent to the on-line computer.A schematic view of the experimental set up is shown in Fig. 2.The charged kaons from the K3 beam channel hit the nuclear target T. The expected tt/K ratio is enriched to 7-10 by a DC separator, and the identification of kaons is easily done by a cherenkov counter C aided by a TOF information. The angles before and after the target are measured with multiwire proportional chambers (MWPC), Cl through C4. The forward scattered kaons are momentum analyzed by a rotatable magnetic spectrome­ter consisting of two quadrapole magnets, Qi and Q2, and an analyzer- magnet of bending angle 68.75°. In order to reduce the path length, we intend to determine the momentum from the information from C5-C7 instead of using an ordinary focal plane hodoscope. It should be remembered, how­ever, that the elastic channel dominates at forward angles so that the momentum measurement is not rigorously needed but is considered to be auxiliary information to confirm the elastic events. Therefore, the essential part of the set up is only 50cm long from the target.We have constructed and successfully tested MWPC's of 1mm spacing to be used as Cl to C4.Large proportional chambers, C5-C7, will have a new type of read-out104in which the signals induced on the cathode strips are led to the ADC's. The particle position is evaluated by fitting an appropriate curve to the charge distribution obtained on the strips.A prototype chamber which has anode wires of 2mm spacings and the cathode strips of 9mm wide has been tested with a pion beam. The test proved that it has a spatial resolution of better than ±lmm with Ar- Freon-C02 mixture. This type of MWPC will cost only about 60% of the ordinary read out thanks to newly available low cost ADC's, while main­taining a reasonably good resolving time and multitrack separation.In order to distinguish the unscattered particle from the ones with the scattering angle 0>2Omr, we are going to use a microprocessor system, CASPH, Cascadable Special Purpose Processor developed in Hiroshima. It consists of bipolar bit slice microprocessor am2903's, supported by 60 bit wide microprogram words. The data words from the MWPC's are encoded and stored in the Buffer Memory Module, BMM, as binary numbers represent­ing the hit wire coordinates. In our system, BMM is regarded as an in­ternal register of the processor so that the subtraction of two wire coordinates can be executed in a single clock cycle, 200ns. The total time needed for the data encoding and the angle evaluation is expected to be less than 50 ys, which is fast enough for the present purpose.We have not decided the incident energy range and the target nuclearspecies, yet. In principle, the kaon momentum can be set at any value below 1 GeV/c. However, the beam intensity will rapidly decrease towardthe low momentum and the K-tt separation will become difficult at thehighest momentum. Therefore, the choice will be made after a further survey on the K3 beam quality. In the first series of the experiment, the nuclear target will be limited to several light elements including 1 2C.REFERENCES1) Hirabayashi et al., KEK-PREPRINT-79-52) D.V. Bugg et al., Phys. Rev. 168(1968), 1466.B. Gobbi et al., Phys. Rev. Letters 2£(1972) , 1278.3) H. Fukuma and I. Endo, Prog. Theor. Phys. 60^(1978), 1588.4) K. Arai et al. , Prog. Theor. Phys. 56^(1976), 1345.105A PRODUCTION IN pd INTERACTIONS BELOW 1 GeV/c*D.W. Smith, B. Billiris, M. Mandelkern, L.R. Price, J. Schultz University of California, Irvine, California 92717ABSTRACT382 A events have been measured and analyzed in a pd bubble chamber experiment at 552, 740, and 905 MeV/c. We compare our data with two other pd experiments1 ’ 2 at beam momenta from 1 to 3 GeV/c. Some_features of the double scattering mechanism are calculated using a K and A as the exchanged particles. The K exchange appears to be a more likely candi­date for the production mechanism.INTRODUCTIONOur study of the reactionpd ■+ A + anything (1)below the pp -> AA threshold has been motivated by the apparently large cross section for reaction (1 ) and also by the possibility of observing baryonium states. Previous studies1 ’ 2 of reaction (1) from 1 to 3 GeV/c have reported the A cross section to be v400 yb. This is well above the measured pp -> AA cross section3 of 58 ± 17 yb at 1.6 GeV/c and has stimu­lated investigations of mechanisms involving both nucleons of the deuteron in pd annihilations leading to a A 1’2. Camerini et al. and Oh and Smith have suggested that a double scattering mechanism may describe the A production observed in pd experiments. The nature of the exchanged particle involved in the rescattering process has not been resolved because of the conflicting data reported by these two experi­ments. If the exchanged particle is an antibaryon, as suggested by Camerini et al., then the search for BB bound states becomes an exciting possibility^.The results reported here are based on a study of 80,000 pictures of antiprotons incident on the BNL 30-inch deuterium bubble chamber.The cross section for reaction (1), not corrected for the neutral decay mode of the A , is shown in Figure 1 along with the data of Oh and Smith2.DOUBLE SCATTERINGSince both nucleons are necessarily involved in the observed A production, we assume that the production mechanism is a result of double scattering. Figure 2 shows an example of double scattering where the incoming antiproton interacts with the first nucleon (e.g. a proton) and creates a particle-antiparticle pair. The antiparticle interacts with the second nucleon of the deuteron to complete the process.Figure 2a shows a AA pair created at the first vertex and the A interacting at the second vertex. The A exchange diagram was suggested by Camerini et al. as the most likely mechanism for A production becauseWork supported by the U.S. Department of Energy106PL a b (G eV /c)Fig. 1. Visible A cross section in pd -> A + MM from .55 to 2.0 GeV/c.Fig._2. Triangle diagrams for the A and K exchange mechanisms.of the striking peripheral production of A's observed in their data and also because of the peak observed in the missing mass distribution (pd -> A + MM) near the AN threshold.We have calculated an estimation of the total A cross section and the missing mass distribution for pd -> A + MM due to the triangle diagram with A exchange. The basic assumptions made in this calculation are as follows:The deuteron is treated as 2 nucleons which are approximately on the mass shell and the momentum distribution is given by the Hulthen wave function.The exchanged A is treated as a particle with variable mass y and off-shell amplitudes are approximated by measured on-shell results.Non-relativistic approximations are made wherever possible.Spins are ignored.For numerical results, we use a(pp annihilations) as an estimate of the unmeasured a(AN annihilations).For the missing mass distribution described by the triangle diagram in Figure 2a., we find that1 .2 .3.4.5.(2)where W , P are the total c.m. energy and final c.m. momentum in thelA2-body reaction at vertex A,P_ , , = beam momentump, labm mnucleonmg = the missing mass recoiling off the A and f(x) =x‘(1-x2)2107Figure 3 shows da/dm^ for the A exchange normalized to our data. In the same figure, the phase space is plotted for 4, 5, and 6-body final states added together and weighted according to their respectivebranching ratios. The phase space seems to fit the data so well that onecould not choose the functional dependence of the A exchange mechanism over the phase space distribution^A serious deficiency of the A exchange calculation is in the expected A cross section shown in Figure 1. One can see that the cross section due to A exchange is very much smaller than the observed cross section for visible A decays.Although one might expect several other similar diagrams to contribute to the A production, the combined effect would probably still fall far short of the observed cross section. Furthermore the cross section is expected to increase with energy at low energy, in contrast to the data which appears to remain essentially constant.Figure 2b shows a KK pair created at the first vertex. This figure can be viewed as a two-step process in which a "real" K is produced at vertex A and interacts at vertex B to produce a A. We have estimatedthe expected rate for this process and we have found thattlM ( G e V / c 2 )Fig. 3. Our missing mass data is shown with the A exchange and phase space curves drawn in. The A exchange is normalized to the number of events.0 . 0  1 . 0  2 . 0  - u  ( G e V / c )2Fig. 4. Chew-Low plot of our data is shown with the kinematical boundary. Possible baryonium states would be found at the right-most boundary.108a(A) - 0.044 a(pp->-KK) . (3)Using the branching ratio for visible A decays (64%), we find that forP, = 772 MeV/c a . (A) = 345 ± 73 ybbeam visand for P, = 900 MeV/c a . (A) = 312 ± 66 yb.beam visThis is in good agreement with the data in Figure 1.A question of considerable current interest is the possibility of producing quasinuclear baryonium states via A exchange. Bogdanova and Markushin^ have suggested that production of strange quasinuclear AN states might be observed in pd interactions, with events concentrated on or near the boundary of a Chew-Low plot, where the missing-mass-squared recoiling off the A is plotted against the momentum transfer, u. Figure 4 shows our data on a Chew-Low plot with the kinematical boundary shown. The hatched area near the boundary is the physical region where one wouldexpect candidates for quasinuclear states produced by A exchange. Nobands are seen, nor does there appear to be an accumulation of events in this region; events are consistent with phase space.In general the u distribution is not in accord with pp -> AA, aperipheral process favoring A production backward with respect to the incident p direction. This should be reflected in the angular distribu­tion of the A's in the pd center-of-mass system. One of the arguments for the A exchange by Camerini et al. was based on the observed peripheral A production. The angular distribution of our A events in the pd center-of-mass system does not shown any significant peripheral production.CONCLUSIONIf the reaction pd A + anything below 1 GeV/c is a result ofdouble scattering, then the K exchange as shown in Figure 2b seemsto be the most likely mechanism. The observations that (i) the A angular distribution does not exhibit peripheral behavior, (ii) the peak in the missing mass recoiling off the A is explainable by phase space, and (iii) the cross section is exceptionally large, tend to rule out the A exchange mechanism. The estimated rate for A production as a result of a K exchanged between the two vertices seems to be in agreement with our data. Further results in which the transverse momentum of the A was fit to a diffractive amplitude involving K exchange also seem to support the K exchange hypothesis.REFERENCES1. U. Camerini et_ al., Nuclear Physics B33, 505 (1971).2. B.Y. Oh and G.A. Smith, Nuclear Physics B40, 151 (1972).3. G. Lynch, Review of Modern Physics 13, 395 (1961).4. L.N. Bogdanova and V.E. Markushin, ITEP-11, (1978).109INELASTIC HADRON-NUCLEUS INTERACTIONS AT HIGH ENERGIESM.A. Faessler, U. Lynen, J. Niewisch,* B. Pietrzyk, B. Povhand H. Schrodert Max-Plank-Institut fiir Kernphysik, Physikalisches Institut der Universitat Heidelberg, Heidelberg, Germany and CERN, Geneva, SwitzerlandP. GugelotDepartment of Physics, University of Virginia, Charlottesville, VA, U.S.A.T. Siemiarczuk and I.P. Zielinski Institute of Nuclear Research, Warsaw University, Warsaw, PolandThe experiment studied charged particle production for ir- , K~ and p” interactions on nuclei at 20 and 37 GeV/c at the CERN SPS. A non-magnet- ic detector, consisting of Csl (Tl) scintillation and lucite Cerenkov counters, distinguishes between fast particles, mainly pions, and slow particles, mainly nucleons, with a cut at velocity B ~  0.7. Angular dis­tributions, multiplicity distributions and correlations between slow and fast particles were analysed. The measurement of the correlations can provide a critical test for different theoretical models of the hadron- nucleus interaction. At the energies studied so far a systematic devia­tion from KNO scaling is observed. This gives support to independent collision models of the hadron-nucleus interaction and it contrasts with predictions of the coherent tube model. The regularity observed for the angular distribution of fast secondaries as a function of the number of slow particles can only be explained by combining features predicted by different models.*Present address: Siemens AG, Erlangen, Germany. tPresent address: DESY, Hamburg, Germany.110HADRON-NUCLEUS TOTAL CROSS SECTIONS IN THE QUARK-PARTON MODELB.Z. Kopeliovich and L.I. Lapidus Joint Institute for Nuclear Research, Dubna, USSRThe total hadron-nucleus cross sections are calculated by means of the eigenstate method (ESM). The eigenstates of interaction are the components of the wave function which have the definite number of wee partons. These components cross a nucleus without mixing, if the energy is large enough. It is shown that such an approach is equivalent to the Glauber model with the addition of all the inelastic corrections. The forward calculation of the inelastic corrections is a difficult problem, unresolved up to now, except the simplest first correction (the Karmanov-Kondratyuk formula), whose role is decreased with energy. The ESM gives a possibility to involve into calculation all the inelastic corrections. The analysis of data on in the quark-parton modelallowed one to estimate the relative weights of the passive (no wee partons) and active components. It is found that the active component weight for u and d quarks is Pq «  0 .5 ,  i.e. the high energy quarks spend about half the time in the passive state and cross any nucleus without interaction. The analysis of o^L^-data gives Ps /Pq ~  0 .5  for s-quarks.IllPHYSICS FOR A  NEW KAON FACILITY AT THE AGS*M. MayBrookhaven National Laboratory, Upton, New York 11973ABSTRACTA new kaon facility is being planned at the Brookhaven National Laboratory Alternate Gradient Synchrotron. This paper discusses experi­ments in hypernuclear physics that might be performed at such a facility. Recent results from the Brookhaven hypernuclear spectrometer and else­where are presented as an indication of future directions in hypernuclear physics research. Expectations for the performance of the new facility are outlined.INTRODUCTIONA brief summary of the major experimental results in hypernuclear physics will demonstrate the gaps that need to be filled by further research. Until quite recently all data about hypernuclei came from emulsion experiments. Table I from the review of Pniewski and Zieminska1 shows the hypernuclear species that have been observed by the emulsion technique. Emulsion experiments, except in special cases, give informa­tion only about hypernuclear ground states. A phenomenological analysis of the ground state binding energies by Gal et_ jil. 2 has defined some of the parameters of the lambda-nucleus potential. Two double hypernuc­lei3 ’ 4 have been observed, He and j^Be. Their binding energies are the only existing data on the A-A interaction. The first excited states of JyH and J^ He have been measured5 by detecting their hypernuclear gamma rays. This data gives information on the spin dependence and charge symmetry of the lambda-nucleus potential. The (K- ,tt~) energy difference technique makes possible the observation of a spectrum of hypernuclear excitations and has been applied by the Heidelberg-Saclay-Strasbourg collaboration6 to ®Li, ^Li, 3Be., ^C, 160, 3^S, and ^Ca, formed at smallmomentum transfer with 2 MeV resolution. The HSS data has yielded a number of interesting results, foremost among them the apparently very small value of the A-nucleus spin-orbit interaction reported at this conference. At Brookhaven, the collaboration7 at the hypernuclear spec­trometer has made an intensive study of 12C using the energy difference technique. An angular distribution was measured with momentum transfer to the hypernucleus up to 260 MeV/c to permit the excitation of additional hypernuclear states.Thus, 1) The list of known hypernuclear species needs to be expanded.2) Observed species are in almost all cases ground states or excited at small (<100 MeV/c) momentum transfer. 3) The resolution of the present (K— ,tt"~) energy difference experiments is 2-3 MeV FWHM. It will be shown below that this is insufficient to resolve many interesting states.4) Detection of hypernuclear gamma rays can, in principle, resolve closely spaced levels. However, distinguishing hypernuclear gamma rays from the background of nuclear gamma rays and deducing a level scheme is a*Research has been performed under contract EY-76-C-02-0016 with the U.S. Department of Energy.112Table I. A-binding energies of the uniquely identified hypernuclei.Ba (MeV)Number of eventsBa (MeV)Number of eventsjHe 0.13±0.05 204 6.8410.05 682.0410.04 155 ABe 6.7110.04 222^HeA 2.3910.03 279 IjjBe 9.11+0.22 3AHe 3.1210.02 1784 ab 7.8810.15 46HeA 4.1810.10 31 1 0b 8.8910.12 107HeA B not averaged 8+(8) ‘iB 10.2410.05 73»He 7.1610.70 6 lXB 11.3710.06 87ALi 5.5810.03 226 12cAL 10.7610.19 4al1 6.8010.03 787 1 3r 11.6910.12 6al1 8.5310.15 8 14CA 12.1710.33 3ABe 5.1610.08 35 15nA 13.59+0.15 14formidable task. Ideally, the gamma rays should be observed in coinci­dence with a (K_ ,tt_) energy difference spectrum of hypernuclear states.The overall efficiency of a gamma-ray detection spectrometer can be roughly 5-10% so that gamma-ray coincidence experiments will require 10 to 100 times the currently available hypernuclear event rate.FORMATION OF HYPERNUCLEI The reaction used to form hypernuclei isK_n -> it-Awhere the neutron is bound in a nucleus and the A is formed in a hyper­nuclear orbit. In the (K“,tt-) energy difference technique, an accurate measurement of the K~ and it- momenta determines the energy transfer to the nucleus and hence the energy spectrum of hypernuclear states. At 0° for appropriately chosen kaon momentum (~550 MeV/c) the reaction can proceed with no momentum transfer to the nucleus. This results in a high proba­bility of forming a hypernucleus and a suppression of the background of quasifree lambda production. However, working at or near the zero momentum transfer condition is not always desirable. At small momentum transfer, the reaction populates preferentially states with the same spin and parity as the target nucleus. In order to understand all the compon­ents of the A-nucleus interaction and excite the full range of hypernuc­lear states the formation of hypernuclei at large momentum transfer must also be studied. This is best achieved by observing the pion at large angles with respect to the incident kaon. Cross sections for formation of states involving angular momentum transfer or spin flip are considerably113lower than for coherent states produced at zero degrees. Their systematic study will require more intense kaon beams.The observation of Z hypernuclear states has been reported at this conference.8 The existence of narrow E hypernuclear states opens a new field of research. The new kaon facility at the AGS will be capable of measuring E as well as A hypernuclei.The reaction K_ +  A-Z -* 4^- + A ( £-2) can be used to form hypernuclei inaccessible to the (K- ,tt- ) reaction. For example, 8Be can be formed using a 9Be target. By comparing hypernuclei formed using the (K~,ir+) reaction with those formed by using the (K_ ,ir~) reaction on the same tar­get charge symmetry in hypernuclei can be tested. The rate of the (K- ,tt+ ) reaction relative to the (K- ,tt“ ) reaction is a measure of the importance of two step processes in hypernuclear formation.DESIGN OF A  NEW KAON FACILITYA discussion of a new kaon facility is best approached through an examination of existing facilities. I will describe the hypernuclear spectrometer at Brookhaven (Fig. 1).Fig. 1. The configuration of the (K ,tt ) spectrometer used in this experiment.The spectrometer utilizes the low energy separated beam I (LESB I) at the AGS. The beam, composed of 8% kaons, is brought to a dispersed focus on the target by a system of dipole and quadrupole magnets (Dl,Q1-Q4). Kaon flux on target is 2.4><101+/AGS pulse. Multiwire proportional planes P1-P3 define the kaon trajectory. The pion from hypernuclear formation is detected by a similar system mounted on a platform that can rotate up to 35° with respect to the beam direction. Particle identifica­tion is made by time of flight between the scintillation counters SI, ST and S2. A Cerenkov counter CK identifies kaons in the beam and a liquid hydrogen Cerenkov counter CH identifies pions formed in the target. The use of a focusing spectrometer to detect the pion gives good resolution (2.5 MeV FWHM, limited by target thickness effects) at the expense of acceptance (12 msr). A loss of a factor of 10 in K- flux at 800 MeV/c is suffered in the kaon momentum analyzing section of the spectrometer, primarily due to kaon decay.A new kaon beam, LESB II, has recently come into operation at the AGS. The K- flux in LESB II has not yet been measured. The value stated in the design report8 is 7*105 K- at 800 MeV/c for IO12 protons incident on the production target. The increased flux relative to LESB I is primarily a114result of larger magnet apertures. During normal operation at the hyper­nuclear spectrometer we have had typically 4xl012 protons on the primary target per AGS pulse. If the beam line of the new kaon facility were to have the same length and aperture as LESB II and, in addition, incorporate kaon momentum analysis, it would represent a hundredfold improvement over the current facility. The beam would have a flux of 2.8><106 momentum analyzed K~/4xl012 protons. A threefold increase in the solid angle of the spectrometer detecting the pion is feasible. With this vastly in­creased event rate, a systematic exploration of the hypernuclear table will be possible.Resolution is intimately connected to flux. Target thickness effects (Landau spread and the difference between K- and ir- energy loss in the target) are the dominant contribution to resolution in current experi­ments. The new facility should aim for a resolution of 250 keV FWHM.RECENT RESULTS FROM THE HYPERNUCLEAR SPECTROMETER AT BROOKHAVENAn angular distribution of the states of excited in the reaction^CCK- ,^-) has been measured7 with kaon momentum 800 MeV/c. Figure 2 shows a spectrum taken at corresponding to a momentum transferto the nucleus of 210 MeV/c. The lower mass peak corresponds to a binding energy of the lambda of 10.79 ± 0.11 MeV. Experiments using the emulsion technique report1 a binding energy of 10.76 ± 0.19 MeV for the ground state of 1 jc. This agreement leads us to identify the lower peak as the ground state.The higher mass peak has 11 MeV excitation energy. This peak could correspond to the particle-hole configuration (AP3/25 nP 3/2_1) or (Api/2 , np3/2-1); the former configuration gives rise to a 0+ and a 2+ state, the latter to a 2+ state. (Unnatural parity states are not expected to be excited with significant strength in our kinematic range.) The angular distribution of the peak at 11 MeV (Fig. 3) shows the steep rise in the forward direction characteristic of a coherently producedFig. 2. The mass spectrum of 12C as recorded at 15°. The solid curve represents a parabolic fit to the quasi-free continuum, while the dashed curve is a linear extrapolation, used to determine the continuum background under the peak. MASS (MeV)115Fig. 3. Angular distributions observed for the ground state of 12C and for the peak at 11 MeV excitation. Eye guide curves are shown connecting the points.0+ state. However, the shoulder at large angles is interpreted as the excitation of the 2+ components. Calculations10 indicate that at 15° the states observed should be predominantly 2 . Making the assumption that at 0° we are exciting 0+ only and at 15° we are exciting 2+ only, we can set limits on the spacing of these states although they are not resolved by our experiment. Assuming that at 15° only one 2+ state contributes, the 0+-2+ spac­ing is less than 420 keV. Assuming that at 15° the two 2+ components contribute equal strength, the 2+-2+ spacing is less than 800 keV. These limits will constrain the spin-dependent parts of the lambda- nucleus residual interaction. The above result is an example of structure in the spectra of hypernuclei which is beyond the resolving power of the present genera­tion of experiments.The existence of core-excited hyper­nuclear states has been predicted.11 These states would consist of a lambda in an s orbit coupled to the excited states of the 11C core. A search was made in the region above the ground state for an event excess using our 15° data. We see The total event excess in the region 2 toThis is to beno evidence for such states.7 MeV excitation is 6% ± 5% of the ground state strength, compared with an expectation of two states, one at 3.29 and one at 5.11 MeV excitation with summed strength 33% of the ground state strength. The disagreement between experiment and theory should motivate additional experiments to search for core excited states predicted in other hyper­nuclei. An experiment detecting gamma rays from the de-excitation of the core in coincidence with a (K- ,tt~) energy difference measurement would be particularly effective in observing these particle stable states. The absence of core-excited states at the expected strength may be attribut­able to uncertainties in the knowledge of the 1JC and 12C wave functions or it may signal some more fundamental problem in the theoretical under­standing of hypernuclei.REFERENCES1. J. Pniewski and D. Zieminska in "Proc. of the Seminar on Kaon-Nuclear Interaction and Hypernuclei", Zvenigorod, September 12-14, 1977, Izdatelstvo "Nauka", Moscow 1979, p. 33.2. A. Gal, J.M. Soper and R.H. Dalitz, Ann. Phys. 113, 79 (1978).3. D.J. Prowse, Phys. Rev. Lett. 17, 782 (1966).4. M. Danysz et al,, Phys. Rev. Lett. 17, 29 (1963).5. M. Bedjidian £t^  al. , Phys. Lett. 83B2, 252 (1979).6. W. Bruckner ert ^1., Phys. Lett. 79B, 157 (1978);R. Bertini et al., Phys. Lett. 83B, 305 (1979).1167. R.E. Chrien, M. May, H. Palevsky, R. Sutter, R. Cester, M. Deutsch,S. Bart, E. Hungerford, T.M. Williams, C.S. Pinsky, B.W. Mayes,R.L. Stearns, P. Barnes, S. Dytman, D. Marlow and F. Takeutchi, Brookhaven preprint.8 . R. Bertini et_ <11., these proceedings, p. 65.9. D. Lazarus, "Design for a New Kaon Beam for the AGS", Proc. Summer Study Meeting on Kaon Physics and Facilities, ed. H. Palevsky,BNL 50579, p. 119 (1976).10. C.B. Dover, R.H. Dalitz, A. Gal and G. Walker, submitted to Phys. Lett.11. R.H. Dalitz and A. Gal, Ann. Phys. 116, 167 (1978).DISCUSSIONPOLLOCK: You showed one spectrum and a five point angular distribution.Could you tell us how much running time was used to obtain these data?MAY: The zero degree point required 24 hours of data taking. The 19°degree point required one week.YAMAMOTO: Did you have some new idea to improve the intense kaon beammore than 100 x current flux?MAY: The factor of 100 improvement mentioned represents a straightforwardextension of current methods. A factor of 10 is gained through larger magnet apertures, a second factor of 10 by using the beam line for kaon momentum analysis thereby shortening the total length of the system.PIETRZYK: What will be the pion rate in your new K beam and how do youplan to work with it?MAY: In electrostatically separated beams in operation today the i t "  toK~ ratio is typically 10:1. The question of whether this ratio can be improved upon requires further study. Momentum analysis is possible with­out placing counters in the beam. The EPICS spectrometer at LAMPF is an example of such a system. Particle identification and background rejec­tion will be a more difficult problem.117A-n u c l e o n pot e n t i a l a nd bin ding e ne rgy of the h y p e rtr itonH. Narumi and K. Ogawa Department of Physics, Faculty of Science, Hiroshima University,Hiroshima, JapanY. SunamiDivision of General Education, Shimonoseki University of Fishery,Yamaguchi, JapanABSTRACTOn the line of a phenomenological approach to the A-nucleon inter­action based on the meson-theoretical potential, the bound state of the hypertriton is searched by solving the Faddeev equation in the coordinate space. Our calculated result B^ = 0.14 MeV of the A-separation energy for the ground state (J=l/2) is in good agreement with the experimental value of 0.13±0.05 MeV. The bound state of J = 3/2 cannot be confirmed by this method.Various phenomenological A-nucleon potentials are discussed from the view-point of the binding energy of hypernuclei. 1 So we attempt to introduce a more realistic potential of the A-nucleon interaction. Then we propose that the A-nucleon potential is attributed to the Yukawa type with soft core on the basis of two-pion, kaon and U) meson exchanges.Each force range of the potential is assumed to be fixed to the Compton wave length of two pions, kaon or u meson, and the corresponding poten­tial depth is chosen so as to reproduce the available A-nucleon scatter­ing length as well as effective range by evaluating the phase shift in the energy region of 0 ^ 20 MeV. These A-N scattering parameters are determined so that the low-energy hyperon-nucleon scattering is describ­ed by the meson-theoretical potential, 2 and are compared with those de­termined by a calculation of the binding energy of j\H by the variational method. 1 The potential parameters reproducing the phase shift obtained by using recently settled scattering parameters3 in Table 1 are given in Table 2.Table 1. Low energy scattering parameters3 (fm)scattering length effective rangeAp singlet a« = -2.18 (-2 .1 1 )* r| = 3.19 (3.19)triplet at = -1.93 (-1 .88) rt - 3.35 (3.16)An singlet a^ = -2.40 (-2.47) r= - 3.15 (3.09)triplet a^ = -1.84 (-1 .66) rt - 3.37 (3.33)* The parameters in parentheses are those used by Gibson and Lehman. 7118Table 2. Potential parameters.Potential depth (Mev) V 2 TT % V uAp singlet -84 (84) -816 (739) 3200 (2900)triplet -80 (81) -763 (616) 3000 (2400)An singlet -87 (88) -914 (892) 3600 (3500)triplet -79 (77) -712 (562) 2800 (2200)range parameter(fm *) A0 =0.7152u A =0.399Jx Au=0.252In this way we evaluate the A-p elastic cross section by using ourphenomenological potential. Fig.l shows that the calculated cross sec-A 4 9 5tion reproduces the result of low energy A-p scattering experiments.O (mb)Ecm (MeV)Fig.l Calculated A-p elastic scattering cross sections in comparison with experimental values.119oNow let us evaluate the binding energy of yyH by solving the Faddeev equation with our proposed potential in the coordinate space, where two states in are considered. The first is the ground state of (T=0, J=l/2). The A-N interaction in this case is described by singlet and triplet potentials. For the n-p interaction we use the Reid soft corepotential including the D state. The second is a possible excited stateof (T=0, J=3/2), where the corresponding force interacts in the trip­let state.We solve an eigenvalue problem reduced to partial differential equa­tions by the inverse iteration. The k-th iteration of (H-E')^(k) = ijj(k-l) converges at k^5 initiating from k=l to an eigenfunction iJj of H if E' is the closest to the eigenvalue. Then we calculate the Ritz quotient<i|/k)|H - H'|ij/k)> / <ijj(k) |lj/k)> = E - E ’ .If a value of (E-E') is the closest to zero, the value of E' becomes aneigenvalue of H. The results of (E-E') values as a function of E 1 are shown in Table 3. Our calculated result B^ = 0.14 MeV of the A-separa-Table 3. Values of E-E' as a function of E' and the result of binding and separation energy of the state J=l/2 .E' value (MeV) (E-E') values-2 . 2 -0.00114 (113)-2.3 -0.000446 (436)-2.4 0.000254 (264)-2.5 0.000956 (966)Binding energy (MeV) -2.36 (-2.36)A-separation energy (MeV) 0.14 (0.14)Experimental value8 (MeV) 0.13 ± 0.05-tion energy for the potential in the ground state (J=l/2) is in good agreement with the measured value By^  = (0.13±0.05) MeV . 6 In this case the tensor force in the n-p interaction plays an important role to make the bound state of jyH. By using the scattering parameters in parentheses shown in Table 1, Gibson and Lehman calculated the A-separation energy by solving the Faddeev equation with a separable potential in momentum space and found to be Byy = 0.37 MeV , 7 although they pointed out that the intro­duction of the n-p tensor force would reduce the binding energy of the hypertriton. 8 It is noted that our evaluation by using their scattering parameters (model B) gives the same separation energy Byy = 0.14 MeV as mentioned above. It is added that almost the same separation energy is also obtained with scattering parameters determined by the variational method. 1On the other hand we cannot find a negative binding energy for the excited state (J=3/2). In fact such an excited state is not confirmed by experiment at the present time.120References1. R.H. Dalitz, R.C. Herndon and Y.C. Tang, Nucl. Phys. B47, 109 (1972).2. M.M. Nagels, T.A. Rijken and J.J. de Swart, Proc. Intern. Conf. on Few Particle Problems in Nuclear Interaction (1972), 42; Ann. of Phys. 79, 338 (1973).3. M.M. Nagels et al., Nucl. Phys. B147, 189 (1979).4. B. Sechi-Zorn, B. Kehoe, J. Twitty and T.A. Burnstein, Phys. Rev. 175, 1735 (1968).5. G. Alexander, U. Karshon, A. Shapira, G. Yekutieli, R. Engelmann, H.Filthuth and W. Lughofer, Phys. Rev. 173, 1452 (1968).6 . M. Jiric et al., Nucl. Phys. B52, 1 (1973).7. B.F. Gibson and D.R. Lehman, Phys. Rev. CIO, 888 (1974); C14, 2346(E) (1976).8. B.F. Gibson and D.R. Lehman, Phys. Rev. Cll 2092 (1976).N.B. In Fig.l the A-p elastic scattering cross section expressed by the dashed line is obtained for reference by using the A-n potential due to only two-pion exchange.121A QUALITATIVE DISCUSSION OF THE A=4 HYPERNUCLEAR ISODOUBLET*B. F. GibsonTheoretical Division, Los Alamos Scientific Laboratory Los Alamos, New Mexico 87545D. R. Lehman**Department of Physics, The George Washington University Washington, D.C. 20052ABSTRACTThe hypernuclear mas| 4 isodoublet provides a furious set of bind­ing energies for the J =0 ground states and J =1 excited stateswhich one would like to understand in terms of the basic YN interactions. We discuss the qualitative understanding of the charge symmetry breaking in the ground state and the ground-state excited-state separation in terms of exact 4-body equations and the effects of AN-EN coupling in the YN interaction.4 4The A=4 hypernuclear isodoublet provides four bindingenergies with which we can test our understanding of few-body cjlynamics and the hyperon-nucl^on (YN) interaction. There are two J =0 ground states and two J =1 excite^ states.  ^ The ground state A separationenergy difference AB. = B^(^He) - B^(.H) of approximately 0.34 MeV implies a charge symmetry breaking in the YN interaction somewhat larger than one might a priori estimate using simple 2-body binding energy con­siderations and the low energy AN scattering parameters:aAp = -1.77 fm aAp = -2.06 fms taAn = -2.03 fm aAn = -1.84 fm s trAp = 3.78 fm rAp = 3.18 fm s trAn = 3.66 fm rAn = 3.32 fm (1)s t4 5 4 4 *Also, the gamma transition energy ^ +E = B^(.H) - H ) of approxi­mately 1.09 MeV implies that the Jir=l ^state is less bound (compared tothe ground state) than the spin dependence of the free interaction might imply. At least a qualitative resolution of these two puzzles would appear to be possible in terms of our present understanding of true few-body physics and the spin-isospin coupling within the nucleus of the AN-EN interaction.*Work performed under the auspices of the U.S. DoE.**Work supported in part by the U.S. DoE.122Consider first the ground state energy difference. The appropriate combination of Ap and An interactions for the two hypernuclei are:4He: v f  - A  4H: v f  -  V^ny/'lN b  iy^P +  — vAn vAN -  — yAP +  iys 3 s  3 s  s 3 s 3 sAn(2)It is readily apparent that the difference in the singlet potentials in these two cases is relatively small compared to the difference between the triplet interactions; thus the differences between Ap and An singlet interactions contribute little to AB^ . Since v P =£ V^11 , if one judges from Eq.(l), one might hope that this would account for AB^ . However, one must be careful to utilize our complete knowledge of few-body dynamics. If, for example, one uses separable, rank-one Yamaguchi potentials (where the scattering length a and the effective range r completely determine the strength ang yange of the potential), then the following binding energy relations hold: ’| a | > | a' | => B2 > B'2 and B3 > b'3 or B4 > b'4r > r' =»• B_ > B' but B, < b' or B. < b'2 2 3 3 4 4(3)>where the subscript denotes 2-body, 3-body, or 4-body. Tj^ is was first understood for the fjwo- and three-body problems by Thomas and reiterated by Bethe and Bacher within the context of proving that the range of the nuclear force was finite (non-zero) or the trition would collapse to a point. For the present problem the implication is that the binding energy difference effects of Aa and Ar for the AN triplet interaction tend to cancel in an effective 2-body calculation of AB^ , whereas they reinforce one another in a true 4-body calculation of AB^ . Therefore, although simple estimates of AB^ based upon the low energy AN scattering para­meters of Eq.(l) might appear to be low, a true few-body calculation will produce a larger estimate; see Ref.7.Now let us turn to the excitation energy question. In this case, it would appear that the important effect comes from modifications of the spin-isospin coefficients for the coupling of the AN and EN channels within the nuclear medium. If we neglect differences between the EN doublet and quartet states for simplicity, then the co^gled AN-EN potentials for the ground state and excited state are:123References1. B. Povh, Ann. Rev. Nucl. Part. Sci. 28^ , 1 (1978).2. M. Juric, et al., Nucl. Phys. B52, 1 (1973).3. M. M. Nagels, et al., Phys. Rev. D15, 2547 (1977).4. A. Bamberger, et al., Nucl. Phys. B60, 1 (1973).5. M. Bedjidian, er al., Phys. Lett. 62B, 467 (1976).6. B. F. Gibson and D. R. Lehman, Phys. Rev. C14, 685 (1976).7. B. F, Gibson and D. R. Lehman, "Exact Four-body Calculation of theHe~AH Binding Energy Difference" (to be published in Nuclear Riysics).8. L. H. Thomas, Phys. Rev. 4_7, 903 (1935).9. H. A. Bethe and R. F. Bacher, Rev. Mod. Phys. 8^, 82 (1936).10. see also J. Dabrowski, Acta Phys. Pol. BjS, 453 (1975).It is clear that the singlet YN interaction in the A=4 ground state differs from the free interaction; in the case of the excited state it is the triplet interaction coupling wh^ch hgs been modified |^om its free value. We note thaj^experimentally v - 0, so that Vg reduces to a single channel V in each case; there is essentially no coupling effect in the singlet interaction. For this reason, the ground-state binding energies can be directly estimated from the free l^w-energy scattering parameters. Such is not the case for the J =1 excited states. Here, the triplet coupling is modified from the free interaction (and therefore that acting in the ground state); in^garticular,^it+is reduced. This reduced ^oupling implies a weaker V in the ^ =1 stajte^than in the J =0 state; hence it is expected that B^^H) >Ba (aH ). However, the exact relationship between the two E 's in this system must necessarily depend upon the details of the various YN interactions.124THE (K ,TT ) STRANGENESS EXCHANGE REACTION ON 6Li, 7Li, AND 9BeHeidelberg*-Saclay-Strasbourg Collaboration CERN, Geneva, SwitzerlandW. Bruckner, M.A. Faessler, T.J. Ketel, K. Kilian,J. Niewisch, B. Pietrzyk, B. Povh, H.G. Ritter, and M. Uhrmacher Max-Planck-Institut fur Kernphysik, Heidelberg, GermanyPhysikalisches Institut der Universitat, Heidelberg, GermanyP. Birien, H. Catz^, A. Chaumeaux^, J.M. Durand, and B. Mayer Departement de Physique Nucleaire, Centre d'Etudes Nucleaires, Saclay, FranceR. Bertini’f" and 0. BingCentre de Recherches Nucleaires, Strasbourg, FranceA. BouyssyInstitut des Sciences Nucleaires, Grenoble, FranceABSTRACTThe y^ Li, y^ Li, and y^ Be hypernuclear spectra have been obtained by means of the (K- ,tt- ) strangeness exchange reaction on 6Li, 7Li, and 9Be. The kaon momentum was either 720 MeV/c or 790 MeV/c. The pions were de­tected at 0° by the SPES II spectrometer and the overall resolution was 2 MeV. An independent particle model gives good account of the hypernu­clear spectra, where the strongly populated states are due to recoilless transitions.INTRODUCTIONIn this paper we report a study of the light hypernuclei yjLi, yyLi, and y^Be produced by means of the strangeness exchange reaction (K- ,tt- ) on 6Li, 7Li, and 9Be. The experiment was performed on a low-momentum (720 MeV/c or 790 MeV/c) separated K- beam at the CERN Proton Synchrotron. The experimental setup has been described previously. 1 The pions were de­tected at 0° in a 20 msr solid angle; an overall resolution of about 2MeV in the hypernuclear mass spectra was achieved.In the (K- ,it- ) reaction the transferred momentum is much smaller than the Fermi momentum, provided the kaon momentum is less than about 1 GeV/c and the pions are detected near 0°. In those conditions one pro­duces preferentially the so-called recoilless transitions in which the A particle takes the same spin space state as the neutron it replaces. A smaller part of the cross section goes to hypernuclear states correspon­ding to the strangeness exchange reaction on one of the outer neutrons accompanied by a jump of the A particle to one of the neighboring orbit­als (quasifree production) . 1 -3With the same interpretation of the experimental spectrum in terms♦Work supported in part by the BMFT. tCERN Fellow.+CERN Associate.125of recoilless and quasifree contributions, the data on p and s-d shell nuclei (from 12C to 40Ca) were analyzed with a distorted-wave-impulse- approximation shell-model calculation.4The single-particle energies for the A particle have been calculated using an energy-independent shell-model potential with a Woods-Saxon form for the central term and a Thomas form for the spin-orbit term.From a phenomenological analysis of the data (see Ref. 4 for detailed discussion) the depths of the two potentials were determined as follows:v£ = (32 ± 2) MeV, mV\$= ( 4 ±2) MeV. ;Our purpose now is, using the same model calculation, to see whether such values are able to give a reasonable fit to light nuclei or not.The difference in the two calculations is the replacement of the j-j cou­pling model by the intermediate coupling model more appropriate for light nuclei with the coefficients of fractional parentage as determined by Cohen and Kurath.5In Fig. 1 the hypernuclear mass spectra are given as a function ofByy, the binding energy of the A particle. Instructive also is the trans-formation-energy scale Mjjy - Q value of the reaction), where M^yand are the masses of the hyperfragment and the target, respectively:“ hy - ma  '  MA - “ n + B» a s t  - bA -  e k -  \  -  EE-Here, and denote the energies of the mesons, E^ is the recoil ener­gy of the hypernucleus and Blast the separation energy of the last-shell neutron.THE REACTION 6Li (K~ ,lT) 6LiFrom (p,d) experiments6 the separation-energy difference between the 1 p 3 /2 and 1 si /2 neutron-hole states in 6Li is 15.7 MeV. One expects the two observed peaks at Byy = -14 MeV and By^  = -4 MeV to correspond to the two recoilless transitions built on the lsi/2 and lp3/2 orbitals, respec­tively. Therefore the 10 MeV difference between these peaks gives 5.7 MeV for the separation-energy difference between the A single-particle energies in the lsi/2 and 1 p 3 / 2 orbitals.This value is rather in agreement with the value 8 MeV estimated with the shell-model potential for the A particle (with the set of para­meters (1)). Moreover, the intensity ratio in the two observed peaks is in rough agreement with the ratio 2:1 of the number of neutrons in the s and p shells of 6Li.The shape of the calculated intensity spectrum agrees quite well with that of the observed one. The weak intensity at Byy = 4.5 MeV corre­sponds to a quasifree transition (1 sin  ,lpl)i)i~ and may probably be as­signed to the ground state of y^ Li. This state, however, would be un­stable against proton emission, since the (y^ He + p) mass is smaller by 600 keV. For that reason it has not been observed in emulsion experi­ments .126M hy - Ma (MeV)160 180 200 220Ba (MeV)Fig. 1. Hypernuclear mass spectra of ^Li, j^ Li, and ^Be. The solid line represents the described fit to the data.127THE REACTION 7Li(K ,TT )7LiThe situation is somewhat more complex for 7Li since in (p,d) experi­ments the 1 p 3 /2 transition strength is distributed over several states in 6Li (actually the five low-lying states) the strongest being the ground state J = 1 + , T = 0 and the state J = 3+, T = 0 at 2.2 MeV excitation en­ergy. The separation-energy difference between the lsi/2 and 1p 3 /2 neu­tron holes amounts to about 20 MeV.One expects the two peaks at Byy = -15.5 MeV and Byy = -3.5 MeV to correspond to the two recoilless transitions built on the lsi/2 and 1p 3 /2 orbitals. The A separation-energy difference between these states is therefore estimated to be 8 MeV, a value in agreement with that given by the A shell-model potential.A comparison between the observed and theoretical intensity spectra shows that the weak intensity at Byy = 5 MeV results from a quasifree transition (1s 1 n  ,lpl/2)1- from a 3/2“ state to a 1/2 state.THE REACTION 9Be(K~,lT)9Be• • 9 • • •The interpretation of ^Be is much more involved. It is well knownfrom (p,d) experiments that the lp3/2 strength is distributed over many states in 8Be, the strongest ones being J = 2+ , T = 0 at 3 MeV excitation energy and J = 2+, T = 0,1 at 17 MeV excitation energy. Therefore the two dominant peaks at B^ = -17 MeV and B^ = -6 MeV are believed to belong to the 1 p 3/2 A-particle configurations built on these states. In addi­tion, the separation-energy difference between the lp3 /2 and lsi/2 neu- tron-hole states is about 23 MeV. Therefore the peak at Byy = -17 MeV is expected to be a mixture of the two recoilless transitions (1 s 1 /2 ,1 s~/2)o + and (1p 3 /2 ,lpI/2)o + . The shell-model calculation reproduces those fea­tures quite well.The weak intensity at B^ = 7.5 MeV is a quasifree transition (Isi / 2» 1 p*3 /2) 1 — from a 3/2“ state to a l/2+ state. This is consistent with the position and the spin determination of the ground state of ^Be obtained in nuclear emulsion.REFERENCES1. W. Bruckner et_ al., Phys. Lett. 79B, 157 (1978).2. R. Bertini «rt al., Phys. Lett. 83B, 306 (1979).3. R.H. Dalitz and A. Gal, Phys. Lett. 64B, 154 (1976).4. A. Bouyssy, Phys. Lett. 84B, 41 (1979).5. S. Cohen and D. Kurath, Nucl. Phys. A101, 1 (1967).6 . B. Fagerstrom et^  al., Phys. Scripta 13, 101 (1976) and referencescited therein.128EXCITED STATES IN LIGHT HYPERNUCLEI FROM (K- ,tt-) REACTIONSN. Auerbach Department of Physics and Astronomy Tel-Aviv University, Tel-Aviv, IsraelNguyen Van Giai Division de Physique Theorique''Institut de Physique Nucleaire, 91406 Orsay Cedex, FranceABSTRACTThe distribution of strengthS(E) = E I < t Z ;n l ^  U_y} | AZ ; g . s . > |2 6 (E-En) ,n jwhere U ^  is the U-spin lowering operator, has been calculated for light hypernuclei in a lambda particle-neutron hole model which includes the effects of the A continuum.The AN residual interaction is taken as an effective zero-range force. The nuclear potential of the A particle is obtained from this force whereas the neutron spectrum is given by a Skyrme-Hartree-Fock calcu­lation. The function S(E) is computed for values of the momentum transfer q from 0 to 80 MeV/c.In 2Be the strength S(E) shows a broad structure with its maximum at Byy = -5 MeV and a width (FWHM) T1" = 7 MeV. This structure is built mainly on the (lp)yy(lp) ^ 1 configuration and its width comes from that of the A single particle resonance. At higher excitation energy the bound (ls)yy(ls) ^ 1 configuration gives rise to a narrow state at Byy = -15.5 MeV with a width T'1 = 500 keV. Comparison with experimental data suggests that the observed width of the structure at lower excitation energy could be almost entirely attributed to the A escape width. On the other hand, the width of the state seen at higher excitation energy is much larger than the calculated and therefore it consists mainly of the damping width of the Is neutron hole. Similar results are obtained for the nuclei ^Li and ^Li.1. METHOD OF CALCULATIONIn the present paper we will deal with certain hypernuclear states in ®Li, ^Li and ^Be. The states will be described in terms of lambda parti­cle-neutron hole (AN-1) configurations. 1 The (AN-1) states we will calcu­late will be related to the excitations observed in the recent (K- ,tt- ) reactions. 2The theoretical framework of the present calculation was outlined in Ref. 1. The particle-hole (p-h) excitation spectrum is computed with respect to the parent nuclei 6Li, 7Li and 2Be. The single-particle ener­gies of the nucleus are determined using the HF approximation and employing a Skyrme type density-dependent force. 2 The nuclear potential of the A is obtained by folding a zero range AN interaction with the nucleon density obtained in a HF calculation. From this potential the lambda single-parti­cle energies are computed. The resulting unperturbed p-h energies and wave functions are then used to calculate the perturbed AN- 1 spectrum.*Laboratoire associe au C.N.R.S.129This is done by means of the Green's function method. 4 The perturbed p-h Green's function is calculated in coordinate space:G(E) = G(0)(E)+G(E) Vph G(0)(E), (1)where Vp^ is the residual lambda-nucleon (AN) particle-hole interaction obtained from the AN particle-particle interaction. The unperturbed p-h Green's function in the TDA isG^0) (rq ,r2 ;E) =T^<})h+ (?i) <r1 | . ■ [r2> cf>h (r2), (2)TT H0-eh“E"inwhere <j>h denote the occupied neutron states and the corresponding ener­gies, Hq represents the A-nucleus one-body Hamiltonian. For a local potential in the particle Green's function in the bra and ket of Eq.(2)can be written in a closed form using the regular and irregular solutionsof Hq . For a zero range AN interactionEq. (1) is solved numerically in coordinate space. We emphasize that in the present method the space is complete and includes the particle continu­um. This enables us to study the A-escape width of the various p-h hyper­nuclear states. 1From the calculated Green's function one extracts the needed informa­tion by computing the distribution strength of single-particle operators.In our case the approximate operator is the Sakata unitary U-spin operator5 and in particular its U_ = 2 U_(J) component which transforms each neutron in the parent state into 3 a A, leaving the orbits unchanged. 1 ’ 4 In order to relate the theoretical results to experiment we will use a more general operator which involves finite momentum transfer. Namely, the distribution strength we shall determine isS (E) = X) l<AZ’n l £  eici‘rju_^) | AZ; g . s . > | 2 6 (E-En) , (4)n :where n runs over all excited states in the hypernucleus, j over all the neutrons, and q denotes the momentum transferred to the nucleus in a strangeness exchange reaction5 (K- ,Tr-). Note that for q=0 the integral of S(E) over the entire energy range should give the total number of neutrons in the parent state |^Z>.2. RESULTSUsing the method described above we calculated the lp-lh spectrum of the 5Li, qLi and ^Be hypernuclei. For the odd-mass number nuclei (9Be, 7Li) the parent stage |^Z> is described by a HF with the filling approximation em­ployed, i.e., the state is considered to have angular momentum J=0+ . Relative to this state we build excitations carrying angular momentum J=0+ , 1", 2+ ,i.e., [a+a^ j] 0+^ 1 - ^ 2+| ^ Z> and with this basis compute the perturbed p-h spectrum.For the NN force we used the Skyrme II interaction3 and as already mentioned for the AN force we used the form given in Eq. (3). The strength parameter t0 was adjusted to reproduce the experimental A binding energy in ^Be equal to Byy = -6.6 MeV. This leads to the value tg = -182 MeV fm3.The results of our calculation are presented in Figs. 1 to 3. The130following notations are used: Byy denotes the A separation energy in theparticular hypernuclear state under consideration EE(^-1Z g .s .)-E(^Z*). The symbol T'1' stands for the A-escape width and is estimated from the dis­tribution strength in Figs. 1 to 3 by taking the width of each peak at its half maximum.In Figs. 1 to 3 we show the distribution strength as defined in Eq. (4) for J=0+ , 1“ and 2+ excitations in ^Li, ^Li and ^Be. The solid curves correspond to q = 40 MeV/c. This is the momentum transfer for which the (K- ,ir-) cross sections were measured in the recent experiments. 2 ’ 7 For momentum transfer q <_ 40 MeV/c the contribution of the J=l“ and 2+ to the calculated strength is small in the region of the main two peaks seen in all the three figures. The contribution of the J=l- is significantly larger for higher excitation energies. The dashed curve in Fig. 3 corre­sponds to the q = 80 MeV/c case and it shows a structure around Byy=-25 MeV which is due to the contribution of a J=l- state.3. DISCUSSIONThe spectra of all three nuclei are characterized by a broad peak at excitation energy of 10-12 MeV and escape width of about = 7 to 10 MeV. This structure is mainly due to the (lpj^  ^Pa) configuration although a small admixture of the (ls^1 Isyy) also contributes. The large escape width results from the fact that the A in the lp state is unbound. A comparison with the experimental data suggests2 that the width of the lower resonance is almost entirely due to the escape width of the A and very little to the spreading width. This is reasonable since we expect that the spreading will be small for the lower states made up of a lp neutron hole. At higher energies about 10 MeV above the broad peak we find a narrow peak which is built mainly on the (Ls^ 1 ls^) configuration. The I'*' width is only a few hundred keV. The state is narrow because the Isa state is bound and the small finite width comes from the small admixture of the (lpjq1 IPa) unbound configuration. A comparison with the experimental data2 indicates that the observed width of a few MeV is mostly due to the spreading width which comes probably from the spreading width of the Is neutron hole. This is consistent with the proton removal experiments which find several MeV spreading width for Is protons in this region of the periodic table.The excitation strength shown in the figures resembles closely the distribution strength found in the strangeness exchange reaction2 (K- ,ir-).A calculation of the absolute strength and more detailed description of the relative strength would require the use of distorted waves of the in­coming K“ and outgoing tt- . These are not readily available because there are still basic theoretical questions concerning kaon and pion optical potentials.In conclusion, we have presented a simple shell-model picture of hyper­nuclear excitation in light hypernuclei. This picture reproduces many of the basic features of the experimental spectrum observed in the strangeness exchange reactions.We would like to thank Drs. R. Bertini, H. Catz, A. Gal, B. Mayer andB. Povh for stimulating discussions.131REFERENCES1. N. Auerbach, Nguyen Van Giai, and S.Y. Lee, Phys. Lett. 68B, 225 (1977).2. R. Bertini et_ a l ., private communication.3. M. Beiner et al., Nucl. Phys. A 2 3 8 , 29 (1975).4. G.F. Bertch and S.F. Tsai, Phys. Reports 1 8 C , 126 (1975).5. A.K. Kerman and H.J. Lipkin, Ann. of Phys. 66_, 738 (1971).6. See for example W. Bruckner et_ a T . , Phys. Lett. 6 2 B , 481 (1976).7. W. Bruckner e t ^  a l .  , Phys. Lett. 7 9 B , 157 (1978).Fig. 1132Fig. 2Fig. 3133POSSIBLE OBSERVATION OF A  y-TRANSITION IN THE ^Li HYPERNUCLEUSM. Bedjidian, E. Descroix, J.Y. Grossiord, J.R. Pizzi,A. Guichard, M. Gusakow and M. Jacquin Institut de Physique Nucleaire, Universite Claude Bernard de Lyon et Institut National de Physique Nucleaire et de Physique des Particules, LyonM.J. Kudla, H. Piekarz, J. Piekarz and J. Pniewski Institute of Experimental Physics, University of Warsaw and Institute of Nuclear Research, WarsawABSTRACTThe y-spectra induced by stopped K - mesons in 8Be target were obtained in coincidence with the accompanying charged pions. The y-line at (1.22 ± 0.04) MeV observed with the 44 MeV charged pions was tentatively ascribed to a y-transition in 8Li hypernucleus. Some interpretation of this line in a frame of the shell-model approximation of the 8Li levels is discussed.In a recent experiment performed at the K19 beam of the CERN PS the y-transitions in light hypernuclei were investigated. The results con­cerning the ^H and ^He y-rays were previously reported in Ref. 1. In this paper we shall discuss some of the y-spectra obtained with the same counter set-up but for K- mesons stopped in 8Be target. The aim of this measurement was to make a primary search for the y-transitions in ^Li hypernuclei. The experimental arrangement was described in Ref. 1.Among all hypernuclei possibly produced due to K~ interaction with 8Be nuclei, there are only two hypernuclear isodoublets with relatively strong two-body decay channels, i.e. j^ H, j^He and ®Li, ^Be. The branching ratio for ^H and JyHe decays is about 50%, and in the case of 8Li and 8Be it is only 20%. In the present experiment the charged pion counter was adjusted to detect the tt~  mesons accompanying the 8Li two-body decay:8Li 8Be*(2.9 MeV) + tt- , E^ = 44.3 MeV .The detection efficiency and resolution of the 44 MeV charged pions were 3% and ±10% (FWHM), respectively.In Fig. IA, the y-spectrum obtained with 3 x 108 K- stopped in 9Be target and taken in coincidence with charged pions of energy above 40 MeV is shown. This spectrum is characterized by the maximum at about 0.5 MeV being most probably a composition of the 0.51 MeV annihilation line and the 0.48 MeV line due to y-transition in 7Li nucleus.In Fig. IB the same spectrum is shown; however, it was taken in coin­cidence with the charged pions of energy (40-48) MeV. It is clearly seen that the 0.98 MeV line is dominant only in Fig. IA, whereas in Fig. IB it is strongly suppressed and a new maximum at (1.22 ± 0.04) MeV became visible (3.5 standard deviation). Such a maximum was not seen in the spectra with K- mesons stopped in lithium targets, particularly if the same physical conditions were applied. On the other hand the energy of this maximum does not fit to the observed or expected nuclear background y-transitions. The fact that this line appeared in coincidence with13444 MeV charged pions qualifies it as a possible y-transition in ®Li hyper­nucleus. The production rate for1.22 MeV transition is about 0.15% per stopped K~ meson, which leads to a reasonable (~0.7%) production rate of ®Li hypernuclei. However, the low statistical significance of the1.22 MeV maximum and the fact thatso far it was observed in one irradi­ation only make the above interpreta­tion of this line still tentative.Assuming that the 1.22 MeV line is a virtual hypernuclear line, we discussed its possible interpretation according to the theoretical approach presented by Gal et^  al.2-i+ In this approach the expected level scheme for the ®Li hypernucleus is shown in Fig. 2. From the transition rate calculated using the formulae given in Refs. 5 and 6 , one concludes that the 1.28 MeV level decays predomi­nantly to the ground state. There­fore one might identify the 1.22 MeV lines with 1 ~ -> 1 “ transition, but(rteV)7Li SLiFig. 2E N E R G Y  O F  Y -R A Y S  (M eV )Fig. 1the transitions at 0.55 MeV and 0.88 MeV should also be observed as a result of the direct population of the 0“ and 2~ levels. The fact that these lines have not been observed does not support the above identification of the 1.22 MeV maximum; however, the vicinity of the background lines at 0.5 MeV and 0.98 MeV makes the observation of the hypernuclear y-transi- tions in the (0.5 t 1.0) MeV interval rather dif­ficult .Besides, the model based on the ground state properties cannot describe precisely the complicated structure of the hypernuclear levels, and the determination of full level scheme of the ®Li hypernucleus is much desired for a correct interpretation of the observed y-spectra.135REFERENCES1. M. Bedjidian, E. Descroix, J.Y. Grossiord, A. Guichard, M. Gusakow, M. Jacquin, M.J. Kudla, H. Piekarz, J. Piekarz, J.R. Pizzi andJ. Pniewski, Phys. Lett. 83B, 252 (1979).2. A. Gal, J.M. Soper and R.H. Dalitz, Ann. Phys. (N.Y.) (13, 53 (1971).3. A. Gal, J.M. Soper and R.H. Dalitz, Ann. Phys.(N.Y.) 72, 445 (1972).4. A. Gal, J.M. Soper and R.H. Dalitz, Ann. Phys.(N.Y.) 113, 79 (1978).5. R.H. Dalitz and A. Gal, Ann. Phys.(N.Y.) 116, 167 (1978).6 . A. De Shalit, Phys. Rev. 122, 1530 (1961);D. Walecka, Ann. Phys. (N.Y.) (13, 219 (1971).136SEARCH FOR E HYPERNUCLEI BY MEANS OF THE STRANGENESS-EXCHANGE REACTIONS (K“ ,7T-) AND (K“ ,1T+)Heidelberg*-Saclay-Strasbourg Collaboration CERN, Geneva, SwitzerlandW. Bruckner, M.A. Faessler, T.J. Ketel, K. Kilian,J. Niewisch, B. Pietrzyk, B. Povh, H.G. Ritter, and M. Uhrmacher Max-Planck-Institut fur Kernphysik, Heidelberg, GermanyPhysikalisches Institut der Universitat, Heidelberg, GermanyP. Birien, H. Catz^, A. Chaumeaux^, J.M. Durand, and B. Mayer Departement de Physique Nucleaire, Centre d'Etudes Nucleaires, Saclay, FranceR. Bertini^ and 0. BingCentre de Recherches Nucleaires, Strasbourg, FranceA. BouyssyInstitut des Sciences Nucleaires, Grenoble, FranceABSTRACTIn the (K-,7T-) reaction performed at 720 MeV/c on 9Be and 1 2C, a narrow structure appears around 80 MeV excitation in the hypernuclear spectra, precisely where E hypernuclear states could be expected. Espe­cially in 9Be one finds a structure very similar to the A hypernuclear states, with peaks narrower than 8 MeV. Those are nearly bound states of E° in the nucleus. The spectrum obtained by the (K- ,tt+) reaction on 9Be also shows a structure which could be due to nearly bound states of E-  in the nucleus.INTRODUCTIONIn recent experiments1 ’ 2 the (K- ,tt_) strangeness-exchange reaction has been successfully used to produce A hypernuclei. The main advantage of this reaction is the small recoil transferred to the A, which replaces a neutron in the same nuclear state without disturbing the residual nu­cleus. This process is called recoilless A production and found to bedominant for light nuclei. 1 ’ 2 It is the aim of this paper to show that, for 9Be and 1 2C, hypernuclear states exist where the constituent nucleon is replaced by a E° or a E-  particle. These states are sufficiently nar­row to allow a study of the E-nucleus interaction.Using a (K- ,tt-) or a (K“ ,tt+) reaction trigger the following reac­tions on neutrons or protons of the nuclear targets may occur:K- + n -> A + tt- , (la)K- + n - > E ° + 7T-, (lb)K- + p E+ + tt-, (lc)K- + p ->■ E- + tt+ . ( 2 )♦Work supported in part by the BMFT. fCERN Fellow.+CERN Associate.COUNTS I 2 MeV137Our experiment was performed at a kaon beam momentum of 720 MeV/c. At this momentum the cross section for reaction (lc) is an order of magni­tude smaller than that for (lb). Therefore a (K~,tt-) trigger will show only A and E° hypernuclei. The (K- ,7T+) reaction, on the other hand, can­not produce A particles but only Z~ particles.EXPERIMENTThe experiment took place at the low-momentum separated K beam (k22) at the CERN Proton Synchrotron (PS). The experimental setup has been de­scribed earlier1 and consists essentially of two spectrometers, the first one for measuring the K- momentum and the second one for the momentum of the outgoing pion at about 0°. This second spectrometer is the specially designed SPES II from Saclay. Its large momentum acceptance of Ap/p = ±18% gives the unique possibility of measuring simultaneously pions stem­ming from A and Z° hypernuclear production in the same spectrum (see Fig. 1). The overall energy resolution in this experiment is about 3 MeV, using 9Be and 12C targets of 2 g/cm2 thickness. In addition to our (K“,7T-)-reaction trigger we used the signal of a scintillation counter which surrounded the target. This counter detected the fragmentation of a hypernucleus or the decay of the A, but not the three-body decay of the kaons near the target which is responsible for a low flat background.The K -*■ 2tt decay background was suppressed by geometrical cuts.E° HYPERNUCLEIFigure 1 shows the (K_ ,tt-) spectra taken on 9Be and 1 2C. At the top we indicate the transformation energy (Mjjy ~ Ma) which is the Q value of the strangeness-exchange reaction in transforming a nuclear ground stateMHy-M a  (MeV)175 200 225 250 275 300 325 350 175 200 225 250 275 300 325 350B-~(MeV) Bs .(MeV)Fig. K  (K“,tt ) spec­tra taken at a kaon momen­tum of 720 MeV/c on 9Be and 1 2C. The transformation energy and the different bin­ding-energy scales are given.COUNTS / 2 MeV138with mass into a hypernuclear state with mass Mgy hypernucleihave to be found at a mass 76.87 MeV higher than the A hypernuclei. We also indicate the binding energy scales: B^0 = 0 MeV corresponds to By\ = -76.87 MeV. Both spectra show in this region a clear enhancement due to E° hypernuclear production. The production of A hypernuclei is four times stronger than of E° hypernuclei, which is in agreement with the elementary cross sections for the reactions (la) and (lb).In 1 the strong peak stems from recoilless A production on the 1 p 3 /2 neutrons.1 In y^ Be the peak at By^  = -6 MeV is due to recoilless production on the loosely bound 1p 3 n  neutron, whereas the second peak contains both recoilless strength from the strongly bound 1p 3 tz neutron pair as well as from 1 s 1 /2  neutrons.3 Comparing the A and the 1 °  spectra one finds for t^)C a nearly disappearing recoilless peak. Such a behavior is expected since the recoilless intensity has to decrease drastically with increased momentum transfer.4 At 720 MeV/c the momentum transfer for the E production is about 130 MeV/c, but for the A it is only about 60 MeV/c. The clear similarity between the A and the E° spectra, espe­cially for 9Be, indicates that we see recoilless-produced E° hypernuclear states. Their width of less than 8 MeV is surprisingly narrow, as the E particles can decay in nuclear matter via the (E + N -> A + N) reaction, where an energy of about 80 MeV is released. There has been no reliable estimate of the lifetime of E particles in nuclei up to now.A B  ( M e V )1“ HYPERNUCLEIThe (K-,tt+) spectrum for 9Be shows a bump of about the same width as the total E° bump sitting above a shoulder which might be produced by free E~ production. In this bump one may see a small peak, which is sta­tistically weak but nevertheless at the expected mass for recoilless-pro- duced E~ hypernuclear states. In or­der to compare A, E° and E~ hypernu­clear spectra, one has to get rid of the hyperon and nuclear mass contri­bution in the transformation energy (Mry ~ MA). For that purpose we use in Fig. 2 the scale Ag = Mgy - -<MA,E - Mn,p) = Bn,p “ BA ,I>  where M denotes the masses and B the bindingenergy of the indexed particles. The peaks in the!0 spectra are shifted by about 3 MeV towards higher Ag values. This indicates that the E-nucleus in­teraction differs from the A-nucleus one.The E-  spectra are produced onFig. 2. Comparison of the A, E° and E_ hypernuclear spectra on 9Be in the Ag scale.the target protons. As expected, the E~ spectrum on the 9Be target shows only one recoilless peak at a position where the A and the E° spec­tra contain the peak stemming from recoilless production on the 1p 3/2 neutron pair and on the 1 s 1 /2 neutrons.CONCLUSIONSWe conclude that the E-nucleus potential appears to be the same for E° and E_ hypernuclei. The data, however, are inadequate for deciding whether the difference between the A- and E-nucleus potential originates from a different spin-orbit coupling or from a different central poten­tial felt by the A and the E particles in the nucleus. Measurements at much lower kaon momentum are necessary to enhance the recoilless E pro­duction, but kaon beams with sufficient intensities at 300-400 MeV/c do not exist at present.REFERENCES1. W. Briickner et_ al., Phys. Lett. 79B, 157 (1978).2. R. Bertini eL al., Phys. Lett. 83B, 306 (1979).3. W. Bruckner et al., The (K~,tt“) Strangeness-Exchange Reaction on 6Li, 7Li, and 9Be, paper contributed to this conference.4. B. Povh, Z. Phys. A279, 159 (1976).139140QUANTUM CHROMODYNAMICS AND THE SPIN-ORBIT SPLITTING IN NUCLEI AND A- AND E-HYPERNUCLEIHans J. Pirner Institut fur Theoretische Physik, Heidelberg, F.R.G.The average spin-orbit potential for a nucleon, A- and E- particle is deduced from the combined quark- and gluon-exchange between the valence baryon and the nucleons of the core. The quarks are treated in the rela- tivistic Fermi gas approximation. The spin-orbit potential for the baryon comes out asV Is - 60 MeV f „2 i  A  Pill I  ^  §Q £  Lp ,0 U,Q u,dwhere p(r) is the nuclear matter density, p0 = p (r=0), n is the number of up- and down-quarks in the baryon, Sq and Lq are the spin and angular momentum operators of the quarks.The different N-, A-, E-potentials are readily obtained from the quark- wave functions of the baryons (Table I). Note the u,d pair in the A has spin-zero; therefore we predict no spin-orbit splitting for the A. The measurements1 on A-nuclei give a strength of less than 1/10 spin-orbit for the A-particle than for the nucleon.Table ISpin orbit potential N A EW 0 4/3 WREFERENCES1. B. Povh, Ann. Rev. Nucl. Sci. 28^ , 1 (1978);W. Bruckner, M.A. Faessler, T.J. Ketel, K. Kilian, J. Niewisch,B. Pietrzyk, B. Povh, H.G. Ritter, M. Uhrmacher, P. Birien, H. Catz,A. Chaumeaux, J.M. Durand, B. Mayer, J. Thirion, R. Bertini and0. Bing (Heidelberg-Saclay-Strasbourg Collaboration), Phys. Lett. 79B, 157 (1978).141SUPERMULTIPLET STRUCTURE AND DECAY CHANNELS OF HYPERNUCLEAR RESONANCES, EXCITED VIA ( K - , tt~ )  ON 6Li TARGETL. Majling, M. Sotona, J. Zofka, V.N. Fetisov and R.A. Eramzhyan Nuclear Physics Institute of Czechoslovak Academy of Sciences,Rez near Prague, CzechoslovakiaEven higher excited states of light p-shell nuclei may be character­ized by Young tableau [f]. Taking hypernucleus with A=6 as an example, the usefulness of such a quantum characteristic is also demonstrated for the hypernuclear states excited in the reaction (K~,tt~) at 0 ^ = 0 ° .  This holds even if NN and AN tensor forces have been switched on. The analy­sis in terms of [f] is especially useful for hypernuclear decay channels. This is most clearly displayed for decays[32]2l+SsA +  ^He(5Li) +  p(A)which are forbidden due to [f] selection rules. The open decay channel leading to j|He(^He*)+d may be suppressed for it lies in the vicinity of the cluster decay threshold. Measurements are thus needed of pion spectra with a high resolution (AE^ < 1 MeV) as well as coincidence data on p-u and d-ir in order to explain the nature of hypernuclear excitations.142SHAPES OF A 1  41 HYPERNUCLEI J. ZofkaNuclear Physics Institute, Czechoslovak Academy of Sciences,Rez, CzechoslovakiaDeformed hypernuclei, consisting of an even-even nuclear core with N = Z and a A-hyperon, have been studied in the Hartree-Fock scheme with­out the J-projection. Phenomenological N-N interactions employed1 made it possible to extract the influence of the nuclear compressibility K on changes of radii and of intrinsic deformations due to A added. Use of central A-N interactions Vy^ j with various ranges and exchange components, which fit ^ 0  and hypothetical ^\Ca ground states, has suggested: Binding energies of A-hyperon Byy in deformed hypernuclei are systematically lower than suggested by a smooth curve extrapolation from spherical ones. This difference grows when reducing strength of the Majorana ax component of V/ysj and/or K and it may be reduced by J-projection. The radial changes Ar of nuclear cores are of the order of 1% and are more pronounced when going to lower values of K, A or ax . The changes of intrinsic quadrupolemoments AQ„ have similar dependence on K and a„, but the A dependence hasocr oq 2ka maximum at j(Mg and (~5%) in s-d shell and may be as much as 10% injyBe. Those values of AQ0 are likely too small to enable distinguishing of nuclear and hypernuclear K = 1/2 y-transitions experimentally. All values studied are much less sensitive to the range of Vy^ j.In order to estimate microscopically a possible influence of ANNinteraction on properties of ^He, ^0 and 4^Ca hypernuclei, a generaliza­tion of the nuclear hyperspherical formalism (e.g. Ref. 1) has been found very useful. A correspondence has been demonstrated between V/VNN ancl a nonlocal two-body N-N interaction.1. M. Sotona and J. Zofka, Czech. J. Phys. B28, 593 (1978).143KAONIC HYDROGEN*tA. Deloff and J. Law University of Guelph, Guelph, Ontario, Canada NIG 2W1ABSTRACTIt is argued that Coulomb corrections to the K p scattering length may affect the latter significantly and reduce the strong interaction effects in kaonic hydrogen.INTRODUCTIONAccording to a recent observation1, the kaonic hydrogen Is level shift e due to the strong interaction is 40±60 eV. The width T is alsogiven as 0 ^ eV. The theoretical prediction is based on the formulae + i I  = 2 a 3 y2 Ac (1 )where y is the K p reduced mass, a- 1 = 137.036, and b = c = 1; A is theK p Coulomb corrected scattering length. Using the current values for the scattering length2, the theoretical prediction is(e,n = (-397,579) eV (2)and is in striking disagreement with experiment. In this note we discuss a possible resolution of this discrepancy.THE SHIFT FORMULASince formula (1) is crucial for the interpretation of the experimental results, it is appropriate to indicate how it originates. 3 To derive (1), all one needs to assume is that the K p forces are not too singular so that an effective range expansion should exist (this assumption is fundamental for KN scattering analysis). The K p bound state energy can be obtained by locating the poles of the corresponding S-matrix which can be split into Coulomb and nuclear parts, viz.F _(k) 1 - gT(k) K (k)Sp(k) - (-1)*-J J ----  , (3)F£(k) 1 - g*(k) K£(k)+ + where ^(k) is the Coulomb Jost function, gT(k) is a Coulomb functiondefined in4 and K£(k) is the Coulomb generalized K-matrix. For small kwe assume the effective range expansionV k)- 1  =  A—l a .  I  1,2= A” + —  k R , (4)where A£ and R£ are the Coulomb corrected scattering length and effective range parameters (we suppress their Z dependence). At the Coulomb bound*Work supported by NSERC Canada.tPermanent address: Institute for Nuclear Research, Warsaw, Poland.144state kQ, F^Ck) has a zero but g^(k) has a pole so that Sj^ (k) does not have a pole at kOJ as long as the strong interaction is present (K^ is not zero). To find the position of the shifted pole we have to solve the equationF+(k) - F+(k) g+(k) K£(k) = 0. (5)+ +' + +For k values close to kQ , we have F„(k) - F„ (k )(k - k ) and Fp(k)g„(k)- 2i k /FT(k ) and the solution of 15) isk - k + o 21 V V V  * t ’ (ko ) W  • (6)+  '  O p_l_l _ p _ i  _For spherical orbits F„ (k ) = F(25,+3)i (2k ) and [2ik /F0(k )] =/ i \ V 4^1 i i ™  1 • f C' -n Q  1 Tl • • O X / O(2kQ) so that the energy shift o E = - e - i ^ r  is given as, 0 21+ 31 o6E = (k/u)6k = - — K ( k )  -------------- . (7)iv r(2£ + 3)This formula is quite general and relates the energy shift to the k- matrix continued below threshold. For the Is state of kaonic hydrogen, neglecting the effective range term in (4), (7) reduces to (1). With the current value of the effective range the neglected term gives a correction of the order of 1 0-3, or less.We wish to emphasize that it is the Coulomb-corrected, not the free scattering length that enters (1). Although our experience with local potentials indicates that these two quantities are not too much different, this is not necessarily the case, especially if the force is non-local at small separations.COULOMB CORRECTIONAssuming that the K p interaction can be represented by a short range complex potential Vs which comprises all strong interaction effects and gives the Coulomb free scattering length A, we want to calculate the Coulomb corrected scattering length A to be used in (1). If u(r) and v(r) are regular solutions of the Schrodinger equations with and without the Coulomb potential V^, then A a n d  A will be given byA = limC k->o'$(R) u'(R)/u(R) - $ f(R)/^(R) 0(R) u ’(R)/u(R) - 0 1 (R)/0(R) (8)A = lim [R - v(R) /v’ (R) ] (9)k->owhere R is the matching radius, and 0 and 0 are the Coulomb wave functions.1* The relation between v and u can be made using the corresponding wave equations in the k+o limit, viz145R u'(R)u(R)- R v ' ( R )v(R) = A(R) = - frR0u(r) v(r) dr u(R) v(R) "~  do)where B Is the Bohr radius which is about 83 fm. Eliminating the log-derivatives between (8), (9), and (10) and expanding the Coulombfunctions in powers of B 1, we obtain_______ A - RA(1 - R/B) (1 + A/R) - R(R + 2A) /B_______  . .c 1 - (2-n-XA/B) + (2R/B) + A(1 + A / R ) ( l  + 2R(1 + ttX)/B)  ^ 'where X = - [2y + £n(2R/B)]/ir and y is the Euler constant.In principle, the matching radius R may be chosen arbitrarily outside the range of the strong interaction d (for sake of argument we assume that the KN force cuts off sharply at r = d). However (11) has to be independent of R while it does of course depend on d, in particular if d-H), the strong interaction vanishes. The difference between (11) and the Coulomb correction derived by Dalitz and Tuan5 is the absence of the A dependence as these terms had been expected to be small of order B-1. However,as pointed out by Sauer5, the actual size of A depends on the behaviour of the integrand (eqn (1 0)) within the range of the forcei.e. on the detailed structure of Vs at small distances. Unfortunately it is not possible to obtain A in a model independent way, without a detailed knowledge of the dynamics of the system. If the latter is such that A is negligible, then using (11) gives us the numerical result quoted in (2). On the other hand, it is possible to devise a model which reproduces the experimental scattering length A, and yet gives a non-negligible A by performing a suitable phase transformation which leaves A unaltered. Accordingly, A can take any value since the phase transformation is arbitrary. For instance if A = 1.47 - i 0.02 with R = 0.4 fm, we obtain A^ - (-0.099 + i 0.080) fm and(e,T) = (-41,66) eV , (12)which is an order of magnitude down in comparison with (2), and is consistent with the measurement. 1CONCLUSIONThe main difficulty in the analysis arises from the fact that the Coulomb correction cannot be introduced in a model-independent way. It appears also not possible to calculate Ac from A without a detailed knowledge of the strong interaction. If it appears that A is large by a reconfirmation of the measurement1 for kaonic hydrogen, then all the analysis for the KN scattering data would have to be repeated by taking this fact into account.146REFERENCES1. J. Davies et al., Phys. Lett. 83B, 55 (1979).2. A. Martin, Phys. Lett. 65B, 356 (1976)3. A. Deloff, Phys. Rev. 13C, 730 (1976); Nukleonika 22, 875 (1977).4. E. Lambert, Helv. Phys. Acta 4^ 2, 667 (1969).5. R. H. Dalitz and S. F. Tuan, Ann. Phys. (N.Y.) JJ3, 307 (1960).6. P. U. Sauer, Phys. Rev. Lett. 3^2, 626 (1974).147X-RAY YIELDS IN KAONIC HYDROGENE. BorieUniversity of Karlsruhe, W. Germany M. LeonLos Alamos Scientific Laboratory, Los Alamos, NM, USA 87545ABSTRACTThe yield of K x-rays in kaonic hydrogen (as well as other forms of exotic hydrogen) has been calculated following the method used by Leon and Bethe. Our results are not incompatible with experiment.INTRODUCTIONRecent investigations of atomic x-rays in various forms of exotic hydrogen have revived interest in the subject of the atomic cascade pro­cess. The relevant processes— Stark mixing, absorption due to the strong interaction, chemical and Auger deexcitation, as well as radiative trans­itions— were investigated some time ago by Leon and Bethe1 (subsequently referred to as L B ) . The present work extends the calculation of LB to the case of gas targets as well as liquid targets, and investigates the sensi­tivity of the cascade process to Stark mixing rates, kinetic energy of the exotic atom, target density, hadronic shifts and widths, etc. It is hoped that such information will be of assistance in the planning of experiments. In this paper we present numerical results for the case of kaonic hydrogen. Other results will be presented elsewhere.2THE CASCADEAlthough our calculation is based on that of LB, some changes have been made. These will be briefly summarized here. More details will be published elsewhere.2After capture in an initial state with n — v^ M (M is the reduced mass of the system, in units of the electron m a s s ) , deexcitation proceeds mainly by Auger ionization of the neighboring hydrogen atoms, or by "chemical" dissociation of the hydrogen molecules. The rates for these processes, as well as for radiative deexcitation, are given in LB.The rates for hadronic absorption are given byrns = rls/n3 5 rnp = 32(n2-l)r2p/(3n5) ;the widths of the Is and 2p states, as well as the hadronic energy shift of the Is state, are input parameters.When the hadronic atom passes near, or through, a hydrogen atom, it is subjected to an electric field which induces transitions among the n 2 degenerate states of a given principal quantum number n. This Stark mixing is treated somewhat differently than in LB; in order to better describe the n-region where Auger and/or radiation become competitive with Stark mixing, as can happen in a gas, we use a shuffling model. Since probability is transferred among the different 1-states at each value of n, we use a difference equation for the arrival probability. This is148solved using standard methods for the inversion of banded matrices. The shuffle rates are given in Ref. 2.NUMERICAL RESULTSA recent experiment from the Rutherford Laboratory3 has reported ob­serving the Ka x-ray from kaonic hydrogen with an intensity of (0.11±0.06)% per stopped kaon. The hadronic shift and width of the Is level were reported to be 40±60 eV and <250 eV, respectively. The shift of the Ka line due to vacuum polarization is about 25 eV. The Kg line was not observed, and an upper limit on its intensity of about half that of the Ka line was reported.Table I shows a selection of our results for kaons stopping in liquid hydrogen, and indicates the dependence on the hadronic shifts and widths, kinetic energy of the kaonic hydrogen atom (as in LB, this is taken to be constant throughout the cascade), and STK, an arbitrary factor multiplying all the shuffle rates. The shift and width of the Is state were taken to be approximately those reported; the width of the 2p state was varied. A reasonable fit to the reported yields is obtained if we take T2p < T2p(rad) = 2.6xl0~tt eV; a larger width for the 2p state gives yields which are too low and a ratio Kg/Ka which is too high. We find Ky/Ka>l in any case, and it would be interesting to look for the higher transi­tions. The cascade time is somewhat too long, compared to the experimen­tal upper limit of 4xlO-3  ^ sec, 11 but this could be corrected without influencing the x-ray yields by increasing the rates for chemical deexci­tation by a factor of about 2 .Finally we remark that if the kaons are stopped in a dilute gas, the cascade time becomes comparable to the kaon lifetime, and a significant fraction (>10%) of the kaons decay before they complete the cascade. A substantial fraction will also be absorbed from a p-state (in liquid, this fraction is always less than 1%). The long cascade times for kaons stop­ping in a dilute gas might permit the detection of the decaying kaons.The time distribution of the decays could also yield useful information.Further numerical results, also for antiprotons and pions, are givenin Ref. 2.REFERENCES1. M. Leon and H.A. Bethe, Phys. Rev. 127, 636 (1962).2. E. Borie and M. Leon, TKP 79-7, submitted to Phys. Rev. A.3. J.D. Davies et^  aJ. , Phys. Lett. 83B, 55 (1979).4. R. Knop et_ al. , Phys. Rev. Lett. L4, 767 (1965).149Table I. x-ray yields in % (Ka , Kg, all K) and cascade time (in picosec­onds) for K- stopped in liquid hydrogen as a function of Stark coefficient STK, atom kinetic energy T, width of Is and 2p states and shift of Is state, including vacuum polarization (all in eV).STK T(eV)rls(eV)SEis(eV)r2p(eV)Ke all K Tc(psec)1 1 250 125 0 . 0 00 1 0.27 0.14 0.83 6.32 1 250 125 0. 0001 0.07 0.02 0 . 2 2 5.05 0.25 250 125 0 . 0001 0 . 0 1 0 . 0 0 1 0.04 4.02 0.25 250 125 0. 0001 0.17 0.07 0.53 6.72 1 250 80 0. 0001 0.06 0 . 0 1 0.18 4.95 0.25 250 80 0 . 0001 0.02 0.002 0.04 5.22 1 250 80 0 . 0 0 1 0.02 0 . 0 1 0.14 4.92 1 250 125 0 . 0 01 0 .02 0.02 0.16 4.92 1 80 80 0 . 0 01 0.03 0.04 0.30 5.52 1 80 80 0.0001 0 . 1 2 0.05 0.41 5.5.aexpt <250 65±60 0.1110.06 <0.09 <4aRefs. 3 and 4.150KAONIC HYDROGEN ATOM AND A (1405)K.S. Kumar and Y. Nogami Department of Physics, McMaster University Hamilton, Ontario, Canada L8S 4M1ABSTRACTA model of the KN interaction at low energies is proposed such that the recently observed, surprisingly small, energy shift associated with the 2p-ls X-rays from K~p atoms can be explained. The essential difference between this and conventional models lies in the interpretation of the origin of A(1405).Very recently the X-rays from K-p atoms have been detected, and a peak consistent with an unshifted 2p-ls transition has been found. 1 This small or no energy-shift would imply that the K-p s-wave scattering ampli­tude at the threshold, i.e. the scattering length, 2 is very small. On the other hand, the KN scattering lengths a0. and a^ (for 1 = 0 and 1, respec­tively) have been estimated from scattering data. 3 Results of such recent estimates1* ’ 5 are given in Table I, and a(K-p) = (ag + a^)/2 is compared with the estimate based on the K_p atom result. The discrepancy betweenTable I. The KN s-wave scattering lengths in fm. The suffices refer to the isospin 1=0 or 1. Statistical errors are not shown.Ref. a0 al a(K p) = -|-(a0+al)Aa / A -1.70+0.711 0.00+0.61i -0.85+0.66i4 IB -1.60+0.75i 0.08+0.69i -0.76+0.72i5 -1 .66+0 .66i 0.35+0.66i -0.66+0.7111 (K_p atom) O.lO+O.OOiSet B incorporates below-threshold constraints, and hence is thoughtto be more reliable than set A.the K~p atom and scattering results is striking. We recall, however, that the scattering data at very low energies, say kqab 4 100 MeV/c, have still some uncertainty, and hence the apparent discrepancy between the K~p atom and scattering results need not necessarily imply a real contradiction.We assume a point of view that the K“p scattering amplitude (actually we have its I = 0 part in our mind) depends strongly on the energy around the threshold, that is, the amplitude is very small at the threshold, increases rapidly as the energy increases, and reaches a maximum beyond which it gradually decreases.In addition to the data at and above the threshold, we have to remem­ber A(1405) which is about 27 MeV below the K_p threshold. Conventionally, A (1405) is interpreted as a quasi-bound state of K- and p due to a strong interaction between them in the 1 = 0 ,  s-state. However, if the K"p in­teraction is that strong, how can the K-p scattering amplitude at the threshold be so small? A successful model of the KN interaction at low151energies has to incorporate the following three features: (i) the scatter­ing data above the threshold, 6 (ii) A(1405), and (iii) the very small scattering amplitude at the threshold. The purpose of this note is to propose such a model. We assume that nothing unusual happens in the 1 = 1  state, and consider only the 1 = 0  state. We ignore the n-p and K°-K“ mass difference.Before introducing our model let us note that the analysis of the KN interaction has always been done, to our knowledge, by means of the K-matrix method with the assumption that the K-matrix elements are con­stants (zero-range approximation) or at most slowly varying functions of the energy. This approach has been quite successful in correlating fea­tures (i) and (ii),^ but feature (iii) cannot be incorporated in it unless some singularity is assumed in the K-matrix elements. Our model leads to such a singularity which is related to the interpretation of the origin or structure of A(1405).The basic idea that underlies our model is as follows. From the quark model point of view, A(1405) is a three-quark system in a unitary singlet configuration, and it should be as "elementary" as the nucleon. Hence we assume that the free part of our model Hamiltonian HQ contains Ag [the bare A(1405)] in addition to K and N. For the interaction Hamiltonian Hj, we assume two terms which are depicted in Fig. 1. Term (a) isa_ usual separable potential for v K K /KN KN. Term (b) is a Yukawa ^ / \ /interaction for A0 -*-*■ KN. Note \ / ^  ^that K and Ag are both of odd---------  — ---- +   — ---parity. All interactions other f\J /\Qthan term (b), such as the p and rnexchanges between K and N , 7 are (a.) (b)represented by term (a). For sim­plicity we do not include the ttZ Fig. 1. Diagram of the interactions,channel explicitly. Instead we Ag is the bare A(1405).assume that the coupling constantfor term (a) is complex. There is no reason why the coupling constant in term (a) is complex while that in term (b) is real. This choice is arbitrary.First we work in the static approximation in which the kinetic ener­gies of N and AQ are ignored, and later we will take account of the recoil corrections of the baryons. We assume the Hamiltonian H = Hq + H 1;i* + r +H0 = mNN N + m0A0Ag + / dk m^a^a^ , (1)H 1 = g-jAgN J  dk ukak + h.c.|- I fdkdk'ukuk takak r . (2)Here mg is the mass of AQ , tok = (y2+k2) 1^ 2 , p is the kaon mass, and uk = (2tt)-3/2 (2toic)_ 1 /,2vk wherevk is the form factor of the interaction source and is normalized by v0 = 1. The same uk appears in the two terms of H 1; this is to simplify the solution to the Schrodinger equation.It is straightforward to solve the Schrodinger equation8 and find the scattering amplitude f, which is related to the phase shift 6 by f = k- 1 e:*-(-’sinS, to be152f 0 = " xkJk>’ (3)where the suffix 0 is to indicate the isospin state,4irAk = G + g2/(A-wk) (4)with A = mg - m^, and- 1  ( 5) TT J  Wn_a)k_:LeJky FWe then include the baryon recoil correction by replacing wk in the denom­inators in Eqs. (4) and (5) with wk = tok + (k2/2mN), and Eq. (3) withf _ mN Xkvk (6)0 “ , 1 T »mN+wk 1 ~ AkJkwhere Ak and Jk are the modified ones described above. The resonance energy is determined fromRe(l - AkJk) = 0 . (7)Before determining the parameters of the model to fit experimentaldata, let us make one general observation concerning the effect of Ag. Ifwe put g=0, our model reduces to a simple separable potential model (SPM).A crucial difference between SPM and our model is that our Ak has a pole at oik = A, and hence the K-matrix element exhibits a singularity. Let us assume for the moment that G is also real. If G is sufficiently largethere is a bound state in SPM, which can be identified with A (1405). Ac­cording to Levinson's theorem, 6 (ai=y) - 6 (°°) = ir; 6 starts from ir at the threshold and tends to zero as to -*■ 00. For a usual form factor vk , 6 mono- tonically decreases; hence the scattering length is negative. In our model, again we can have a bound state, but the pole at to = A modifies Levinson's theorem to 6(y) - 6 (°°) = 0.^ The scattering length is expected to be positive.The above observation is qualitatively valid even if G is complex unless ImG dominates. The phenomenological aQ with Rea0 < 0 shown inTable I is consistent with the existence of A (1405) within the usualK-matrix approach. Our model, however, would not be compatible with Refg <0. At this point we would like to point out that the sign of Refg has not been determined completely independently of fitting A(1405). The sign of Refg can be determined from the Coulomb interference in the dif­ferential cross section, but the data so far available do not seem to be sufficient to do so unambiguously. Therefore Refg could well be positive, and we assume so in fitting the scattering data above the threshold.Figure 2 shows our f0 for the set of parameters (in units of p): g = 0.461, G = 17.07+5.011, A = 0.977, and kc = 2 . 10 Here kc is a cutoff parameter in vk which we assumed to be vk = 0(kc-k). In choosing theparameters we imposed the following conditions: (a) fQ = — [fg of Chao et^ad. 's B]* at k ^  = 0.3y [w-y = 33 MeV], and (b) Re(l-AkJk) = 0 at m^ f+a) =1405 MeV. At the K~p threshold we obtained fg = 0.167+0.258i (fm).Figure 2 also shows fg of Chao et al.'s solution B. Our fg is not very different from -fg* of Chao et_ a^. for to-y 20 MeV. With a slight read­justment of fj, the K-p scattering data above the threshold can be fitted quite well. At the threshold, if we combine our fg with Chao et al.'s153a 1 = 0.08+0.69i, we obtain a(K-p) =0.12+0.47i which is consistent with the K~p atom result. For the width of A (1405) we obtain T ~  25 MeV which is too small as compared with the experi­mental value of F ~  40 MeV. We plan to extend the model such that the ttE chan­nel is explicitly taken into account.We expect that the fit can be signifi­cantly improved by such an extension.In summary, we have proposed a model which satisfactorily reproduces features (i), (ii) and (iii) enumerated in the beginning. Our model predicts that Refg > 0 above the threshold.This, together with the rapid variation of fg just above the threshold, will be a crucial test of the model. For other larger kaonic atoms, it has been known that the real part of the KN scattering length for a bound nucleon is positive; opposite in sign to that for a free nucleon. 1 1 This change of the sign could be achieved by a. strong binding effect. However, our model may not require such a strong binding effect.YN wishes to thank Dr. H.W. Fearing and Dr. D. Kiang for warm hospitality at TRIUMF, Vancouver and at Dalhousie University, Halifax, respectively, where part of the work was done. KSK is obliged to McMaster University for the award of graduate scholarships.The work was supported by NSERC of Canada.REFERENCES AND NOTES1. J.D. Davies, G.J. Pyle, G.T.A. Squire, C.J. Batty, S.F. Biagi, S.D. Hoath, P. Sharman, and A.S. Clough, Phys. Lett. 83B, 55 (1979).2. This is the so-called nuclear scattering length.3. We consider only s-states, and use the sign convention for the scatter­ing length; kcot<5 = a- 1 + ... . The effective ranges are known to be very small.4. Y.-A. Chao, R.W. Kraemer, D.W. Thomas, ,and B.R. Martin, Nucl. Phys.B56, 46 (1973).5. A.D. Martin, Phys. Lett. 65B, 346 (1976).6 . Here and henceforth, by "above the threshold" we mean k^a^ ^ 100 MeV/c.7. M. Atarashi, K. Hira,and H. Narumi, Progr. Theoret. Phys. 60,209 (1978).8 . Alternatively one can solve the Low equation and select a solution which has one CDD pole.9. M. Ida, Prog. Theoret. Phys. 2d, 625 (1959).10. If we put g=0, but use the same values of G, A and kc, the KN boundstate disappears.11. R. Seki and C.E. Wiegand, Ann. Rev. Nucl. Sci. 25, 241 (1975) sec. 4.2. Their sign convention for a is opposite to oursT3"1400 1500 C M eV )Fig. 2. The scattering amplitude fg in fm vs the total c.m. ener­gy in MeV. The solid and dashed lines represent Refg and Imfg, respectively. A is our result, while B is that of Chao et al.1s solution B. The K-p threshold energy is 1431 MeV.154A SEARCH FOR K“p -+ Ay AND K~p -> E°y AT RESTJ.D. Davies, J. Lowe, G.J. Pyle, G.T.A. Squier and C.E. Waltham University of Birmingham, Birmingham, EnglandC.J. Batty, S.F. Biagi, S.D. Hoath and P. Sharman Rutherford Laboratory, Chilton, Oxon., EnglandA.S. Clough University of Surrey, Guildford, EnglandA search has been made for photons from K“p -*■ Ay and E°y produced by K- stopping in a liquid hydrogen target. A 25 cm x 30 cm Nal(Tl) detector was used to detect gammas. The spectrum from 3 x 107 stopping K- is shown in Fig. 1. No signal for these reactions was found; upper limits on the branching ratios areRi = !^ -P AY -- « 4 x IO"4; R„ = ^ ^ 4 x 10~3.1 K p -> anything  ^ K p ■-> anythingA calculation of the expected rate has been made using the formalism of Korenman and Popov, 1 together with recent values of coupling constants and scattering amplitudes. The prediction is R 1 = 3.6 x 10-3 and R2 = 2.5 x 10-1+. The former is inconsistent with the present result.1. G.Y. Korenman and V.P. Popov, Phys. Lett. 40B, 628 (1972).155KAONIC ATOM OPTICAL POTENTIALS WITH PAULI CORRELATIONSI. E. Qureshi and R. C. Barrett University of Surrey, Guildford, U.K.ABSTRACTThe KMT method is used to evaluate the equivalent local optical poten­tial for 12C up to second order. The scattering amplitudes used are those obtained by Martin using analyticity constraints. The results using Fermi gas correlations and the closure approximation are substantially different from those obtained using correlations corresponding to shell model wave functions, both with and without closure.The strong interaction in a kaonic atom changes the energy by an amount e - i r / 2 .  The kaon-nucleus interaction_has frequently been represented by an optical potential VK proportional to Apm = Appp + &npn , where pm is the matter density and Ap and An the K- scattering lengths. Values of A" used (for pp = pn) have varied from -0.42 + i0.702 to -0.11 + i0.59. 3 If A is allowed_to vary freely to fit the data, the resulting effective scattering length Agff has the opposite sign for the real part_ (typically 0.34 + iO. 81. )4 Some analyses have included attempts to calculate Ae£jc by including the energy dependence of A 5 and others have calculated VK from a folding model6 or from a Brueckner type approximation to the many body theory.7^ 10 The last two of these have included a coupled channels treatment of the KN-Att system.In this work we calculate the kaon nucleus optical potential using the multiple scattering expansion of Kerman, McManus and Thaler. 1 1 The first order term is proportional to the nuclear matter density but the second or­der term due mainly to Pauli corrections is much more complicated due to energy dependence and nonlocality. We have calculated this term for the case of 12C using three different approximations. 12In terms of the two-body t-matrix the first order term in the opticalpotential is Ej_(o|t^|o) and this gives a potential proportional to theaveraged scattering length and matter density. The second order term is given byui2) = (o1y t.GQt.lo) - y. (0 11. |o)G.(o|t. |o) (1)K ... l "j 1 l 1 0 ' l 1= - i- y t [E - K - (e - e ) + ie]  ^ tA ^a,y<F ay 0 y a ya+ y t G t , (2)2 ^a,y<F aa 0 yyAwhere t = <a|t|y> and |a>,ea are nuclear single particle states and ener- . aygies.The results for several different scattering amplitudes using fermi gas correlations are shown in the table and the corresponding potential is given156in Fig. 1. The can­cellation between the first and second order terms reduces both the shift and width considerably but the imaginary potential has a pos­itive part over a longer region than is physically reason­able. The effect of using single part- cle wave functions is dramatic. In Figs 2 and 3 we show the potentials derived in this way, in this case using the atomic K“p wave function to obtain the equival­ent local potential.In Fig. 2 the dotted, dashed and full curves give the first-order potential, second- order potential and their sum respective­ly. In Fig. 3 they represent the sum of the first- and second- order potentials with the inclusion in the kaon propagator of average kaon-nucleus potentials with equal real and imaginary_i2o i parts and of depth0.5, 5 and 10 MeV, respectively. Some Fig. 1. First- and second- order equivalent local results from thesepotential using a plane-wave kaon wave function. calculations areshown in Table I .The inclusion of the second-order term reduces the shifts and widths far more in the case of Fermi-gas correlations than in the case of shell model correlations. This is mainly due to the fact that in the latter case the second-order correction is small near the edge of the nucleus, where the kaon wave function for the 2P state is increasing rapidly. For a much higher angular momentum state the positive imaginary part of the potential in the surface region could lead to a negative width, which is one reason for avoiding the use of plane w a v e s . An equally important reason can be seen in the results shown in Table I : the results vary strongly withthe values of the average nuclear excitation energy E and the average157Table I. Shifts and widths for the 2P state in 12C (in K e V ) .ReferenceType of calculationV(MeV) E(MeV) e rBackenstoss et a l 13 Experiment -0.59(8) 1.73(15)Bardeen and Torigoe5E-averaged K-N a-0.67 1.58Alberg, Henley and Wilets3Coupledchannel-0.62 1.27Th i e s 10 Coupledchannel-0.64(3) 1.50(6)Qu r e s h i 12 Fermi gas 0 10 -0.34 0.72II I I 0 30 -0.43 1.24II -30-i30 10 -0.45 2.72I I II 30 -0.14 2.42I I Shell model 0 -0.74 1.62I I II -10-ilO -0.73 1.60I I I I -50-i50 -0.69 1.63II Shell model + closure0 10 -0.74 1.64I I l l 0 30 -0.74 1.66II l l -50-i50 15 1 o u> 1.63kaon-nucleus optical potential used in the kaon propagator. In contrast the results of_the mioroscopic calculation are very insensitive to the values used for E and V. The results obtained are extremely dependent on the values used for the kaon-nucleon scattering amplitude.The coupled channel calculations and the microscopic calculations des­cribed here all produce a value for the shift within experimental error. The values for the widths differ somewhat although the rather low value obtained by Alberg et al. may be increased when that calculation is repeated with updated K-N scattering amplitudes. It may be possible to use the simpler microscopic calculation for the analysis of experiments and the investigation of nuclear matter distributions, but only after comparison with coupled channel results for each region of atomic numbers.158Fig. 2. The equivalent local potent­ial for K-12C using nuclear harmonic oscillator wave functions for the kaon in the 2P state.Fig.3. The sum of first and second order potentials as in Fig. 2, with the addition of an average ^-nucl­eus potential in the propagator.REFERENCES1. T.E.O. Ericson and F. Scheck, Nucl. Phys. B19, 450 (1970).2. J.K. Kim, Phys. Rev. Lett. 19^ 1074 (1967).3. A.D. Martin, Phys. Rev. 65B, 346 (1976).4. C.J. Batty, et al., to be published (1979).5. W.A. Bardeen and E.W. Torigoe, Phys. Lett. 38B, 135 (1972).6. A. Deloff, Nucl. Phys. B67, 69 (1973).7. S. Wycech, Nucl. Phys. B28, 541 (1971).8. J.R. Rook and S. Wycech, Phys. Lett. 39B, 469 (1972).9. M. Alberg, E.M. Henley and L. Wilets, Ann. Phys. 96_, 43 (1976).10. M. Thies, Nucl. Phys. A298, 344 (1978).11. A. Kerman, H. McManus and R. Thaler, Ann. Phys. Q_, 557 (1959) .12. I.E. Qureshi, Ph.D. Thesis (Univ. of Surrey), unpublished (1979)13. G .Backenstoss, J. Egger,H. Koch, H.P. Povel, A. Schwitter, and L. Tauscher, Nucl. Phys. B19, 189 (1974).159X-RAYS FROM ANTIPROTONS STOPPED IN GASEOUS H2 AND D2 TARGETSE.G. Auld, K.L. Erdman, B.L. White and J.B. Warren Department of Physics, University of British Columbia,Vancouver, B.C., Canada V6T 1W5J.M. BaileyDaresbury Laboratory, Daresbury, Warrington, U.K. and Inst, voor Kernphysisch Onderzoek, Amsterdam, The NetherlandsG.A. BeerDepartment of Physics, University of Victoria,Victoria, B.C., Canada V8W 2Y2B. Dreher, H. Kalinowsky, R. Landua, E. Klempt, K. Merle,K. Neubecker and W.R. Wodrich Institut fur Kernphysik and Institut fur Physik,Universitat Mainz, West GermanyH. Drumm, U. Gastaldi and R.D. Wendling CERN, Geneva, SwitzerlandC. SabevVisitor at CERN, Geneva, SwitzerlandX-rays from pp and pd atoms formed by stopping antiprotons in hydrogen and deuterium gas targets and 4 and 8 atm were detected in an array of Ar-methane proportional counters. This paper reports the results of more detailed analysis of the X-ray spectra, following our previous reports of the yield of L-X rays and the limit on the yield of K-X rays in antiproton­ic hydrogen and antiprotonic deuterium. 1 *21. E.G. Auld et al., Phys. Lett. 77B, 454 (1978).2. E.G. Auld et^  al., Proc. IV European Antiproton Symposium, Barr, France, June 26-30, 1978.160THE ATOMIC BOUND STATES OF THE pp SYSTEMWilliam B. Kaufmann Arizona State University, Tempe, Arizona, USA 85281The purpose of this calculation is to compute the strong interaction level widths and shifts for the Coulomb bound states of a proton and an antiproton. The real part of the hadronic potential is described by a meson-exchange potential and the annihilation by an incoming wave boundary condition. The incoming or "black sphere" condition is expected to give an approximate upper limit on the level widths consistent with smoothly vary­ing potentials. The calculation is an improved version of work published earlier in collaboration with H. Pilkuhn. 1 ’ 2The atomic states of pp- are bound approximately 10 keV or less, hence we use the non-relativistic Schrodinger equation. Both Coulomb and meson- exchange forces are included as is (in an approximate way) the n-p mass difference. Pion exchange dominates the long-range meson-exchange force and requires us to use coupled channels since it mixes the pp" and nn chan­nels (through 1 1 *1 2 ) and the £ and £+2 partial waves (through S^2 > coupled triplet case). From Refs. 1 and 2 the Schrodinger equation iswhere -2Vmo ttp2/2m + 2(mn-mp) + + V,0)0/In the kinetic energy terms we have approximated by nip = m; the primary effect of the mass difference has been included through the term 2 (mn -mp). The Coulomb potential is Vc = -a/r outside approximately 0.8 fm and is negligible inside that distance compared with the strong interactions. The pion-exchange force is the conventional form:V = (1/3) f2[o1 *a2 + Y(m7Tr)S12] exp(-mTrr)/r ,where Y(x) = 1 +3/x +3/x2 , f2 = 0.079 and S 12 is the tensor operator. Theshort-ranged rn and "a" exchange are taken to be of the simple formVmo = “G? exP(-mur)/r, G2 = 30.The results are not strongly dependent on GQ for the atomic (vs quasinuc­lear) states. 1 We plan to use a more realistic form for the short rangeexchanges in a more complete calculation now in progress.To introduce annihilation we have used a variant of a very old method. The WKB method is used locally to separate incoming and outgoing waves at a "boundary radius" rc . 3 We then impose the condition that no outgoing waves pass rc . This is essentially the "black sphere model". Annihilation occurs via coupling to mesonic channels for a radius less than Annihilation ~  0-5 fm < rc, but the details of the annihilation process are irrelevant in this extreme black sphere model. If the annihilation region reflects some incoming wave, the ratio of outgoing to incoming parts of the wave function could be fixed at some small value ("grey sphere model"). A theoretical value of this ratio would require a model for the161annihilation mechanism. Present data are not precise enough to rule out the extreme black sphere model (see contribution 5E8 to this conferenceof a grey sphere model.The mathematical structure of the boundary condition is, for a singleTo apply the boundary condition to a coupled channel problem we diagonalize the potential matrix V at rc and apply the boundary condition to each com­ponent of ^ at rc . In classically forbidden regions we use the analytic continuation of the above boundary condition— an outgoing exponential. Forr. This method of handling coupled channels differs from that of Ref. 2 and gives results more nearly independent of rc . I would like to thankH. Pilkuhn and F. Myhrer for advice and correspondence on this point.To get an intuitive feeling for the dynamics, consider the schematic picture given in Fig. 1. The Coulomb well is exaggerated to make it visi­ble on this scale. The inner turning point is typically 1-2 fm while the Coulomb well is at approximately 60 fm. Particles from the Coulomb well leak through the barrier and are pulled into the annihilation region by the strong hadronic attraction. Assuming no reflection from the annihilation region any flux which gets within the turning point r3 will eventually be absorbed provided that the potential is smooth enough in the region ra to r^ for the WKB method to be valid. Under this condition the choice of rc in the interval ra to r^ is arbitrary (see result 2 below).The solution of the Schrodinger equation was done numerically as is described in (2). The only role of the WKB approximation is to define the boundary condition at rc.The results may be summarized as follows:I. The predictions for the n = 1 s-states and n = 2 p-states with earlier models is given in Table I (the 2s states are soon to be calculated).2. The annihilation width Tann, the level shift e(= Re(E) - ECou2) and the relative normalization of the components of ^ are nearly independent of rQ . See Table II. This suggests that the WKB approximation is valid between ra and r^. The anomaly at small rc found in Ref. 2 is absent when the present boundary condition is employed.3. Angular momentum mixing: The total percentage of £+2 state mixed into the dominantly i state is very small; however, for small r (^1 . 2  fm)and ip£+2 are comparable. This is illustrated for the 3PF2 state in Fig. 2. The addition of the 3F2 component into the 3P2 state gives a sizeable change in F and e as can be seen in Table I.4. Isospin composition at r£ : In the 3PQ and 3P 3 cases i^ (rc) is nearly an eigenstate of isospin. This is clearly seen in Fig. 3 for the 3PQ case. The pp" components dominate at large values of r but for small r the pp- and nn components are nearly equal in size but opposite in sign, corresponding to isospin zero. In the other cases the isospin is mixed at rc but still favors the "dominant isospin component", i.e. the isospin of the most attractive eigenpotential of Ref. 1. The percentage of I = 1 at rc is listed in Table Borie and Leon4) ; hence it is premature to introduce the complicationschannel, 2k Hi'/3 (g) _ 1Hi/3(5) 2[k'/k - k/£;] ,all n = 1 , 2  there is at least one classically allowed channel1 for small1625. Suppression of the transitions to the K-shell: See also Ref. 1 andfurther references therein. Even in dilute gases for which Stark mixing is negligible, transitions to the K-shell are rare. This can be understood by taking together a) the cascade process preferentially populates circular orbits (n = L+l) , b) the radiative dipole transition 2p -*■ Is has a rate r-y = 3.7><10-l+ eV while the annihilation width from 2p levels (in the black sphere limit, spin averaged) is rann = 3xl0~2 eV. Thus the probability of radiative transition to annihilation from the 2p level is of the order of 1%. If annihilation were described by a grey sphere, Tann would be smaller and the radiative probability correspondingly increased. On the other hand, the radiative 3d -* 2p transition has a width = 3.8xl0- 5 eV com­pared with the 3d annihilation width of roughly 10" ^ eV; thus the L line is expected to be (and is) seen. The prediction of intensities requires the calculation of the full atomic cascade process.1*I would like to thank H. Pilkuhn, F. Myhrer, E. Borie and M. Leon for their advice and comments.REFERENCES1. W.B. Kaufmann and H. Pilkuhn, Phys. Rev. C17, 215 (1978).2. W.B. Kaufmann, Phys. Rev. C19, 440 (1979).3. See, for example, O.D. Dalkarov and F. Myhrer, Nuovo Cimento 40A, 152 (1977) and references therein.4. E. Borie and M. Leon, X-ray yields in protonium, Univ. of Karlsruhe preprint TKP 79-7 and #5E8, Abstracts of Contributed Papers, 8th Int. Conf. on High Energy Physics and Nuclear Structure, p. 148.Table I. to the FSummary of Is wave while 3PFand 2p widths, 2 includes it.The state labelled 3P2 ignores the couplingStatePresent work Ref. 2 Ref. 1 Fraction 1=1 at rc£ (eV) r (eV) £ (eV) r (eV) r (eV)23P0 -0.070 0.116 -0.069 0.118 0.194 0.0323Pi 0.033 0.015 0.035 0.016 0.030 0.982 3P2 -0.003 0.016 small 0.010 - 0.4423PF2 -0.007 0.027 - - 0.043 0.372*Pi -0.029 0.020 -0.028 0.014 0.020 0.321'Sq 500 1350 430 1060 - 0.31l3SDi 750 1000 - - - 0.542lso 58 180 - - - 0.3023SD! 94 132 - - - 0.54Table II confirms resultsDependence of T and e on rc. The weak dependence the consistency of the black sphere model. The are similar for the other partial waves.rc (fm)3pro ise (eV) r (eV) e (eV) r (eV)0.5 -0.0699 0.116 490 13020.8 -0.0699 0.116 504 13501.0 -0.0699 0.115 473 13901.2 -0.0695 0.114 441 13701.4 -0.0685 0.114 433 13501.6 -0.0675 0.116 446 13861.8 -0.0667 0.119 passed turning point163Boundary radiusFig. 1. Schematic picture of the effective potential for protonium.Fig. 2. Angular momentum mixing in the 3PF2 state. Note that although pp” dominates for large r, for small r they are comparable. The nff com­ponents are not shown.Fig. 3. 3PQ wave functions. As r decreases, the curves become almost symmetrical about the x-axis. This indicates annihilation from the 1=0 state.164EN EFFECTIVE POTENTIALS IN E_ ATOMSJ.A. Johnstone McMaster University, Hamilton, Ontario, Canada L8S 4M1J . LawUniversity of Guelph, Guelph, Ontario, Canada NIG 2W11. INTRODUCTIONEN scattering parameters of Alexander et_ al . 1 are consistent with two sets of scattering lengths. Combining these sets with the recent E- atom data2 ’ 3 we perform an analysis of all data in an attempt to distinguish between the two sets of scattering lengths.2. EN POTENTIAL MODELWe assume complex, Yukawa-shaped potentials to describe the EN inter­actions :e-prVEN<r) = Vj! —  .These are folded4 into the nuclear density distributions to calculate the E atom level shifts. Since the E“n interactions are real, we essentially have seven potential parameters, assuming that the range y- 1 is the same in all interactions.Initially, the strength parameters Vjj were determined to fit the central values of the scattering lengths, and the range y- 1 varied to mini­mize the x2 fit to the level shifts of the E atoms. It was found with this procedure that the fits to the atoms were consistent with both sets of scattering lengths and that the x2 did not favour either set. In view of this we decided to perform a joint fit to the atomic and scattering length data by varying all six strength parameters Vjj and the range y-1.Our final results are shown in Tables I and II. The total x2 °f the fits for 16 degrees of freedom are 1 0 . 1  and 8 . 1  for scattering length sets 1 and 2 of Alexander's data, respectively. Although the total x2 seem to favour set 2 , a comparison of the results indicates that the difference is due mainly to the scattering lengths. The E atomic x2 are almost in­sensitive to the differences between the sets.The resultant potential strengths favour a weak, repulsive E-n trip­let interaction, rather than strong attraction. The overall indication is that the EN potentials are weak relative to the NN case and the resultant range is between the one- and two-pion ranges.3. CONCLUSIONSOur results indicate that it is still not possible to distinguishbetween the two sets of scattering lengths of Alexander et_ al., even withthe inclusion of the E atom data. This is probably due to the large ex­perimental errors in the latter. However, our results do indicate thatboth sets of solutions prefer a repulsive E~n triplet potential.165REFERENCES1. G. Alexander et_ Al. , Phys. Rev. D6  ^ 2405 (1972).2. C.J. Batty et al., Phys. Lett. 74B, 27 (1978).3. H. Koch, Proc. 5th Int. Conf. on High-Energy Physics and NuclearStructure, Uppsala (1974), p. 225.4. A. Deloff and J. Law, Phys. Rev. CIO, 1688 (1974).Table I. Scattering lengths and potential depths (MeV) for best fit to data with y = 1.20 and 1.30 fm-1for set 1 and 2, respectively.Scattering Experimental Calculated Potential DepthLength Set (1) Set (2) Set (1) Set (2) Set (1) Set (2)(fm) Re (a) Im(a) Re (a) Im(a) Re (a) Im(a) Re (a) Im(a) Re (V) Im (V) Re (V) Im(V)E'n (s=0) -1.4+1.3 0 0.812.0 0 -1.70 0 -0.07 0 -51.24 0 -5.55 0£"n (s—1) 0.7±0.4 0 0.810.7 0 0.32 0 0.31 0 24.82 0 31.32 0£ p (s=0) 0.4±0.9 -0.510.6 -0.611.7 -1.011.8 0.15 -0.11 -1.00 -0.42 9.81 -8.32 -50.11 -11.1T. p (s—1) -0.5±0.5 -1.110.5 -0.610.6 -1.010.9 -0.75 -0.48 -0.81 -0.66 -35.30 -13.04 -48.11 -19.6Scattering x2 3.,36 0.,66Table II. Best fits to level widths and shifts consistent with the scattering data.Element Transitionn+l+n enExperimentalr rn ‘n+l (eV)£nSet (1) rnCalculated rn+l EnSet (2) Fn Fn+1C 4+3 - - 0 .031±0.012 24.2 17.6 0.020 25.1 18.9 0.0180 4-+3 320±230 - 0.983;!! 212.8 171.4 0.313 222.5 189.7 0.297Mg 5+4 25+40 <70 ii-S: o°7 35.1 25.3 0.087 35.8 26.4 0.082AlSi5+45+468±28159±3643±75217±100 24+0-(l6-0.05 n ai+0.11-0.0964.9143.949.1108.40.1870.50462.9148.651.1116.20.1730.483P 5+4 - - - 258.3 205.0 1.063 256.7 219.7 1.019SCa5+46+5360+220 8701700 1 47+1‘01 -0.560.4010.22480.837.5385.126.82.2950.181502.537.2424.027.22.2450.165Ti 6+5 - - 0.66+0.43 96.9 75.2 0.616 86.7 76.3 0.568Ba 8+7 - - 1.68+3.60 49.4 40.5 0.930 33.1 38.1 0.806Atomic x2 6.71 6.99Total x2 10.07 8.10166SHORT RANGE CORRECTION TO THE ENERGY LEVELSF . AndoIryo-Gijutsu Tandai/Physics, Shinshu University, Matsumoto, JapanABSTRACTBound state level shifts due to the short range interaction are studied by means of the Jost function in nonrelativistic potential scatter­ing. A convenient parametrization has been used to describe the shift in cases where the usual expansion of the amplitude in the strength of the perturbation is inadequate, thus the dynamics of the shift may be inferred easily. The formalism is illustrated by the use of soluble two square well potentials to obtain the displacement of levels.INTRODUCTION AND SUMMARYEffects of short range strong interactions on the energy levels of hadronic atoms have been widely studied. 1 In particular, whether the levels shift upward or downward under the influence of a strong attractive force has drawn much attention recently. 2 When the Coulomb potential is disturbed by an attractive short range force, atomic levels are deepened when the perturbation is weak, but are pushed out when it becomes strong enough to develop its own bound state. Away from such a situation, the Born approximation may be used to estimate the energy shift, but in order to see its variation with the potential strength, either one resorts to numeri­cal solutions of Schrodinger equation or makes use of a simple model to infer physics.Although a realistic calculation should be rather involved, the basic mechanism of such effects may be understood transparently by means of Jost functions when the potential is of simple form. Zeros of the Jost function on the negative imaginary axis of the complex momentum plane will determine the bound state energies. One considers two potentials of different range and strength to simulate the Coulombic and nuclear interactions. Suppose one knows the energy levels of the longer range potential in terms of its Jost function fQ(k). The shift of any particular level due to the short range force can be evaluated from the complete Jost function f(k). Obvi­ously, to obtain f(k) is just as hard as solving the complete Schrodinger equation itself in general. In this article, it is attempted to express the Jost function f(k) as a sum of regular and irregular solutions of the unperturbed Schrodinger equation, the ratio of the two depending in turn on the perturbation, which can be determined iteratively. If one takes two square well potentials as long and short range forces, respectively, the effect of the latter is describable with a simple parameter. The exact and approximate level shifts are then compared. The Born approximation does not tell when the shift changes its sign. For this it seems necessary for any approximate Jost function to satisfy the boundary condition at the edge of the short range force. One such form is presented and its validity is discussed.GENERAL APPROACH TO DETERMINE 6fConsider an attractive potential V(r) of range r^ outside which there is no interaction. Throughout this paper we consider only s-wave167interactions for simplicity. The regular solution <j>0(r) is characterized by (jq (0) = 0 and <j>J (0) = 1. Then the Jost function fg(k) is expressed asf0 (k) = e lkrA(ik<}>0 (rA) + <f>0'(rA)) , (1)where k is the wave number for the total energy E. When there is a short range perturbation 6V of range r^ which is much smaller than rA , the Jost function f(k) for V + 6V is similarly expressed in terms of the corre­sponding regular solution <J>(r):f (k) = e ikrA(ik<j)(rA) + 4>f (rA)) • (2)The function c)>(k) is a linear combination of <f>0 (k) and ^0(r), a solution of V independent of <J)Q (r) , in the region between r^ and rA :<(>(r) = C ^ q (r) + C2<)>o (r) •The boundary condition at r = rN determines the coefficients:andwhereand(3)(4)(5)The Eq. (3) is not an integral equation: <}>(r) for r^ < r < rA is determined if <j)(r) for r < r^ is known. Now <}>(r) for r < r^ in turn satisfies the integral equation:Hr)  = <f>0O ) - ^  f [<f>0 (r)ijj0(r ') - (r) <|)0 (r ' ) ]  <$V<(> (r ') dr ' . (6)0One may try to solve Eq. (6) by iteration, which however is not suit­able for our present purpose. When the perturbation is of very simple form, e.g., a square well, the equation has analytic solution if the argu­ment in the parenthesis is a function of r - r ' only. This suggests thatAlternatively C's are described in 6V:168one expresses 6V as a sum of a square well and the rest 6U, which is then treated as a small perturbation.Bound states may be found from zeros of f q (k.) or f (k) on the negativeimaginary axis of the k-plane, i.e., fg (-ii<) = 0 or f(-iK) = 0 , wherek = -iK and k > 0. Level shifts due to the perturbation <5V may be found by inspecting f(k) and fQ(k). As a simple case, consider a potential V(r) consisting of a square well, disturbed by 6V of another square well. One has then the explicit form:e-KrAf0(k) = -----  sin k2r^(< + k2 cot k2rA) ,k2f(k) = Cj [e KrA (k sin k2rA + k2 cos k2rA)]+ C2 [e KrA (< cos k2rA - k2 sin k2rA)] . (7)On the other hand,f(k) = e KrA[i<cj>(rA) + <f>'(rA)]= Ae KrA sin(k2rA + 6)[k + k2 cot(k2rA + 6)] , (8)where k2 is the wave number for the kinetic energy in rjq < r < rA ; andA _ q cot q - E, cot g® q + 5 cot £ cot q ’£ = kiRn , q = k2r^ ,A = l/rN (l/ £ 2 sin2£ + 1/q2 cos2q) - 1 ^2 ;and kj the wave number for the kinetic energy in r < r^.The Eq. (8) implies that the zeroes of f(k) are shifted from those of fq(k) by the amount determined from the "phase shift" 6 , which in turn depends on the strength of the perturbation. Thus 6 increases from zero as SV increases, resulting in the increase of binding energies, a result familiar in the perturbation theory. As 6V increases further, levels appear to move upward as if pushed; a result elaborated by Shapiro's group is now well known. The interpretation in terms of 6 will have physical implications and will be possible in general. Take, for instance, an un­perturbed square well plus an arbitrary short range potential. The fore­going statement is valid and the effect of the short range interaction can still be described in the phase shift. If the unperturbed potential does not vary rapidly in its range, it looks possible to make a similar statement.APPROXIMATIONSLet us now confine ourselves to calculate the level shift or equiva­lently the shift of wave number 6Kn of nth level due to perturbation. For illustration we use the familiar potential: two square wells. Away from the anomalous region where the shift varies strongly and changes its sign, the Born approximation may be used. If one is interested in where the sign changes, such approximation is not useful at all.169If the variation 6f of the Jost function fg(k) due to the short range potential 6V is evaluated, then the 6Kn may be determined:6Kn = -6fBf rBk(9)The question is how to calculate 6f. Calculated by iteration in 6V as indicated in the previous section, the first approximation is simply the Born term. On the other hand, if one makes use of the fact that fg(Kn) = 0 and f(Kn+6Kn ) = 0 and keeps only the first order term in <SKn , one obtains1 2pV <5k„ = ------7T-n kg h2k s i n x c o s x  -  Xk2 sin2x(sin^cosp - —  cos^sinp) , (1 0 )nwhere x = ^2rA*Only the last factor depends on the strength of perturbation, which is used to locate zeros of f(k) with good accuracy when the perturbation is strong, where zeros of sin 5 and cos 6 of Eq. (8) are getting close together, imply­ing the level rearrangement occurs in a very narrow region. When the per­turbation is strong and rN << r^, the region depends little on energy. An analytic formula of 6i<n in this narrow region can be obtained straightfor­wardly with Eq. (8).In order to treat cases where the effect of annihilation on the energy levels within the potential theory, one has to examine coupled-channels equations. Again the Jost matrix can easily be constructed when the anni­hilation is represented simply by a square well potential.The author would like to express his gratefulness to Professors J.S. Blair and L. Wilets of Summer Research Institute on Nucleus-Nucleus Interactions, University of Washington, for the hospitality extended toward him, where a part of this work was done.REFERENCES1. See, e.g., I.S. Shapiro, Phys. Reports 35C, 129 (1978).2. A.E. Kudryavtsev et al., Sov. Phys. JETP V7 (2), 225 (1978).170DATA OF HADRONIC ATOMS: A SURVEY ON X-RAY ENERGIES, LINEWIDTHS AND INTENSITIESH. Poth*Institut fur Kernphysik, Kernforschungszentrum Karlsruhe, and Institut fur Experimentelle Kernphysik, Universitat Karlsruhe, Karlsruhe, Federal Republic of GermanyA survey of the experimental data for hadronic atoms is given. The compilation1 covers 58 pionic, 54 kaonic, 23 antiprotonic and 20 sigmonic atoms and contains the energies, linewidths and intensities of the X-ray transitions.The data and the strong interaction effects are discussed. The intensities are analysed with a simple cascade model. A listing of the measured X-ray energies is given.1. H. Poth, Compilation of Data from Hadronic Atoms, Physics Data 14-1, 1979, Fachinformationszentrum Karlsruhe, Federal Republic of Germany.-'Visitor at CERN.171AN IMPROVED KAON BEAM AND SPECTROMETER FOR THE AGS E,V, Hungerford XII University of Houston, Houston, Texas 77004t ABSTRACTThis paper reports on the properties of the existing low energy separated kaon beams at the Brookhaven AGS, and the preliminary plans to construct an improved kaon beam line with a high resolution spectrometer for this facility,INTRODUCTIONLet me begin with an illustration, I was told a number of years ago that in a certain community two dairies were competing for the rather limited business in the area, Each dairy, in selling its product, tried to project an image that would favorably impress its potential customers. One advertised "milk from contented cows". This sounded so reasonable and appealing that everyone became convinced "milk from contented cows" was the superior product. However, the other dairy was rescued, in a moment of inspiration, by advertising "Our cows are not contented-they are always striving to do better'"In recalling this story I am reminded that there are those who say "why consider a kaon factory now?", in other words "Why can't you be con­tent with the physics provided by the present machines?" The answer, of course, is nuclear physics cannot be so confined if it is to survive.New ideas must be pursued with vigor and determination.I leave for others at this conference the task, if it really needs to be done, of convincing you that the kaon is one of the exciting nu­clear probes of the future, I will here describe the present plans to provide an improved kaon beam line for nuclear research at the Brookhaven Alternating Gradient Synchrotron (AGS). I must first tell you that these plans are extremely tentative at the present time and though I take full responsibility for any inaccuracies in reporting them to you, the plans are being developed by a number of physicists. There are two existing low momentum kaon beam lines at the AGS. You should note that they are not only transport kaons but antiprotons as well. In fact the newest o£ the beam lines, LESB II, has been used exclusively for p experiments. After describing these beam lines I will outline in general terms the plan to develop an improved beam line and spectrometer system for nuclear experiments at the AGS, I will conclude with a few summarizing remarks and personal comments.EXISTING BEAM LINES AT THE BROOKHAVEN AGSThe Alternating Gradient Synchrotron (AGS) at the Brookhaven Nation­al L a b o r a t o r y  accelerates protons to 28,5 GeV/c with a spill every 2.4 seconds. The length of the spill can be varied to some extent, but in general it is about one second in length. Proton intensities incidenttWork supported in part by DOE contract EY-76-S-05-3948172.0012 0  3 0  4 0PROTON MOMENTUM (GeV/c)on a production target range from 2x10^2 to about 4xl012 per spill.' The present kaon production target is a platinum plate with an effec­tive length of about 3,5 inches,The cross sections for par­ticle production as a function of1 9incident proton momentum are shown in Figure 1). The main feature of the kaon production curves is a rapid rise with a "knee" below 10 GeV/c. However at K a o n s / s r - G e V / c - I n t e r a c t i n g  P ro to n  30 GeV/c the kaon production cross I GeV/c p rod u c e d  at 5 deg. . . . , . 0  • b i ­section is about 3 times the pro­duction cross section just above the knee. This is not an insig­nificant factor for present ex­periments using the existing beam intensities. Designs for kaon factories have generally selected a primary beam momentum just above the "knee" of the production curve (-10 GeV/c) , 3 As can be seen from Figure 1), this momentum is some­what too low for p production and it also gives away some intensity if compared to the number of kaons that could be produced with higher beam momentum, However the over­riding consideration for a kaon factory is the cost to build the acceleration ring, compared to the cost of increasing the intensity of the primary beam.At the AGS, the beam line that has been used for the kaon experiments reported at this work­shop is the Low Energy Separated Beam I (LESB I) , 4 The beam line is shown in Figure 2 . 5 , It is 15.24 meters in length and transports particles up to 1 GeV/c in momentum with a variable momentum bite. Ty­pical values of Ap/p are ±1.5%.The ir/k ratio is about 10 if the electrostatic mass separator is properly tuned, Actually, this ratio is almost a universal con­stant for all existing separated beam lines. Kaon intensities of about 2x 1 0  ^ into an area of 1 cm by 10 cm have been obtained at the focal postion, about lm downstreamPROTON MOMENTUM (GeV/c) Figure 1) Particle production for kaons and antiprotons as a function of a primary beam momentum.173LESB I BEAM LINEFigure 2) LESB X Beam Linean angular bite A0 equal meter is relatively flatfrom the output quadrupole, As is obvious, all bends in the transport system are horizontal, and the mass separation is vertical. The pro­duction angle is 10° with an acceptance of 2.65 msr. The production target is 3,5" of Pt.The spectrometer constructed at the end of this line was built of standard beam transport magnets, with field clamps added to improve the fringe field characteristics. It is shown in Figure 3), The power supplies are regulated by Hall probes to 1 part in 1 0 The spectrometer is of the energy loss type with a dispersed fo­cus at target, A series of multiwire propor­tional detectors are used to define the particle trajectories. The analyzing portion of the spectrometer has an acceptance of 12 msr, with to 5°, The momentum acceptance of the spectro- over a region with a momentum bite of Ap/p = 6%.Figure 3) Brookhaven Kaon Spectrometer Ln the notation S represents Scintillators,P-wireplanes, C ~ Cerenkov detectors, DC- drift chambers, Q-^quadrupole magnets, and D-dipole magnets.Kaons are identified by a differential Cerenkov detector, CK, and time of flight. Time resolution of about 500 psec FWHM has been achieved over both the front and rear elements of the spectrometer system. Back­ground from K decays near the target is reduced by a liquid hydrogen Cerenkov detector, CH. Figure 4) shows the energy loss resolution of the spectrometer, analyzing the kaon beam with no target in place. Best resolution is achieved by restricting the solid angle acceptance. Full acceptance gives a resolution of about 1.4 MeV/c FWHM and shows that the higher order corrections to the transport problem are not yet understood. This has not been a limiting factor at the present time because the resolution has been determined by target thickness. Work is continuing in trying to understand the spectrometer, however.The spectrometer described above has been used for hypernuclear studies with the (K~,tt“) reaction, and kaon elastic scattering. Future experiments will continue the investigations using a series of target174nuclei including, xLi, ll+N, iiiC, lb0, and 180,A new low energy separated beam (LESB II) was designed to provide an in­creased flux of k's and p ’s. It is shownin Figure 5). It features two separators and optic corrections to the beam trans­port using a sector magnet with curved pole edges for the front dipole and a sextupole between the separators. The length of the beam line is about 15.25 m. The production angle is 5° and the solid angle acceptance 12.9 msr. Mainly because of the larger solid angle the line is ex­pected to have about 6 times the intensity of LESB II, In addition the improved optics and dual separation of the beam was expected to provide an improved ir/k ratio. The beam line has both a dispersed and a recombined focus after the last quadrupole. The momentum resolution in the dispersed beam is poor although the momentum dis­persion is Ap/p = .5%. To date the line has only been used for p experiments and no serious attempt to determine the k flux has been made. The measured number of p's compares favorably with the predicted intensity (1.5xl03p/1012 protons), but a much greater pion cdn- tamination than was anticipated was observed. Vertical images at the mass slit are consistent with the beam Monte Carlo calculations without optic corrections. This would indicate that the k flux should be near the calculated value of 2xl05sec-1 but the ir/k ratio will probably be much larger than predicted. It is not clear why the background pions are so intense. However, it does seem clear that before this line can be used for kaon physics this problem must be carefully studied and the problems eliminated.Some consideration is being given to mov­ing the existing spectrometer on LESB I to LESB II, Advantages would be increased flux and possibly larger angular coverage. However the increased flux on LESB II is accomplished by an increased beam line acceptance so that a spectrometer on this beam line needs to be carefully matched to the beam line acceptance to take ad­vantage of the higher intensities. Table I compares and summarizes some of the characteristics of these two lines.- C  - I  UENERGY LOSS (MeV) Figure 4) Energy loss reso­lution of the Spectrometer for straight through beam.The histogram is for the full solid angle, the dashed line is for a restricted solid angle.Figure 5) LineLESB II BeamNEW BEAM LINE/SPECTROMETER AT THE AGSThere have been a number of informal discussions, and one workshop meeting7 to plan a new beam line-spectrometer system for nuclear physics at the AGS, The need for a new system is based mainly on intensity.175TABLE I, Comparison of the LESB I and LESB II Beam LinesLESB I LESB IIAS7A£ 10.6 mr% 77.2 mr%PA£ ± 0.02 ± 0,03PA9 2.65 msr 12.9 msrA9v ± 11 mr ± 15 mrA9r + 60 mr ± 215 mrLength 600" 600"1524 cm 1524 cmDecay Factor K~/1012p0.079 0.079 800 MeV/c8 x 1 0 1* 4.7 x 1 0 5 <3 800 MeV/c4 x 10^ 2.4 x 1 0 5 <3 700 MeV/c2 . 2 x IO4 1.3 x 1 0 5 <3 600 MeV/cOptical calculations and measured angular distributions show that positive kaon elastic cross sections in regions where interesting nuclear physics should occur are about lyb/sr or less. 8 The (K- ,tt~) reaction to a number of important hypernuclear levels is also about thisorder of magnitude. 9 Several other reactions such as (K-,K+) have muchlower cross sections (-lnbarn) . 10 With present beam intensities (~2xl0i+/ spill) count rates are about 3 per ybarn-sr-hr using reasonable target thicknesses,TABLE II. Tentative Design Goals for a new Beam LineSpectrometer for Kaon-Nuclear Studies at the AGSBEAM LINEChannel Length - 8-10 m Momentum Bite - Ap/p-4%Flux - K+0800 MeV/c-106 ir/k ratio - 1 0  or betterBeam size - (3x10)cm Range - 500-800 MeV/cSPECTROMETERAngular Resolution - .25°-.5° Energy Resolution-Ap/p=7xl0-Lf(200 kev @ 800 MeV/c) Momentum Bite - Ap/p=6%(AE 38-MeV with a 30" focal Plane-lmm resolution) Solid Angle - 30 msr Momentum - <.800 MeV/c Angular Coverage - 0°-140°To develop the field of kaon and hypernuclear physics a gain of at least a factor of 10 in intensity is needed. Given the primary current capabilities of the present machines this can best be achieved by short­ening the beam transport length, and to a lesser extent by increasing176the acceptance of the transport and spectrometer system. A short beam line is also advantageous because kaons with lower momenta (300 - 600 MeV/c) seem to hold the most promise for nuclear physics research. 8It is probably necessary to use the beam line itself as the dis^ - persing system for the energy loss spectrometer. One might consider placing counters of some type in the beam line to determine the particle trajectories, but more than likely the intensity will be too high for reliable operation. Therefore the beam line needs to be carefully de­signed to provide proper dispersion at the target, and it should be matched to a large solid angle spectrometer.Tentative design goals for the new system are outlined in Table II. Preliminary design work has begun and a second working group meeting will be scheduled this fall. Provided funding can be obtained the new system might be operational by 1984 or 1985 which also matches the pro­posed construction shutdown and startup dates for ISABELLE. As can be observed from the figure the beam line spectrometer system requirements are modest and are well within present technical capabilities.CONCLUSIONSKaon physics is in a position similar to that of pion physics about 15 years ago. Beams are not sufficiently intense or pure to allow de­tailed work in nuclear structure. What can be done is a series of ex­periments observing strongly excited states or reactions with larger cross sections, looking for rather large effects. Statistics will be a major limitation in the extraction of useful information.With the existing beams cross sections on the order of a pb/sr or so can be measured, and perhaps some coincidence experiments such as (Kj K', y) may be attempted, but these will be difficult and will not yield in­formation of high quality. What can be done is to provide the justifica­tion for a major construction program to provide more intense sources of K-mesons, Hopefully this program can be initiated in the not too distant future.ACKNOWLEDGEMENTSThis paper is a report and as such is primarily based on the work of others, I appreciate the information and help of D. Lazarus, M. May,R, Regge, C. Dover, P. Barnes and numerous other colleagues. The en­couragement of H, Palevsky is gratefully acknowledged.REFERENCES1) J.P, Sanford and C.L. Wang, "Empirical Formulas for Particle Produc­tion in p-Be Collision between 10 and 35 BeV/c", BNL-11299 and BNL- 11479 (1967),2) Bevatron Handbook, LBL—1973Argonne National Laboratory High Energy Physics Division InternalReport ANL/HEP 6801,3) See reports in New Facilities Session in the Proceedings of the Conference on Meson-Nuclear Physics, AIP Conference Proceedings Vol54, E.V. Hungerford, editor, (1979).4) M. May, "Physics with a New Kaon Facility at the AGS,' report to this177conference,R. Eisenstein, "Experimental Elastic and Inelastic Kaon Scattering", report to this conference,5) H. Palevsky, "K- Beams Available Now and in the Future", "Proceed­ings of the Summer Study Meeting on Nuclear and Hypernuclear Physics with Kaon Beams", BNL-18335 (1973),6) D,M, Lazarus, "Proceedings of the Summer Study Meeting on Kaon Physics and Facilities", BNL-50579 (1976),D.M. Lazarus, private communication.7) Organized by H, Palevsky,8) C.B, Dover and G.E. Walker, "Kaon Elastic Scattering and Charge Exchange on Nuclei", preprint (1979),9) R.H, Dalitz and A. Gal, "The Formation of, and y Radiation from,the p-shell Hypernuclei", Annals of Physics, 116, 167 (1978),10) C.B. Dover, private communication.DISCUSSIONPOLLOCK: Can the kaon lines share a production target?HUNGERFORD: Yes.POLLOCK: Will the proposed new kaon facility replace one of the existingchannels or will it be in addition?HUNGERFORD: I don't know. I believe that present plans are for a newaddition.POVH: Why is the LESB II resolution bad? Was it intended to be goodor not?HUNGERFORD: LESB II was not designed to provide good momentum resolution.Flux and tt/K ratio were emphasized.POVH: The new facility will have about the same characteristics asLESB II. Why do you believe it will be better?HUNGERFORD: The new line should be shorter, the dispersing section of thespectrometer will be included in the beam line, and in general the spec­trometer and beam line will be matched to provide good resolution with high count rate.BROWN: Have you considered lowering the proton beam energy and increasingthe repetition rate to get better K-flux? Isn't it true that if you lower the primary beam energy, the r-to-K ratio gets worse?HUNGERFORD: This is true; however, it will depend somewhat on the sourceof the pions in the K beam and the operation of the separator.178THE FERMILAB BOOSTER AS A KAON FACTORYB. Brown and C. Hojvat Fermi National Accelerator Laboratory*, Batavia, Illinois, U.S.A., 60510ABSTRACTWe review the performance of the Fermilab rapid-cycling Booster em­phasizing those aspects which allow acceleration of up to 4 . 5 xlO-^ protons per second to energies of 8 to 10 GeV. Characteristics of a kaon factory based on this machine will be discussed.INTRODUCTIONWith the success of the high intensity medium energy accelerators (the "meson factories", TRIUMF, SIN, LAMPF) attention has shifted to the design of accelerators of sufficient energy and currents (tens of yA) to provide large kaon fluxes for research. Designs for new accelerators are the reason for this workshop. It is our purpose to evaluate thepossibilities of the Fermilab Booster as a kaon factory. To this aim wewill ignore the_increasing commitment of the Booster to the future HighEnergy Physics pp collider program at Fermilab.1The potential of existing synchrotrons as kaon factories was already discussed by L. Teng.^ The advantage of the proton flux obtainable from a rapid-cycling accelerator like the Fermilab Booster was clear from that comparison. On the other hand, methods of increasing the naturally low duty factor are mandatory.In the first section we describe the Fermilab Booster accelerator, its present performance and possible maximum intensity achievable. In the second section the characteristics of a kaon factory based on the Booster will be discussed.THE FERMILAB BOOSTEROThe Fermilab Booster accelerator0 has an injection energy of 200 MeV and a nominal top energy of 8 GeV. At present it is operated at 9 GeV as part of an upgrading program towards future operation at 10 GeV.The guiding field is provided by combined function magnets excited with a resonant power supply at 15 Hz. The vacuum vessel is provided by the laminated pole pieces, and no vacuum chambers are utilized in the regions of magnetic field.^ The average radius is 75.47 meters.The Booster lattice consists of 24 identical periods, with no super­period structure. Each period consists of 4 combined function magnets, two focussing and two horizontally defocussing magnets. Each period has two straight sections; a 6 meters long (LS) and another 1.2 meters long (SS). The considerable length of the long straight sections, 30% of the machine circumference, gives the machine great flexibility. Of the 24 LS one is used for injection and one for extraction; 9 of them are utilized for rf stations; 2 of them are committed for antiproton injection/ extraction, 1 for reversed injection into the Main Ring and a total of 6*0perated by Universities Research Association, Inc., under contract with the United States Department of Energy.179are presently utilized for correction elements.The nominal operating point is for betatron frequencies of Vjj = 6.7 horizontal and V v = 6.8 (at injection 6.9) vertical. Transition energy occurs at y = 5.446. The 8 -functions vary between 6.1m and 33.7m (at SS) horizontal and between 20.0m (at LS) to 5.3m in the vertical plane.The rf system consists of 18 cavities, each one with two accelerating gaps. The harmonic number is 84 resulting in frequencies which change from 30.3 MHz at injection to 52.8 MHz at extraction. The maximum energy gain per turn is a function of frequency and varies between 300 keV at the low end to 750 keV at the high end. The total bucket area is of the order of 2 eV/sec for Ap/p of ~l.lx 10- .^ Present modifications^ to the power amplifiers are expected to better handle the ferrite tuners' losses and raise the available bucket area.The originally designed apertures of 90tt x  10~^m horizontal and 40 IT x  1 0“6m vertical have not yet been achieved. Understanding the Booster aperture is the subject of present interest. 6 Hardware modifica­tions are underway to improve the vertical aperture. The quoted numbers for the present Booster apertures are 2 5 TT x  10-^m horizontal and 16TT x  1 0"^m vertical.Since March 1978 the Booster has operated with H~ multiturn charge exchange injection.^ A linac provides an H_ beam pulse with 200 MeV emittances of 8 rr x 10~ m both vertical and horizontal, up to 43 mA and 60ys long. This injection method allows injecting a maximum of protons far larger than the maximum accelerated so far of 3.02 x 10-*-^  per booster cycle. Figure 1 shows the present Booster transmission for H- operation vs. the injected beam intensity. For comparison, the best recorded transmission with single turn H"1" injection is also shown (the number of protons in this figure is expressed per 13 Booster cycles as normally operated for injection into the Main Ring).The incoherent space charge tune-shift limit has been studied as a guide to what maximum intensity could be obtained. This limit depends strongly on the assumptions about available aperture, beam blow-up and the details of the charge distribution. Figure 2 shows the result of two calculations for a uniform charge distribution, and A v = 0.38, calculated using the incoherent space charge tune-shift formula,^ and plotted versus time into the Booster cycle. The lower curve is for no beam dilution with emittances at 200 MeV of 8 l x 10“6m. The upper curve assumes beam dilution as to always fill the available aperture of 25tt by 16tt . The decrease of the maximum number of protons in the early part of the cycle is due to the increasing charge density because of rf bunching. This effect predominates until ~ 3ms, where the kinematical effects start to dominate. The charge injected and accelerated to 8 GeV for the Booster intensity record are also shown. The largest fraction of the loss of in­tensity during operation takes place in a time period of 2 to 3 ms more or less as it would be predicted from Figure 2. (The minimum of the RF bucket area also occurs at the same time.) From measurements of beam sizes at extraction there is evidence for intensity-dependent beam blow-up, but not as large as to fill the available aperture. As expected, Figure 2 is optimistic and the curves for real charge distributions should be de­pressed by a factor of approximately 2. We conclude that the present record of 3.02 x 1 0 -*-^ p's/booster cycle could probably be improved to maybe 5 x l O ^  p's/booster cycle if beam blow-up is tolerated, someINJECTED PROTONS X IO 15Fig. 1. Fermilab Booster transmission versus injected number of protons per Main Ring cycle (13 Booster cycles), from Ref. 7.BOOSTER CYCLE TIME (ms)Fig. 2. Number of protons versus time in the Booster cycle resulting in a tune shift of Av = 0.38, assuming a uniform charge distribu­tion. The lower curve assumes no dilution.The upper curve assumes beam blow-up to always fill the presently available aperture.181gains in aperture and longitudinal bucket area are realized, and no limits other than space charge tune-shift exist. The present H~ multi­turn charge exchange injection system is capable of delivering to the Booster up to 1.6 x 1C)13 protons in 22 injected turns.The initial complement of correction elements consisted of a package containing skew-quadrupole, quadrupole, vertical and horizontal dipole elements each operated from individual dc supplies, at each LS and SS. These elements obtain appropriate injection apertures and tunes. Initial operation of the Booster resulted in intensities near 1 x K j H  per cycle. The elements which contributed most importantly to the increased inten­sity to the present record include injection improvements, aperture im­provements, increases in rf power and control of instabilities.An important low intensity instability is the head-tail effect which occurs in the Booster^ at intensities above 1.5 x 10H. Chromaticity control through use of sextupoles effected a cure over a large range of intensities. One circuit of sextupoles in three symmetric long straight sections and a circuit of 24 sextupoles in the short straight sections are now operated from programmed supplies to provide flexibility in operation. Note however that compensation of the width of some resonance lines in the working area is available but has not been fully implemen­ted. 10 Programmed control has been added to the quadrupole correction elements in circuits for short and long straight sections. Further control of transverse instabilities has been provided through active, bunch-by-bunch dampers for vertical and horizontal control.H Coupled bunch longitudinal instabilities have been controlled through "harmonic damping". One rf station is operated one harmonic number lower than the beam and another station is operated one harmonic number above the beam during the last 5 ms of the Booster cycle. This provides a bunch to bunch modulation on the rf voltage with harmonic number 1 and no phase error, thereby decoupling the b u n c h e s . 12Current operation for injection in the main synchroton requires in­tensities from 1.5-2.2 x 10^2 protons per cycle. Since the installation on the negative ion injection system, three periods of operation have been devoted to high intensity Booster operation. Intensities greater than2.5 x 1012 p per cycle have been achieved in all cases with a record intensity of 3.02 x 10^2 achieved in September 1978.BOOSTER AS A KAON FACTORYThe most relevant parameter to evaluate the Fermilab Booster is the flux of kaons obtainable. To this effect on Table I we have scaled the conclusions of reference 2 to the present Booster performance and to the future maximum intensity and energy. For comparison the fluxes for a kaon factory such as the ring cyclotron proposal are included.13182TABLE I. Yield of 2 GeV/c K+ and K for the Fermilab BoosterEnergy(GeV)p/pulse(1012)p/sec(1013)I(yA)K+/sec*(io8)K /sec* (1 0 8)Present 8.0 3.0 4.5 7.2 7.2 1.7Future 10.0 5.0 7.5 12.0 16.0 3.7Ref. 13 8.5 - - 100.0 110.0 26.0(*) Acceptance: cone 0O = 3.5°, momentum = 2 x IO-2 GeV/c . Allprotons interactFor single turn extraction onto the production target the duty factor is 2.4 x 10-5. This is unreasonably low and would render the kaons useless for conventional nuclear or particle physics experiments. Two schemes could be utilized to improve the duty factor: slow extrac­tion from the Booster and the utilization of a "stretcher" ring.Slow resonant extraction from the Booster could be implemented over a momentum range where the kaon production cross section does not vary significantly. As deceleration can take place in the B o o s t e r ^  ex­traction could be extended to the downward part of the guiding field ramp. The significant requirement is that the proton targeting trans­port line would need to follow the momentum excursion of the proton beam. This may be possible if targeting could be performed close to the Booster ring. As an example from the production curves of reference 2 we select 7 GeV as the minimum momentum. Extraction could then take place between 19.2 ms and 47.5 ms into the Booster cycle, for a result­ing duty factor of 42%. However, resonant extraction may be an un­pleasant complication.The use of "stretcher" rings (SR) to provide suitable duty factors has been previously discussed.13 A SR for the Fermilab Booster does not exist but it could provide more flexibility to a kaon factory than the resonant extraction discussed above.16 a suitable DC ring of small aper­ture could be constructed; variable transition energy could provide a variable debunching time. Complete debunching within a few hundred micro­seconds could provide a spill with no time structure, by using a transi­tion energy below that of the proton beam. By raising the transition energy, the Booster bunch structure could be preserved for experiments that require accurate time measurements. Such an SR could utilize the same single turn extraction area and part of the transport line now under construction for reversed injection into the Main Ring. A ring of the Booster circumference but with a race track design to allow for a long straight section to locate an intricate resonant extraction, could be placed near to the Stochastic Cooling Ring under design.1 This location provides enough ground space for a targeting system, par­ticle separation and an experimental hall. The use of the Stochastic Cooling Ring as a SR would be less desirable due to the large aperture required for its application.FINAL REMARKSThe Booster accelerator at Fermilab with improvements in average power capability of its rf and pulsed-magnet systems can provide inten­sities greater than 4.5 x 10 protons per second at 10 GeV. Although such intensities are a factor of fourteen below the kaon factory designs being considered, they can still provide interesting fluxes of kaons at modest investment. No plan exists at Fermilab for implementing such a facility although a site location could certainly be found. Operation would be compatibly interspersed with 400 or 1000 GeV fixed-target opera tion at Fermilab but incompatible with pp collider operation.FOOTNOTES AND REFERENCES1. "A Conceptual Design for a High Luminosity Antiproton Source at Fermilab", Fermilab July 1979 (unpublished). This design requires the utilization of the Booster to decelerate antiprotons every cycle between proton acceleration cycles.2. Lee C. Teng, "The Potential of Existing Synchrotrons", 1976 Summer Study on Kaon Physics and Facilities, BNL 50579, p. 189.3. Design Report, National Accelerator Laboratory, Batavia, Illinois, second printing, July 1968.E.L. Hubbard, ed., Fermilab Internal Memo TM-405 (unpublished).4. Average vacuum achieved <10-6 Torr.5. Q.A. Kerns et_ aT., IEEE Trans. Nucl. Sci. NS-26, 4111 (1979).6. D.F. Cosgrove eX^  al_., IEEE Trans. Nucl. Sci. NS-24, 1263 (1977);B.C. Brown et al., IEEE Trans. Nucl. Sci. NS-26, 3173 (1979).7. C. Hojvat et_ al^ . , IEEE Trans. Nucl. Sci. NS-26, 3149 (1979).8. C. Bovet et al., CERN/MPS-SI/Int. DL/70/4, April 1970, p. 26.9. E.L. Hubbard et al., IEEE Trans. Nucl. Sci. NS-20, 863 (1973).10. K. Schindl, IEEE Trans. Nucl. Sci. NS-26, 3562 (1979).11. C. Ankenbrandt et_ ad., IEEE Trans. Nucl. Sci. NS-24, 1698 (1977).12. C.M. Ankenbrandt et_ aJ., IEEE Trans. Nucl. Sci. NS-24, 1449 (1977). The system described in the text is an upgrade of the one described in the reference.13. M.K. Craddock et al., IEEE Trans. Nucl. Sci. NS-26. 2065 (1979).14. C. Hojvat et_ a^., IEEE Trans. Nucl. Sci. NS-26, 3586 (1979).15. F.E. Mills, 1976 Summer Study on Kaon Physics and Facilities,BNL 50579. This contribution was not published in the report.16. This was previously proposed in:R. Stiening, Fermilab Internal Report TM-6, 1968 (unpublished).184DISCUSSIONDALPIAZ: Do some plans exist at Fermilab to use cooled antiprotons at lowenergy?BROWN: Although operation of a kaon factory at FNAL would be compatiblewith fixed target experiments, the production of antiprotons, which requires the main ring (which is the Tevatron injector and in the same tunnel), would be a substantially more painful compatibility problem.BLASER: The transmission through the booster is rather low at highcurrents. Where and when do the main losses occur and what would activa­tion problems be?BROWN: The predominant beam loss occurs at times before 3 msec in thecycle, much as would be expected from the space charge curves shown. After this time transmission of >99% is achieved unless we have instabilities not properly controlled or when low on RF power.Most important losses occur at the vertical aperture limit at the ex­traction septum when injection plus extraction losses result in activations of 10-25 rem/h on contact. Some areas near the injection point reach1-2 rem/h on contact while remaining points in the booster only reach 5-100 mrem/h.Cures for both injection and extraction losses at the extraction girder are known. The extraction losses will not be cured for injection to the main ring but would be new and important for higher duty cycles. Nevertheless one would expect to use "scrapers" to limit the aperture and accept the losses in a localized fashion.BLASER: Have you estimated the transmission of a possible stretcher ring?BROWN: As an accelerator amateur I can only suggest that given 80% mainring transmission one would expect to work to achieve near 100%.POLLOCK: In going from your 5 to 10 pA to ~100 pA in a future machine onehas to be concerned about the selection of a proper magnet aperture.Could you comment on the difference between the 25tt mm-mrad horizontal acceptance which you quote and the IOOtt of the original design?BROWN: When the RF system was designed the design acceptance dropped to~60t\ . However, the 25 tt to 60 tt discrepancy is not well understood. We suspect that the limited vertical acceptance combined with horizontal vertical coupling may account for some fraction of the limitation. We await completion of magnets for vertical aperture improvements to aid further study.185POSSIBLE KAON AND ANTIPROTON FACTORY DESIGNS FOR TRIUMF*M.K. CraddockUniversity of British Columbia, Vancouver, B.C., Canada V6T 1W5C.J. Kost and J.R. Richardson^TRIUMF, Vancouver, B.C., Canada V6T 2A3ABSTRACTTwo alternative designs— based on proton synchrotrons and isochronous ring cyclotrons, respectively— are considered for accelerating high cur­rents (>30 pA) from TRIUMF (0.45 GeV) to energies high enough for the pro­duction of high fluxes of kaons (8-10 GeV) and antiprotons (25-30 GeV).The first synchrotron would be fast cycling at 20 Hz, with third harmonic flat-topping to aid in injection and extraction. The cw beam from TRIUMF would be extracted in 100-turn "macropulses" at 22 psec intervals. With 400 pA in TRIUMF and injection over 8-20% of the magnet cycle, 30-80 pA could be accelerated to 10 GeV. A second synchrotron would accelerate 30 pA to 30 GeV for production of antiprotons.The ring cyclotron option would also be built in two stages, 0.45 to 3 GeV (15 sectors, 10 m radius) and 3 to 8.5 GeV (30 sectors, 20 m radius). With superconducting magnets (5 T) the weight of steel could be kept below 2000 tons for each ring. Large field-free regions between the spiral sector magnets allow room for multiple SIN-style accelerating cavities, permitting energy gains of many MeV/turn. Second or third harmonic cavi­ties and the phase compression effect help in achieving separated turn extraction. Up to 100% of the beam in TRIUMF could be accelerated to8.5 GeV.INTRODUCTIONThe possibility of building an accelerator to provide several hundred times the currents available from most present accelerators in the GeV or tens of GeV range (c^ 0.3 pA) is a challenging one. (The Fermilab 8 GeV Booster Synchrotron has recently provided a 7 pA proton beam,1 but this is not at present available for experimental use.) Such a machine could open up the fields of kaon and antiproton physics in the same way that the pi- meson factories have done for pion and muon physics. The wide range of problems in nuclear and particle physics which could be studied is described in other papers to this Workshop and, e.g., in the Proceedings of the 1976 Meeting on Kaon Physics and Facilities at Brookhaven2 and of the 1979 Workshop on Physics with Cooled Low Energy Antiprotons at Karlsruhe.3The threshold for kaon production is — 1.1 GeV, but to produce intense and clean beams higher energies are needed, well above the (3,3) resonance. Berley^ has analysed various kaon beams, showing that their intensities rise very strongly with incident proton energy at first, but flatten off at ~7 GeV for K+ and ~9 GeV for K- . A high-intensity accelerator operat- ing near these energies could produce not only intense secondary beams of*Work supported in part by the Natural Sciences and Engineering Council of Canada.tOn leave from University of California, Los Angeles, CA, U.S.A. 90024.186kaons (themselves a source of E- and A-hyperons) but also non-strange beams of protons, neutrons, pions, muons and neutrinos. For the produc­tion of intense antiproton beams higher energies are desirable (>15 GeV).With 100 yA currents already available, the meson factories are in an unrivalled position to act as injectors to a future generation of high- current accelerators in the GeV range. In the case of TRIUMF, with its capability for simultaneous extraction of several proton beams, the prob­lem of splitting off a portion of the main beam for further acceleration is a particularly simple one. It should be possible to accelerate 400 yA of H_ ions up to the onset of significant electric stripping at 450 MeV without exceeding the radiation spill limits; the whole of this beam could be extracted for further acceleration. Alternatively a 100 yA beam of good quality could readily be extracted by inserting an additional strip­ping foil and dispatched to a higher energy accelerator without causing any interference with the 200-500 MeV experimental programme.To accelerate to higher energies two alternative designs have been proposed, one utilizing two proton synchrotrons,5 the other two isochron­ous ring cyclotrons.6 The synchrotron design is potentially unlimited in energy, but limited in current (80 yA at 10 GeV) by the problem of captur­ing sufficient of the cw beam produced by the TRIUMF cyclotron. The "CANUCK" ring cyclotrons (Canadian University Cyclotrons for Kaons) can capture all the available current (400 yA) but are limited in energy (3 GeV and 8.5 GeV).PROTON SYNCHROTRONSKaon Factory5The magnitude of the average current which can be accelerated in syn­chrotrons used as after-burners for the TRIUMF cyclotron depends funda­mentally on the beam current of TRIUMF and the fraction of the synchrotron cycle time used for injection. Considering a reasonable TRIUMF beam of 300 yA at 450 MeV for injection and a fraction of 1/9 to 1/4 as the frac­tion of synchrotron time spent on injection, one obtains an upper limit of 2 to 4.5 x 1011+ protons per second as the output beam of the synchrotrons. In the cyclotron there will be 8 x 107 protons/RF pulse or 4 x 108 protons in one turn. Using the method described below, 500 RF pulses or 100 turns are stacked near the outer edge of the cyclotron and then injected as a packet over a period of 2 turns (0.43 ysec) into the (first) synchrotron. The time between injections would be 22 ysec. The repetition rate required for the synchrotron is thus set by the injection period required to fill up the allowable current limitation per turn for a reasonable synchrotron design. As an example synchrotron we will take a radius of 50 m, a radial aperture 100 mm and a vertical aperture 60 mm (see Table I). The space charge limit at injection is given byN < L  vB g2y3 b(a+b)  ^ ^2 rpRwhere B is the bunching factor (1/3), the tune v ^  10 and rp = 1.54 x 10~16 cm. Inserting the appropriate values we get 3 x 1011+ protons/turn for the space charge limit in a single turn. The phase space limit comes from the ratio of the phase space admittance of the synchrotron to the emittance of the cyclotron. This ratio is 5600 for the plane transverse to the beam and 13 along the beam direction. This gives a current limitation of187Table I. Combined kaon and p factory for TRIUMF.Kaon ring P ringFinal energy (GeV) 10 30Radius (m) 50 50Aperture (l/2xl/2) (mm2) 50 x 30 20 x 20Type of magnets fast cycling superconductingInjection time 10 msec 4 secRepetition rate (Hz) 10-25 0.1Acceleration time 10-20 msec 1 secNominal energy gain per turn (MeV) 1.0 0.05Space charge limit in one turn 3 x IO14 9 x 1015Phase space limit in one turn 2.9 x io13 5 x 1015Number of protons per pulse 2 x 1013 2 x 1015Number of protons per second 2-5 x io14 2 x IO14In association with the pT ring a combined storage and coolingring will be required to cool and energies < 100 MeV.lower the p energy to2.9 x 1013 protons/turn from phase space considerations. Taking a conser­vative limit of 2 x 1013 protons to be accelerated we see that this would require the injection of 500 packets over a period of some 10 msec. This injection time requires a synchrotron cycle time between 40 and 90 msec or a repetition rate between 25 and 10 Hz and a final output current from the synchrotron of 2 to 5 x 1011* protons sec-1.Antiproton FactoryFor the production of large fluxes of antiprotons it appears to be desirable to raise the energy to 25-30 GeV. This could be done by in­creasing the average beam radius from 50 to 150 m, but this would result in an accelerator which is rather large for the TRIUMF site. An attractive alternative is to raise the magnetic field by a factor of three in the bending magnets by using an additional ring which is slow cycling and superconducting and thus retaining the average radius of 50 m. With this situation one could consider making the two synchrotrons concentric, using the same beam tunnel. However, the leakage magnetic flux from the super­conducting magnets might be a problem.Since the momentum at injection for the p synchrotron is some 10 times as large as that for the kaon synchrotron, this factor more than compensates for the smaller aperture (40 mm diam) suggested for the super­conducting magnets. The result is a limit on the beam of 4.5 x 1015 pro­tons in a single turn for the p" synchrotron from phase space considerations. The space charge limit turns out to be 20 times less stringent. We are led, then, to suggest a 10 sec cycle time for the p synchrotron, allowing a large fraction of the protons accelerated in the kaon synchro­tron to be injected into the p" synchrotron. Something like 4 sec of the cycle time could be used for injection, ensuring, with the 25 Hz repeti­tion rate for the kaon synchrotron, a final beam at 30 GeV of 2 x l01Lf protons sec-1.188For research with low-energy antiprotons it would be desirable to in­clude a combined storage and cooling ring. Antiprotons from the produc­tion target would be cooled in the storage ring and then injected into the kaon ring and decelerated to low energy and then reinjected into the storage ring for final cooling and use in stopping "p experiments.Further analysis is required in conjunction with the best available data on p" production to evaluate the relative merits of the two-synchro­tron vs a one-synchrotron system. However, it should be pointed out that the system proposed here would have the potential of producing a flux of low-energy antiprotons some 40 to 100 times that envisioned for the PS-AA-LEAR complex under construction at CERN. Simultaneously the kaon ring would be producing low-energy kaons with some 200 times the intensity that could be produced at Brookhaven.H+ InjectionThe problem of matching the time structures of the cyclotron and the synchrotron can be reduced by stacking some 100 turns in the cyclotron and then injecting them over a period which matches the receptive time of the synchrotron. The stacking process makes use of the decelerated beam7 which has been observed at TRIUMF® and used for a number of beam measure­ments. In accordance with a well-known cyclotron theorem, the spread in phase angle a represented by Asina will remain constant through the acceleration process. Thus the spread in phase angle which might go from 0° to 10° at injection into TRIUMF can be made to go from 52° to 75° at a radius of 7.6 m (450 MeV). Over the next radial interval of 25 mm the field can be tailored so the ions take approximately one hundred turns in going from 52°-90° and back to 52° and also from 75°-90° and back. The result is some hundred turns of all phases collected in a pocket 25 mm wide in radius. An axial electric field of 15 kV/cm applied over an azi­muthal distance of 25 cm is sufficient to sweep all the ions in the packet onto a foil stripper, which removes the two electrons from the H- ions and allows the protons to escape the magnetic field. This is accomplished over two ion revolutions (10 RF pulses) for a pulse length of 0.43 ysec which fits comfortably into the proposed ion revolution period of the synchrotron of 1.4 ysec for optimum capture. This process is repeated every 100 TRIUMF ion revolutions (21.7 ysec). In the 100 turns at 450 MeV, the total loss due to stripping (both electromagnetic and gas) is less than 2%. The energy spread in the extracted beam will be about 2.5 MeV FWHM.In tailoring the falling magnetic field to ensure a similar number of turns for all the initial phases between 52° and 75°, it is necessary to vary the departure from isochronism over the 25 mm radial region where the extraction is to take place. If B^ is the isochronous field and 6B is the departure from B^, then in practice one sets 6B/B-^  at about 0.0012 over the first 10 mm in order to turn back those ions at large phase angles.In order to take care of those ions with phases down to 52° it is neces­sary to increase 6B/B^ to 0.0033. Other falling field regimes can be used; in the case of a smaller initial phase spread the problem of obtain­ing a similar number of turns for all phases in the 25 mm packet becomes easier.H~ InjectionTRIUMF normally accelerates H“ ions to 180-525 MeV. It is therefore natural to consider the possibility of extracting the H- ions (as negative189ions) from TRIUMF and injecting them into the synchrotron by stripping two H+ ions near the equilibrium orbit of the synchrotron.Injection by stripping circumvents Liouville's theorem and thus avoids most phase space problems of injection into the synchrotron, leav­ing space charge as the most important limit on the intensity. Assuming that 100 pA of H~ ions can be extracted from TRIUMF, using the amplifica­tion of radial motion observed at SIN, one has about 2.7 x 10 7 ions per RF pulse and 3.7 x 105 pulses spread over 16 msec to give 1013 protons per synchrotron cycle. A synchrotron repetition rate of 20 Hz yields 2 x IO19 protons sec-1. The synchrotron magnets would have a dc bias with flat-topping— the 20 Hz repetition rate will allow the application of third harmonic at 60 Hz.The phase space of the synchrotron can be filled by stripping in anumber of alternative ways. For example, the stripper in the synchrotron magnetic field can be moved mechanically across the synchrotron aperture—  together with vertical and horizontal steering of the H“ beam. Fastbumper magnets are another possibility. There are approximately 10,000synchrotron turns in the 16 msec injection time. The particles will traverse the stripping foil some 400 times, assuming a 2 mm wide stripper and a horizontal aperture of 50 mm. Multiple scattering would not cause any difficulties and the momentum compaction would only be Ap/p =2 x 10-3/mm. The stripper lifetime would have to be investigated.Ideally, for this type of injection, the synchrotron RF should be at the same frequency as the cyclotron (23 MHz), increasing by about 30% to the time of beam extraction. This would result in highly efficient capture in the synchrotron since the excellent phase spread from the cyclotron would remain in the synchrotron. An energy gain of 1 MeV per synchrotron turn would be readily achievable for this application.The high intensities achieved by cyclotron meson factories are in large measure attributable to their cw operation. However, we have seen that matching them to the (pulsed) synchrotrons conventional for accelerat­ing protons to GeV energies poses some technical problems and results in a tenfold loss in intensity. It is therefore natural to consider the possibility of designing isochronous cyclotrons for accelerating protons to ~9 GeV, an energy close to the shoulder of the cross-section for kaon production. Cyclotron designs in the GeV range have previously been con­sidered by Sarkisyan,9 Gordon,10 Mackenzie11 and Joho.12The chief problems in designing a high-energy cyclotron are, of course, the rapid rise of average field with radius (dB/dr ~  8y3) needed to maintain isochronism, and the consequent axial defocusing. The flutter F2 = (B/B - l)2 and spiral angle e needed to keep the axial tune vz real therefore rise drastically with energy. Using the rough approximation"CANUCK" HIGH-ENERGY CYCLOTRONS6v| ~ -g2y2 + F2(l + 2 tan2e) ( 2 )we see that for y >> 1 we require/2F2 tane y . (3)To avoid excessive spiral it is therefore vital to have a large flutter190(F2 > 1). In this respect the design criteria lead naturally to the choice of a ring cyclotron with separated sector magnets. The magnetic field is then restricted to the hill regions, giving in hard edge approxi­mation1 ^F2 = £v/&h , (4)£v and being the orbit lengths in valley and hill, respectively. Ob­taining sufficient flutter is thus dependent on arranging sufficient separation between the magnets. In the designs described below we have chosen F2 ^  2 at maximum energy, so that for example at y = 10 (8.5 GeV)Eq. (3) requires a spiral tane £ 5— a value still within the bounds of practical possibility.Separated sector machines have other important design advantages:1) Large magnetic field-free regions between the magnets where the injec­tion, extraction, pumping, diagnostic and acceleration systems may be located (with all the advantages of separated function design).2) The high &v/&h ratio increases the cyclotron radius and hence the turn separation (making extraction easier) and reduces the radial deriva­tives of flutter, spiral and average field (making the magnets easier to construct).Of course, wider valleys and larger radii also imply higher costs in equipment and buildings. This argument was perhaps crucial until the advent of reliable superconducting magnets over the past few years. With the factor 2 gain in hill field which these provide the machine radius required is halved and the costs drastically reduced— in the case of the magnet steel by about a factor 8. That the savings in capital costs and power bills more than offset the extra cost of refrigeration is, of course, the reason for the growing wave of interest in cyclotrons with supercon­ducting magnets.111Supposing then that we can obtain a hill field = 5.0 T, how large will the machine be? In hard edge approximation, isochronism requires» - iijr ■ *Bc • <5>where the "central field" Bc is related to the cyclotron radius rc and the angular frequency Wp of the proton (charge e, mass m) by eBc/m = top = c/rc . For y = 10 and F2 = 2, Eq. (5) gives Bc = 0.17 T. However, our choice of Bc is not entirely free; to ensure an integral number of proton bunches per turn we must keep Bc commensurate with its value in TRIUMF, namely0.30 T. We therefore choose to give Bc and top half their TRIUMF values (i.e. 0.15 T and 2.305 MHz), making the cyclotron radius twice as large, namely 20.6 m (and raising F2 to 2.3).If a single machine were used to accelerate protons at 450 MeV (8 =0.71) from TRIUMF to 8.5 GeV (8 = 0.995) the sector magnets would still be undesirably large^the gain in radius being ~6 m. However, by designing the machine in two stages, the lower energy one with a smaller value of rc, substantial saving can be achieved, together with greater versatility in the shape of beams of intermediate energy— advantages which should out­weigh the complication of additional extraction and injection systems. Choosing the same cyclotron radius (10.3 m) and frequency (4.61 MHz) as in TRIUMF the lower energy orbits are halved in size. For a maximum y of 4191(6 = 0.968, T 3 GeV), the gain in radius is only 2.4 m (similar to SIN) while Eq. (5) shows that the flutter factor F2 = 3.2.Betratron Oscillations and Fringing Field EffectsTo proceed further and decide on the optimum number of sectors (N) and variation of spiral angle with radius, we need to know fairly accurately how the radial and axial tunes vr and depend on the machine parameters. For vr the expression derived by Schatz in the hard edge approximation is sufficiently accurate (as we have confirmed by numerical orbit studies for edges of realistic softness— see below). This expression shows that vr grows much faster than the simplest approximation vr ~  y when the flutter is high, and the TT-stop band is reached well before y = N/2. For F2 — 2 vr reaches N/2 for y N/3 in the cases studied. It is therefore necessary to choose the number of sectors N 3ymax- Thus we have chosen N = 15 for the first stage (y = 4) and N = 30 for the second stage (y = 10).For axial motion the usefulness of hard edge theory is rather limited, the reason being the growing importance of fringing field effects as the spiral angle increases, for pole gaps of realistic height. Enge16 shows that while the radial focusing strength is (to first order) unaffected by the fringing field, the axial focusing strength is reduced by two effects — firstly the bend is incomplete at the point of maximum field gradient so that the effective crossing angle y is reduced, and secondly there is a thick lens effect. To minimize the loss in focusing the field edge must be kept as hard as possible by using a small vertical gap between the poles (2.5 cm in the present design).To explore the orbit properties in the proposed machines accurately we have tracked protons through a simulated magnet field with Woods-Saxon shaped field edges, using the equilibrium orbit code CYCLOPS. Starting from the hard edge solution the spiral profile tane(r) was adjusted iter­atively until the desired value of v| (— 3) was obtained at all radii. For a y = 4 to 10 cyclotron with N = 30, rc = 20.6 m, a uniform field =5.0 T and a pole gap g = 25 mm, the spiral required rises smoothly to a maximum tane = 6.5, and the resulting pole shape is shown in Fig. 1.Fig. 1. Plan view of superconducting sector magnet design for a second stage 3 to 8.5 GeV isochronous ring cyclotron.192The variation of v z and v r with energy is illustrated in the resonance diagram (Fig. 2). We avoid crossing the dangerous v z=l resonance up to8.6 GeV; with a little more adjustment to the edge shape near maxi­mum radius it should be possible to avoid crossing the v z=2 resonance also. The crossing of the inte­ger and half-integer radial resonances should cause no seri­ous problems with sufficient energy gain per turn.Magnet and RF DesignThere is an intimate relationship between the design of the magnets and the RF system, particularly when one is trying to achieve final ener­gies between 5 and 10 GeV. For example, the fact that one needs 15 sectors to reach y = 4 and 30 sectors to reach y = 10, in order to avoid the 7T-stop band in the radial focusing, precludes the use of "dee" type RF structures (because of lack of space) and forces the use of SIN-type cavities. Con­versely, the length of the magnets in the radial direction, together withthe wavelength of the RF to be used, dictates the use of two cyclotron stages, instead of one, in accelerating to y = 10.The proposed arrangement of sectors and cavities for the two cyclo­trons is shown in Fig. 3. In the 8.5 GeV machine the cavities are arrangedin three groups of seven in order to keep groups of three neighbouringvalleys clear for injection and extraction systems.In considering the radio frequency to be used in coupled cyclotrons the conventional wisdom states that the frequency should be the same in the two stages. This requirement would present a serious problem in our case since TRIUMF operates at 23 MHz and SIN-type cavities at this frequen­cy are very large and expensive and would require large amounts of RF power. The reason for the requirement is that a phase spread of ±14° in TRIUMF would become ±28° at 46 MHz, resulting in an increase in the spread in energy gain per turn from 3% to 12% over the phase interval. However, superposition of 25% 2nd harmonic (92 MHz) would reduce the spread in energy gain per turn to less than 1%— at the cost of a reduction of 25% in peak energy gain per turn.In this case we are using "flat-topping" to make the transition fromthe low TRIUMF frequency to a higher frequency in the second cyclotronwithout increasing the spread in energy gain.It is also possible in a two-stage post-accelerator to use the firststage cyclotron as a phase compressor by arranging that the cavity voltage increase with radius.17 If the first stage accelerates from y = 1.5 toFig. 2. Betatron oscillation frequencies computed in the simulated magnetic field of a 30-sector 8.5 GeV ring cyclotron..Fig. 3. Possible arrangement of the 3 and 8.5 GeV ring cyclotrons fed from beam line 2A of the present 520 MeV cyclotron.194y = 4 with a cyclotron radius rc = c/u)p = 10.3 m, the increase in radius is 2.3 m. An RF cavity can be arranged so that its peak electric field coincides with the final orbit, and if its dimensions are 5.9 m (horizon­tal) by 3.6 m the accelerating voltage will increase by a factor of 3 from initial to final orbit, resulting in a phase compression by a factor of3. The beam can now be injected into the second stage cyclotron with aphase spread for an accelerating frequency of 69 MHz just equal to that onleaving TRIUMF at 23 MHz. Third harmonic cavities (207 MHz) can beinstalled in the second stage to give "flat-topping" there— at a loss of1/9 of the peak energy gain.An important possibility in magnet design for superconducting ring cyclotrons is the use of part of the return flux along a channel or "gully" between a hill and valley to increase the flutter. This gully would have a reverse field of 12-20 kG, be parallel to the edge of the hill and increase the flutter by some 30-50%. In making the extremely crude esti­mate of magnet weight shown in Table II it has been assumed that enough iron will be provided to provide a complete return flux in iron (except for the gullies).Table II. Ring cyclotron kaon factoryFirst stage Second stageInjection energy (MeV) 450 3000Extraction energy (MeV) 3000 8500rc = c/o)p (m) 10.3 20.6Number of sectors 15 30Primary cavities 8 at 46 MHz 15 at 69 MHzHarmonic cavities 4 at 92 MHz 6 at 207 MHzApprox. dimensions ofprimary cavities (mz) 5.9 x 3 . 6 4 x 2.6secondary cavities (m2) 5.9 x 1.6 4 x 1.5Total RF power (MW) 2.0 1.7Peak energy gain/turn (MeV)at injection 1.2 7.9at extraction 3.6 7.9AE/Ar (MeV/mm)at injection 0.23 1.9at extraction 5.6 30Radius gain per turn (mm)at injection 5.3 4.2at extraction 0.64 0.26Crude estimate of magnetweight (m tons) 2000 1800Approx. number of turns 900 700It therefore appears that it is not only technically feasible to accelerate a high-intensity beam of protons to many GeV in a cyclotron, but that with the help of superconducting technology it is economically feasible also. Provided pole gaps are kept small and separated sector195magnets and gullies are used to obtain high flutter, axial focusing can be maintained to 8.5 GeV with not unreasonable spiral angles. The use of 2nd and 3rd harmonic cavities and phase compression can reduce the energy spread to 1% or better. The major question remaining to be tackled is that of extraction. If the full 3tt mm-mrad emittance of TRIUMF were in­jected the incoherent radial amplitude of the beam would be 1.1 mm at 3 GeV and 0.7 mm at 8.5 GeV— several turns in each case. A 1% energy spread corresponds to 10 turns. With the help of radial resonances (vr = 6 at 3 GeV and vr = 12 at 8.5 GeV) and some reduction in energy spread and emittance, reasonably efficient extraction would seem to be within reach.Both the synchrotron and the cyclotron designs presented above are very much in their preliminary stages; during the coming months they will have to be looked at in more depth and the feasibility assessed of sub­mitting a formal proposal for one or the other.REFERENCES1. B. Brown and C. Hojvat, these proceedings, p. 178.2. Proc. Summer Study Meeting on Kaon Physics and Facilities, Brookhaven, 1976, ed. H. Palevsky, BNL 50579.3. Proc. Joint CERN-KFK Workshop on Physics with Cooled Low Energy Anti­protons, May 1979, KFK 2836.4. D. Berley, Reference 2, p. 257.5. J.R. Richardson, IEEE Trans. NS-26, 2436 (1979).6. M.K. Craddock, C.J. Kost, J.R. Richardson, IEEE Trans. NS-26, 2065 (1979) .7. J.R. Richardson, Nucl. Instr. & Meth. _24_, 493 (1963).8. M.K. Craddock et al., IEEE Trans. NS-24, 1615 (1977);G.H. Mackenzie, IEEE Trans. NS-26, 2312 (1979).9. L.A. Sarkisyan, Proc. 2nd All-Union Conf. on Charged Particle Accele­rators (Moscow, 1972), I, p. 33; Nucl. Instr. & Meth. 142, 393 (1977); these proceedings, p. 202.10. M.M. Gordon, quoted by H. Blosser in C y c l o t r o n s —1 9 7 2 , AIPCP//9 (AIP,New York, 1972), p. 16.11. G.H. Mackenzie, private communication.12. W. Joho, private communication.13. H.A. Willax, Proc. Int. Conf. on Sector Focused Cyclotrons and Meson Factories, Geneva, 1963, CERN 63-19, p. 386.14. J. Ormrod et al., IEEE Trans. NS-26, 2034 (1979);H.G. Blosser, ibid., p. 2040;E. Acerbi e_t al. , ibid. , p. 204815. G. Schatz, Nucl. Instr. & Meth. 12_., 29 (1969).16. H.A. Enge, F o c u s in q  o f  C ha rged  P a r t i c l e s , ed. A. Septier (Academic,New York, 1967), II, p. 203.17. W. Joho, Particle Accelerators 6, 41 (1974).196DISCUSSIONDZHELEPOV: Can you tell us what might be the time scale for constructionof a kaon factory at TRIUMF?CRADDOCK: If the project were funded now (which it isn't), the earliestcompletion date would perhaps be 1985.ANDERSON: What will the machine cost, approximately?CRADDOCK: No detailed engineering design or cost estimates have yet beenmade. However, a comparison with estimates approved by the U.S. Dept, of Energy for the Michigan State University second stage (K = 800) supercon­ducting cyclotron suggests that the costs of the 3 and 8 GeV cyclotrons would be about $20M and $25M, respectively (in 1979 Canadian dollars).For the 10 GeV synchrotron we may refer to the Fermilab 8 GeV booster, which cost $17M (U.S.) in 1970: allowing a factor 2.0 for inflation wouldbring this to $44M (Canadian) in 1979. For comparison, the cost of the present TRIUMF cyclotron was $12M in 1970— or about $25M in 1979 dollars.HUNGERFORD: How would operation of the TRIUMF machine as an injector forthe proposed K factory impact the operation of TRIUMF as a it factory?CRADDOCK: Not significantly, provided extra current were accelerated inthe present machine to supply the kaon factory. Thus if (as has been pro­posed) the current were raised to 400 yA, 300 yA could be accelerated to higher energies while 100 pA would still be available for use at 500 MeV; the ratio of the two beam currents would be fully adjustable. For the ring cyclotron kaon factory both beams would be cw; for the synchrotron option the split would be made timewise, and the macro-duty cycle of the beams for 500 MeV use would be reduced to — 90%.BLASER: When considering beams of megawatt power level going through super­conducting magnets one should be careful about beam spill. At SIN, for example, neutrons heat the first coils of p-channel to quench at currents above 100 pA in certain conditions. Also, in the medical pion applicator a proton current limit of 20-30 pA is given by heating the first supercon­ducting horns by neutrons from the target.A LAMPF KAON FACTORYDarragh E. Nagle Los Alamos Scientific Laboratory, Los Alamos, NM 87545ABSTRACTThis talk is about a possible design of a high intensity 16 GeV pro ton synchrotron using the 800 MeV proton linac at LASL as an injector.In 1962 J. R. Richardson organized a conference on sector-focused cyclotrons and their uses.l That UCLA conference led to a number of proposals for "meson factories," usually defined to mean accelerators capable of producing intense secondary beams of pions. So in some meas­ure the pion factories we have today, namely TRIUMF, SIN, and LAMPF, trace their origins back to that conference. These facilities by and large are fulfilling the promises made for them when they were proposed; namely, they are providing intense primary and secondary beams, are at­tracting a broad clientele among physicists interested in nuclei and in basic interactions of particles, and are producing an impressive flow of new experimental and theoretical results and insights, as evinced by pub lished data, workshops, and conferences, such as the 8-IC0HEPANS Confer­ence here.Can we expect that this workshop will have a similar outcome, name­ly that in ten year's time several kaon factories will come into be­ing? One should ask what would be the impact of a kaon factory ten years hence. Would the scientific benefits justify investing scarce re­sources of money and of able people in this way rather than in some oth­er way? Is such a project technically feasible? How are the energy and current to be specified?Many studies have been done to outline interesting new physics in the 10-20 GeV region. Examples are the 1976 BNL Summer Study on Kaon Physics, the 1977 CERN Workshop on Intermediate Energy Physics, confer^ ences on polarized beams and targets at the Argonne Laboratory in 1975 and 1978, the 1978 BNL workshop on the AGS Fixed Target programs. A series of working seminars on physics in this energy region was held at LAMPF, spring 1979. (See Silbar, Physics I, this workshop.)Some specific research fields are listed in Table I. These are ac­tive today, and one must ask where we might be after the next decade of work with existing facilities. The physics sessions of this workshop discuss these topics.Table I. Physics at 10-20 GeV.1. Nuclear scattering with kaons - Kaonic Atoms2. Nuclear spectroscopy with kaons3. Neutral kaon physics4. Hypernuclear physics5. Exotic hadronic states6. Pion scattering7. Physics with polarized beams and polarized targets1988. Rare decays of the kaon9. Neutrino-electron scattering10. Hadronic atoms11. Quark and gluon physics?12. Antiproton physicsWhether a kaon factory will see the light of day depends strongly on political factors. We live in a period of economic turmoil. The nuclear physicist today is not exactly a folk hero. Nevertheless parti­cle accelerator technology is a shining success of our age, and has had a number of benefits directly understandable to the public, in addition to what as physicists we would consider the more practical applications of producing pions, kaons, hypernuclei and so on.So we turn our attention to the specific proposal. The 800 MeV proton linac at LASL is considered as an injector into a fast-cycling synchroton.The synchrotron reference design is adapted from the Fermilab boost­er. The energy is doubled by doubling the ring diameter. The repetition rate is kept the same. Figure 1 shows a possible site plan.Fig. 1199Table II gives some parameters of the linac and Table III some param­eters of the synchrotron.Table II. Properties of LAMPFEnergy: 800 MeVCurrent: Present PlannedH+ 500 yA 1 mAH- ~30 yA 400 yArmsEmittance: H+ .035 tt cm mrH“ .06 tt cm mrRep Rate: 120 HzPulse Length: 600 ysPolarized Beam Available: YesTable III. Properties of the synchrotron.Final Energy 16 GeVFinal Average Current ~50 yARep Rate 15 HzDiameter of Orbit 300 mMagnets Laminated Iron:Peak Field 6.7 kGMagnet Power 2.6 MWRF Frequency Swing f^/f 1.19Injection is by stripping an H~ beam. A high current H" source is being developed at LASL for use with a proton storage ring. Adiabatic capture of the beam is planned, eliminating the need for prebunching the beam.The advantages of LAMPF as an injector are its high energy, high current capability, and small emittance. The limit on injected charge comes from the perturbation of the transverse tune V of the synchrotron by the electromagnetic fields of the beam, bringing the tune near a half­integral resonance where the beam would strike the chamber walls. The usual f o r m u l a ^  for the injection tune limit on the charge is= 2 | <Sy | y (g 2Y3) Sr R o—18where S is the beam area, <5v ~ 0.2. r0 = 1.5 x 10 m, and R is the av­erage radius. We see that the (3 Y^) factor is 8 times larger at 800 MeV (LAMPF) than at (200 MeV) Fermilab. The 50 yA figure for average current is consistent with this limit.A first look at the reference design does not reveal any insuper­able problems. A difficulty is the quadrupling of the energy gain per turn. If the number of cavities is doubled, the total cavity RF power200goes up eightfold, neglecting beam loading. It is advantageous that the frequency swing is four times less, reducing the amount of ferrite need­ed per cavity, if indeed ferrite turning is used. The whole RF system would be a good place to try to make improvements: for example the en-ergy gain per meter in fixed frequency linacs is 1 to 5 MeV/m, whereas for the booster it is 25 keV/m.The choice of 16 GeV in Table I is rather arbitrary. For production of, say, 750 MeV/c kaons there is a pronounced knee at about 10 GeV, after which the curve flattens.3 For antiproton production, the knee is less pronounced, but 16 GeV would appear to be a reasonable compromise be­tween adequate cross section and cost.It should be noted that the available data are rough yields of actual channels vs energy. It would be very desirable to have experimental data of production cross sections vs angle and energy.Very important to the success of kaon beam physics and of kaon- nuclear spectroscopy would be advances in the design of secondary beam lines. These lines should have high f number; i.e., big aperture and short length. The use of superconducting magnets is certainly indicated. New designs of separators must be developed. The experience at LAMPF with high-power targets and secondary beam lines underlines the impor­tance of designing a target, main beam line, secondary beam line, shield and a maintenance and servicing complex, as an integrated system to a- chieve reliability, good access, and bright beams. Some criteria fromH. A. Thiessen for a kaon beam and spectrometer are appended.1. Proceedings of the International Conference on Sector-Focused cyclo­trons held at the University of California, Los Angeles (17-20 April 1962). Nuclear Inst. & Methods v. 18,19 (1962).2. See, for example, H. Bruck, Accelerateurs Circulaires de Particules, Saclay 1966.3. Bunce, BNL 50874.APPENDIXPROPOSAL FOR KAON BEAM AND SPECTROMETER FOR NUCLEAR PHYSICS ATLAMPF KAON FACTORYProduction Target: 5 cm Tungsten or PlatinumProduction Angle : 0°BeamMomentum Range Sol id Angle Momentum Acceptance Resolving Power Dispersion Spot Size Separation LengthExpected Flux0-500 MeV/c 5 msr5% -Better than 10 2 cm/%10 cm x 2 cm; 200 mrad x 10 mrad 2 stage8 meters , r10' K+ /sec 0 10 protons/sec on target201SpectrometerMomentum Range Solid Angle Momentum Acceptance Resolving Power Length0-500 MeV/c 30 msr + 20% , Better than 10" 5 metersOverall Resolution Counting Rate Cost200 keV1/10 that of EPICS, similar to SUSI $10? in Orwell (1984) dollarsThis system would be used for the nuclear reactions (K ,K ), (K~,K~), (K- ,u- ) with bound A ° ,  and (K- ,tt-) with bound E ° .  The nuclear physics results which are expected would be most impressive and would foster a program of experiments that would last for several decades.DISCUSSIONANDERSON: What is the cost of the facility?NAGLE: Scaling roughly from the Fermilab booster, the ring accelerator,injection and ejection ring and support buildings would be about $65 million (1979 dollars). The experimental facilities and buildings would after ten years development cost an equal amount.ANDERSON: It seems like a lot of money.NAGLE: After all, what can you buy these days for $100 million?202FUTURE PLANS FOR SINJ.P. Blaser SIN, Villigen, SwitzerlandStudies are being conducted at SIN on future developments towards higher current and higher energy with neutron spallation sources and a K-meson factory in view.Present operation (1979) is at 100 yA (600 MeV). Transmission is 100%. A new injector (also a ring cyclotron) is under construction. It should, starting 1982/83, allow currents above 1 mA, still at practically 100% transmission. RF power for beams (continuous) up to 2 mA will be available, and the space charge limit is estimated at 4-5 mA. The beam dump of a new meson production target is planned to be laid out as a spallation source, especially for cold neutrons.For developments towards higher energy we feel that injectors and main accelerators should be of the same type (pulsed or continuous). So a linac-synchrotron or 2 or 3 stages of isochronous cyclotrons should be coupled together.A preliminary design study for a second stage has been started at SIN. A 2-3 GeV ring cyclotron using magnets and RF cavities very similar to the ones of the 600 MeV stage could be used. Extraction and injection could be obtained up to currents of 4-5 mA with practically 100% trans­mission. Such a machine could be used as a high flux spallation neutron source (continuous) and feed at the same time a current of perhaps 100-200 yA into a third stage isochronous ring of around 8 GeV as a kaon source.For the realization of such a project a co-operation between several European countries would, however, be required.203A CYCLOTRON KAON FACTORYL.A. Sarkisyan Institute of Nuclear Physics, Moscow State University Moscow 117234, USSRPION FACTORIESIn 1972-1974, high-current proton accelerators in the sub-GeV range, the so-called pion factories, were constructed in Los Alamos (the USA),1 Zurich (Switzerland)2 and Vancouver (Canada).3 At present the average beam current of the 800 MeV Los Alamos linac is 500 pA (planned value be­ing 1000 yA), but in the next few years it will be increased to 700 yA.In the cyclotrons in Zurich (590 MeV) and Vancouver (525 MeV), the average current has reached the planned value of 100 yA. Since the Zurich ring cyclotron operates as a "separated orbit" accelerator with single-turn beam extraction (extraction efficiency of 99.9%), it has been planned to increase by 1982 the beam intensity to 1 mA by replacing the injector (a 72 MeV cyclotron). Further increase in beam current to2-4 mA may be reached by modifying the high-frequency system of the cyclo­tron. It will be noted that in Vancouver the average current of the 450 MeV H- ion beam could eventually be raised to 300 yA.KAON FACTORIESThe first design of a high-current kaon factory was proposed in 1960 when the MURA group (USA) studied a ring phasotron for a proton energy of 10 GeV and an average beam current of 30 yA,1* the maximum orbit radius being 72 m and the radial track of the accelerator 2.5 m. A 200 MeV linear accelerator with a pulsed current of 20 mA was to carry out 20 turn injection into the phasotron.In 1963, the possibility was considered in Oak Ridge of accelerating protons to an energy of 12.5 GeV at an average beam current of 1 mA on the basis of a cascade of three cyclotrons with separated orbits.5 The orbit radius of the third stage was chosen to be equal to 60 m. The cost of the project was estimated as 160 million dollars.In 1967 a superconducting linac was proposed in Karlsruhe (the FRG) to accelerate protons to 7 GeV with an average beam current of 100 yA, which was to operate in a continuous mode.6 The energy gain was taken to be 5.5 MeV/m. The project cost is 50 million dollars.However, for various reasons these projects have not been executed.In 1970, when the pion facilities in Los Alamos, Zurich and Vancouver were under construction, the author proposed a ring cyclotron with passage of integral radial betatron oscillation resonances (Qr =2,3,4,...) which permitted the proton energy to be increased from~0.5 to0.8 GeV to several GeV.7’8 Such a ring cyclotron allows pion factories (both operating and being designed, Tables I and II) to be used as injec­tors. Note that a cascade of the proposed ring cyclotrons makes possible a significant increase in proton energy, their number being determined both by the final energy and economic considerations.7’8The suggestion to use ring cyclotrons with passage of integral204Table I. Possible parameters of a kaon-neutron factory based on a two-stage cyclotron for a proton energy of ~4.2 GeV. First stage - the Dubna cyclotron project.Parameter Stage I Stage IIInjection energy, MeV 50 80Final energy, GeV 0.8 4.2Average current, pA (stage I) 100-500 100-500mA (stage II) 10-100 10-100Magnetic field at the centre, kG 4.08 2.04Infinite energy radius, cm 766.529 1533.0588Initial radius, cm 220 1314Final radius, cm 650 1507Field-structure periodicity 8 24Archimedian spiral parameter, cm 9.85-11.05Magnetic field at r^, kG 4.27 3.68Magnetic field at rf, kG 7.5 10.5Field variation 0.35-1Axial oscillation frequency 1.3-1.4 1.1Radial oscillation frequency 1.06 ^ Qj- 'z* 1.9 1.9 » Qr » 6Energy gain per turn, MeV 2 3Number of resonators 4 6Particle rotation frequency, MHz 6.2 3.1Operating frequency, MHz 49.6 49.6Order 8 16Magnet weight, t 5800 8500Magnet consumption power, MW 1.7 2.8Radio-frequency power, MW (stage I) 1-1.5 2-4(stage II) 9-81 44-442Acceleration loss of beam io- ^ io-4 io^ - io-1*Extraction efficiency required, % 100 100Table II. Possible parameters of a kaon factory for a proton 8.5 GeV. Injector - the 525 MeV Vancouver pion ofParameter Stage I Stage IIInjection energy, MeV 450 3000Final energy, MeV 3000 8500Magnetic field at the centre, kG 3 1.5Infinite energy radius, m 10.3 20.6Radial width of acceleration, m 2.3 0.5Number of sectors 15 30Number of main resonators 8 at 46 MHz 15 at 69 MHzNumber of harmonic resonators 4 at 92 MHz 6 at 207 MHzSize of main resonators, m2 5.9 x 3.6 4 x 2.6Size of extra resonators, m2 5.9 x 1.6 4 x 1.5Total radio-frequency power, MW 2 1.7Energy gain per turn, MeV at injection 1.2 7.9at extraction 3.6 7.9Radial step per turn, mm at injection 5.3 4.2at extraction 0.64 0.26Number of turns 900 700Betatron oscillation frequency radial 1.5 > Qr > 4 4 >y Qr » 10axial 1.5 5- Qz > 2.8Magnet steel weight, t 2000 1800205resonances in Qr to increase the proton energy from the existing cyclotron pion factories to several GeV was later repeated in refs. 10 and 11. In Vancouver, M. Craddock considered in 1978 a variant of the ring cyclotron kaon factory.11 The 450 MeV protons from a pion facility are successively accelerated by a cascade of two ring cyclotrons to 3 and 8.5 GeV with an average beam current 100-300 yA (Table II). The cyclotrons have been considered in a superconducting variant (a maximum magnetic field of 50 kG). At the same time, in Vancouver, Richardson proposed to increase proton energy from 450 MeV to 8-10 GeV by using a fast-cycling synchrotron (frequency 20 Hz, radius 50 m)12 with expected average beam current ~30 yA. The main difficulty in the design is to maintain the pulsed beam structure in a fast-cycling synchrotron with respect to the quasi-continuous cyclo­tron beam.In connection with the development in the USSR of a pion facility based on a linear accelerator (600 MeV, 500 pA), two possibilities have been considered for increasing the proton energy to 7 GeV— a linear accelerator13 and a synchrotron with multiturn injection of H~ ions (ave­rage current < 50 pA).14 In both cases, however, it is necessary to use a stretcher to increase the beam duty cycle.Let us discuss the question of the final energy for a kaon factory.Usually, a proton energy ~7 to 10 GeV is chosen. In this case, alongwith kaons, the increasingly heavier hadrons, up to antiprotons, will be produced. There is the opinion, however, that the above-threshold kaons with energies to 0.5-1 GeV present the greatest interest. In this case, we need shorter meson channels, lower background and less costly kaon facilities (proton energy ~  2.5 GeV is enough).The present paper discusses a kaon factory based on a ring cyclotronfor proton energy ~  4.2 GeV and average beam current 100 to 500 pA(Table I),15-18 for which the 800 MeV cyclotron9 being developed in Dubna (average beam current 1 to 100 mA) will serve as the injector.The possibility of accelerating protons in a ring cyclotron to several GeV is associated with the passage of integral resonances in radial betatron oscillations (Qr = 2,3,4,...), of which the most dangerous is the integral resonance Qr = 2 (energy ~  845 MeV).On the basis of an approximate treatment within the framework of linear theory19 the conclusion was usually made of the necessity of a rapid passage of a resonance (a particle stays in the resonance zone dur­ing several turns), which led to an energy gain of several tens of MeV per turn9 thus making the ring cyclotron economically unprofitable. Believing that a slow passage of an integral resonance (a particle stays in the resonance zone for several tens of turns) is impossible,20 the Dubna group has proposed a ring cyclotron (initial energy 2 GeV, final energy 7 GeV) with a dynamical orbit similitude (Qr = const, Qz = const) attained by choosing a special configuration of the magnetic field.9In view of the aforesaid, a study was made of the slow passage of the integral resonance Qr = 2 with subsequent acceleration to Qr = 2.3 (~1200 MeV) by simulating the dynamics of the motion of protons in theI r I omagnetic field with the spatial variation in the complete equations13 according to a method proposed in ref. 21. The set of differential equa­tions that describe the motion of a proton in the electromagnetic field is of the form2062K'2 1 .5 " -  — - 5 - - / 7 1 + *(,2 n,2+1/2A  + n'2- nn 'K 'Ar - on 'A(IO3 / i + d3Hr5 2 +  V 2 + n '2x I Er -2 £ V  = i _ f 1 + i ^ + n'2? ?e- 5 rn 'Az - e, rnA(x I Er - —  I ,1/2e;2 + n' 2 J Arn10 3 /I+i]3Hr5 2 + £'2 + n f 2where £ = r/rco> = r,/r0O and n = z/ra , n f = z'/r,,, are the relative normalized particle coordinates, r^ , = EQ/eH0 .In the plane z = 0, the magnetic cyclotron field isH = H + T  Hs cos|as (5) - s*] + Hn cos aN (5) - N<J>J ,where H is the average magnetic field, s the number of the lowest field harmonics (s < N).The components Az, Ar and A^ are related to those of the magnetic field intensity Hz, Hr and by the expressions/ itAz = Hz = Fo + FS sin(r + as - S(M  + fN sin T  + aN - ^  ;V2 V2Ar = Hr-dFn dFc—  i — sin( 1- ag - sd) +dF* / Tlsinl 1- - Ncf>dC \2dac ' TT- F — 2. sinl s<j> - Fns d? \2 7  N d?daN . ASln\2 " N<i> ’Ad = Hd7 = sFs sin(as _ S<J>J + n f n sln(aN " N7 ;Fo =H(g)H„p . , M h i l . c  , i ^ 5 .1  tt ’ U 1  Ti »H,o A.lV ( w _  avk(l + —  + 0 . 1 2m Fo- i ;2 AVj^  is the gain of energy at the KtA gap in hundreds of keV m times (m = 0,1,2,...); Ez, Er , Ej, are the components of the accelerating electric field (Er = Ez = 0) ; E^ = E ^  = A V ^ / b h ^ r ^ ; b is the number of steps207inside the accelerating gap; H is the step's number, h^ is the step of azimuthal integration.The calculations were made with the following ring-cyclotron param­eters: H0 = 2 kG, N = 20, £ = 1, Qz = 1.1, 1.6 < Qr << 5, r,^  = 1563.72 cm.Computations were made for particles of different initial coordinates, also varying the number of accelerating gaps, energy gain at a gap, ampli­tude of the second field harmonic and phase shift between the fundamental and second field harmonics (0 < 6 < tt/N). The initial data were given as tables at forty-four radially equidistant points (5^ = 0.790422,E,f = 0.900416 step A£ = 0.002588). The number of computation points at an azimuth was 800; the azimuthal extension of an accelerating gap was 8 points. Acceleration was achieved with the aid of four equidistant gaps placed at fixed azimuths. The injector is displaced relative to the gaps at an angle of 45°. The injected proton energy was chosen to be 665 MeV (Qr = 1.75).Figures 1-4 illustrate the behaviour of the radial and vertical co­ordinates of particles with integral turns at an injection azimuth as functions of the second field harmonic and the energy gain per turn. The character of the trajectory (scalloped/smoothed) of particles of constant energy W inside one turn is shown in Fig. 5 (the calculation is for the static regime eV=0). The calculations indicate that in passing the zone of the integral resonance Qr = 2 in the case of H2 > 0 free radial oscil­lations of particles are perturbed (the action of the resonance upon the particle-oscillation amplitude is coherent), the magnitude of the pertur­bation is rather well (to ~80%) described by the asymptotic formula of the linear theory.19 Further, as the particle energy increases (with increas­ing frequency Qr and orbit radius), there occurs a strong postresonance oscillation damping, which disappears as Qr is increased by~0.25 (W ~  1120 MeV). At the resonance zone, width AQ^ = ±0.05, where the second field harmonic is equal to 0.5 G (in the remaining zone along the radius the harmonic is 5 G), and at an energy gain per turn of 3 MeV, the initial amplitude of the free radial particle oscillations (~1 cm at an energy of 665 MeV) increases in passing the resonance zone to~5.6 cm and, with increasing particle energy, decreases again to ~1 cm at Qr ~  2.25.The radial emittance of the beam (diam 6 mm) is practically unchanged in the course of acceleration. The observed strong postresonance damping of oscillations (~70%) prevails over the known adiabatic damping ~(QrH)-1/2 = 12.5% when Qr increases from 2 to 2.25.The observed, previously unknown, phenomenon of strong postresonance (in comparison with the known adiabatic) damping, with increasing orbit radius, of the amplitude of free radial oscillations of charged particles perturbed in passing an integral resonance, which is caused by the departure of the frequency of the radial oscillations from the resonance in the magnetic field with spatial variation, makes it possible to assure a slow passage in cyclotrons (having a wide region of magnetic-field formation along the radius) of integral resonances (Qr = 2,3,4,...) with a per-turn energy gain of ~3 MeV and a tolerance for the lowest field harmonics of ~0.5 G in zones of the corresponding integral resonances.As is known, in passing the internal nonlinear resonance of the fourth order p = 4, the increase in the free radial particle-oscillation amplitude in the resonance zone is proportional to the initial amplitude cubed. In order to eliminate additional antidamping of particles in the course of acceleration and to assure a compact cyclotron (a minimum number208of sectors) the integral resonance at a finite radius Qr = 6 is brought to coincide with the nonlinear structural resonance p = 4. In this case the number of sectors N = pQr = 24.The approximate values for the betatron oscillation frequencies in an isochronous cyclotron are given byWith a final radius of the ring cyclotron, r = 1507 cm, and with the parameters Qr = 6, Qz = 1.1, N = 24, n = 32.5, A = 11.05 cm, e = 1 (the amplitude of the fundamental harmonic should decrease if the higher field harmonics are taken into account), the spiral angle is y a  5.7 rad. Withsatisfied that, in a half period of the magnetic-field structure tt/N=7.5°, the spiral angle changeswith radius by not more than 6°; (thus, with the initial radius r = 1314 cm and X = 9.85 cm, the angle y w  5.6 rad). In this case, it is possible to use rectilinear resonators as in the Zurich cyclotron.Since at the final radius the average magnetic field is ~10.5 kG, in ring cyclotrons for proton energy up to several GeV, the flutter may be formed at e = 1 without the use of superconductivity. The latter is attractive for reducing operational costs (true, at increased capital in­vestment) and is undoubtedly necessary for accelerating protons in ring cyclotrons from several GeV to ~10 GeV (e > 2 is required).At a proton injection energy of 800 MeV, an energy gain per turn of 3 MeV assures separation of orbits at initial radii by 6 mm, which is suf­ficient at a beam diameter of 5 mm. High-efficiency beam extraction (~100%) from a ring cyclotron can be assured on the basis of the effect of expansion of closed orbits, which was suggested and tested experimentally on the electron cyclotron in Dubna.9 The radial and vertical beam emit­tances in a ring cyclotron at an initial radius are about equal Ar = Az =1.3 mm-mrad, being Ar = 1.5 mm-mrad and Az = 0.5 mm-mrad at the finalNote that in perspective proton ring cyclotrons for energies to several GeV may be used not only as kaon factories (stage I), but also as neutron factories (stage II at an average beam current 10 to 100 mA) forThe further perspectives of development of the pion factories already in operation or under construction are associated not only with the en­hancement of beam intensities, but also with their utilization as injec­tors for kaon factories. Safe passage of the integral resonances makes creation of a cyclotron kaon factory feasible.2the radial width of the accelerating track ~2 m, the condition can beradius.industrial production of nuclear fuel (Table x ) . 1 7 , 1 8 , 2 2  g u t  t g e creation of neutron generators involves further development of prototypes of various device units.CONCLUSION209REFERENCES1. P.A. Jameson, Proc. 4th All-Union Conf. on Charged Particle Accelerators, Izd. "Nauka", Moscow, 1975, vol. 1, p. 1312. H.A. Willax, Proc. 10th Int. Conf. on High Energy Accelerators, Serpukhov, 1977, vol. 1, p. 199.3. G.H. Mackenzie, ibid., p. 184.4. B. Waldman, Int. Conf. on High Energy Accelerators, BNL, 1961, p. 57.5. M. Russell and R. Livingston, Proc. Int. Conf. on Accelerators,Atomizdat, Moscow, 1964, p. 1085.6. C. Passow, Proc. 6th Int. Conf. on High Energy Accelerators, Cambridge, 1967, p. 383.7. L.A. Sarkisyan, Proc. 2nd All-Union Conf. on Charged ParticleAccelerators, Izd. "Nauka", Moscow, 1972, vol. 1, p. 33.8. L.A. Sarkisyan, "Atomnaya energhiya" _30^, 446 (1971) ; ibid. 32, 55(1972).9. V.P. Dzhelepov et_ al_., Preprint JINR, P9-7833, Dubna, 1974.10. H. Blosser, Proc. 6th Int. Cyclotron Conf., Vancouver (American Inst, of Physics, New York, 1972), p. 16.11. M.K. Craddock et_ al., IEEE Trans. Nucl. Sci. NS-26(2), 2065 (1979).12. J.R. Richardson, ibid., p. 2436.13. B.P. Murin, Proc. 3rd All-Union Conf. on Charged Particle Accelerators, Izd. "Nauka", Moscow, 1973, vol. 1, p. 234.14. Yu.G. Basargin et_ aH. , Dokl. Akad. Nauk SSSR 209, 819 (1973).15. L.A. Sarkisyan, Vestnik MGU R7, 282 (1976).16. L.A. Sarkisyan, Nucl. Instr. & Meth. 142, 393 (1977).17. L.A. Sarkisyan, 6th All-Union Conf. on Charged Particle Accelerators, Abstracts, D9-11874, Dubna, 1978, p. 37.18. L.A. Sarkisyan, Workshop on Technique of Isochronous Cyclotrons,Krakow, Nov. 13-18, 1978, Inst. Nucl. Phys. of Poland Publishers,p. 10.19. P.D. Dunn et_ aH., Proc. Symp. on High Energy Accelerators and Pion Physics, CERN, 1956, vol. 1, p. 9.20. V.P. Dmitrievsky, Preprint JINR, P9-9341, Dubna, 1976, p. 168.21. V.P. Dmitrievsky et_ jtl., Preprint JINR, P9-5498, Dubna, 1971, p. 24.22. L.A. Sarkisyan, Vestnik MGU 213, 10 (1979).21050.9Fig. 1. Behaviour of the radial co­ordinate of a particle at a fixed azi muth with integral turns (eV = 3 MeV/ turn) with varying second field harmonic: 1. H2 = 0; 2. H2 = 0.5 G;3. H2 = 2 G; 4. H2 = 5 G.Fig. 3. Behaviour of the radial par­ticle coordinate at a fixed azimuth with integral turns for a stepwise character of the second field har­monic (Fig. 2, curve 1) and eV =3 MeV/turn for various beam parti­cles. For curves 1, 3 and 4, counts in the £ axis should be shifted by 0.01, -0.01 and -0.02, respectively.Fig. 2. Behaviour of the radial parti­cle coordinate at a fixed azimuth with integral turns for a stepwise varia­tion with radius of the second field harmonic and for different energy gain per turn (initial particle coordinates- point 5, Fig. 3):1. Resonance zone width AQr = ±0.05, where H2 = 0.5 G; eV = 3 MeV/turn.2. Resonance zone width AQr = ±0.05, where H2 = 1 G; eV = 3 MeV/turn.3. Resonance zone width AQr = ±0.05, where H2 = 1 G; eV = 4 MeV/turn.Fig. 4. Change in the vertical particle coordinate at a fixed azimuth with integral turns (eV = 3 MeV/turn) for a stepwise character of the second field harmonic (curve 1, Fig. 2).Fig. 5. Constant-energy particle trajectories (scalloped/smoothed) with­in a single turn. Initial coordinates ' and particle energies aretaken from a) curve 1, Fig. 1, and b) curve 1, Fig. 2.212LOW ENERGY KAON BEAM WITH SUPERCONDUCTING COMBINED FUNCTION MAGNETSAkira Yamamoto, Shin-ichi Kurokawa and Hiromi Hirabayashi National Laboratory for High Energy Physics Oho-Machi, Tsukuba-gun, Ibaraki-ken, 300-32, JapanINTRODUCTIONLow energy kaon beams inevitably require large solid angle acceptance, short length of the beam and excellent mass separation because of the low production rate and the short decay length of the low energy kaons. On the basis of our experience of the low energy kaon beams at KEK,1 we have formulated a unique design to shorten the total beam length and to enlarge the solid angle acceptance, using superconducting combined function cur­rent sheet magnets. In these magnets, the quadrupole field is superposed on the dipole field by independent current sheets. By the use of these magnets with a high field electrostatic separator, it is possible to get a very intense kaon beam with good beam quality.A brief description of the design of the magnets, the electrostatic separator and the beam optics is given.SUPERCONDUCTING COMBINED FUNCTION MAGNETUtilization of superconducting coils with high current density of several tens kA/cm2 makes it possible to design an excellent current sheet magnet which is suitable for high energy beam handling. It is well known that an ideal magnetic quadrupole field can be produced by a set of current sheets with iron yoke,2 and also a window frame dipole magnet can be made by the current sheets and the iron yoke. In high field regions, the field calculation is somewhat complicated due to the magnetic satura­tion in the iron yoke; however, a practical magnetic field can be produced in these magnets.213The basic principle of the superconducting combined function magnet is the superposition of dipole field and quadrupole field produced by the independent cur­rent sheets. In this type of magnet, it is very important to get the centers of the two kinds of current sheets located at the same position.3 The basic princi­ple and the schematic view are shown in Fig. 1. In spite of the complication of coil winding and of inductive coupling between the coils, the merit of shortening the magnetic elements should not be ignored, since total length of the beam line is an essential parameter for the low energy kaon beam.Development of a few superconducting current sheet magnets has been carried out at KEK,11-6 and a superconducting combined function current sheet magnet has been designed for this low energy kaon beam. The magnet­ic fluxes have been calculated by programs LINDA and TRIM.7’8 An example of the magnetic field lines is shown in Fig. 2.ELECTROSTATIC SEPARATORIn order to separate kaons from the other particles with good mass separation in the short beam, the field of the electro­static separator should be as high as possible. Electrostatic separators with built-in high voltage generators have been developed at KEK,8 and a maximum field of 1005 kV/10 cm has been achieved at the latest 6 m separator without serious problems.18 We are sure to be able to develop a very high field separator with the operational electro­static field of 1000 kV/10 cm, in near future. The front view of the separator with built-in high voltage generators is shown in Fig. 3.Fig. 3. A front view of the KEK electrostatic separator.BEAM DESIGNUsing these magnets and the electrostatic separator, it is possible to save the beam length and to enlarge the solid angle acceptance, as are inevitably required in a low energy kaon beam. A design of a short kaon beam of maximum momentum 700 MeV/c has been studied. The basic parameters are as follows:Fig. 2. An example of the magnetic field lines of the superconducting combined function magnet.214Maximum beam momentum 700 MeV/cTotal beam length 8.5 mCentral production angle 5°Solid angle acceptance 12 msrHorizontal acceptance ±200 mrVertical acceptance ±15 mrMomentum bite ±3%The central production angle of 5° is chosen to keep the beam flux high while getting the beam away from the primary beam direction.Basically, this beam consists of two stages as shown in Fig. 4. The beam is doubly focused at the end of each stage (IF and FF). In the first stage, the momentum and the mass of the beam are analysed by DQ1, DQ2 and SEP and selected by the mass and the momentum slits, where DQs and SEP mean the com­bined function (dipole and quadrupole) magnets and the electrostatic separator, respectively. A quadrupole (Q) acts as the field lens.In the second stage, the beam is recombined and focused at the end of the line. The beam optics was calculated by the program TRANSPORT.11 The first order beam envelopes are shown in Fig. 5.A calculated mass separation quality factor (S) of 2.3 at the beam momentum 500 MeV/c is acceptable to separate the kaons from the other particles. The factor S is defined by the ratio of the spatial separation of the beam and the second order beam size (o) at the IF. The electric field of the electrostatic separator is assumed to be 900 kV/10 cm.The kaon intensities were estimated, by extrapolating the experi­mental results at the ZGS and KEK.12’13 Fluxes of 1.4 x 105 K+ and 3.2 x IO4 K" are expected at 500 MeV/c momentum for 1012 incident protons of momentum 13 GeV/c into a 6 cm long Pt target.All of the magnets used in this beam are superconducting combined function magnets. The DQ1 is the most critical one, requiring horizontal and vertical apertures of 40 cm and 20 cm, respectively, and the super­position of the dipole field of 1.45 T upon the quadrupole field of 10 T/m at the maximum momentum.Finally, we should mention about the radiation shield around the pro­duction target. It is necessary to have a radiation shield such as iron blocks and heavy concrete blocks. The minimum thickness of the shield for transverse direction to the primary beam is 5 m for 2 x 1012/sec incident primary proton intensity of momentum 13 GeV/c. The minimum beam length is in practice limited by the thickness of the radiation shield.FF - *Fig. 4. The layout of the beam.215MOMENTUM SLITCONCLUSIONWe have designed an intense kaon beam with superconducting combined function magnets. The length of the beam is only 8.5 m. Fluxes of2.4 x 105 K and 3.2 x IO1* K- at momentum 500 MeV/c are expected for 1012 incident primary protons of momentum 13 GeV/c into the 6 cm long Pt target.REFERENCES1. H. Hirabayashi, S. Kurokawa, A. Yamamoto and A. Kusumegi, IEEE Trans. NS-26(3), 3191 (1979).2. L.N. Hand and W.K.H. Panofsky, Rev. Sci. Instrum. _30, 927 (1959).3. Y. Takada, private communication.4. H. Hirabayashi, Y . Doi, N. Ishihara, A. Maki, T. Sato and K. Tsuchiya, Proc. 5th Int. Cryogenic Engineering Conf. (1974), p. 395.5. K. Tsuchiya, H. Hirabayashi, S. Kurokawa and K. Oishi, "A Super­conducting Quadrupole Magnet with the Large Rectangular Aperture", to be reported.6. A. Yamamoto, H. Hirabayashi, K. Tsuchiya, S. Kurokawa and M. Taino,"A Superconducting Septum Magnet", to be reported.7. K. Endo and M. Kihara, KEK ACC-1 (1972). An original program was written by J.H. Dorst of LBL.8. K. Endo, KEK ACC-2 (1974). An original program was written byA.W. Winslow of LLL and improved by J.S. Colonias of LBL.9. A. Yamamoto, A. Maki and A. Kusumegi, Nucl. Instrum. & Methods 148,203 (1978).10. H. Ishii, A. Yamamoto, Y. Yoshimura and H. Hirabayashi, to bereported in KEK report.11. K.L. Brown, D.C. Carey, Ch. Iselin and F. Rothacker, CERN 76-13(1973).12. E. Colton, Nucl. Instrum. & Methods 138, 589 (1976).13. S. Kurokawa, E. Kikutani and H. Hirabayashi, to be reported.216DISCUSSIONRICHARDSON: We heard yesterday that there was some good physics to bedone at 300 MeV/c. What are the chances of getting a K beam of that momentum?YAMAMOTO: I think it will be feasible, if every condition described inthis report is improved. We will be able to shorten the beam length a little bit, if the momentum is 300 MeV/c. But it is very difficult to get an intense kaon beam at 300 MeV/c because of the extremely low pro­duction rate and the very short decay length at that momentum.217SUMMARY OF KAON FACTORY WORKSHOPErnest M. Henley University of Washington, Seattle, Washington 98195ABSTRACTSome highlights of the physics sessions of the workshop are presented. Particular emphasis is placed on the different investigations which can be carried out with kaons and antiprotons than with pions and protons.I . INTRODUCTIONThe organizers of the Kaon Factory Workshop chose a non-expert to summarize the physics discussion. Perhaps they reasoned that they would get a more balanced overview. Undoubtedly, I will disappoint them in that my own biases color the presentation that you are about to hear. I apologize beforehand. In my review I will give names of speakers or other references only when they are required, as several speakers overlapped in the physics they presented. (I must admit that another reason is cow­ardice, as I am not certain in all cases as to who deserves the credits.)1 apologize to all the speakers and contributors beforehand. Table I lists the speakers in the sessions I attended. There was also a technical session, which was held simultaneously with a plenary session, and which I missed.What is the interest in an accelerator to produce kaons? In general terms, the interest centers on the nuclear physics studies which can be carried out with the next generation of higher-energy (3-40 GeV), high- intensity (1-100 pA) accelerators. The range of parameters is large; de­sign studies are not complete. To my knowledge, such accelerators are be­ing considered at TRIUMF, at LAMPF, at CERN (the proposed low-energy antiproton ring - LEAR), and in the USSR. The lure of such accelerators lies in the high-quality kaon and antiproton beams that they can produce. Since LEAR has been proposed as a definite facility, let me describe it in a little more detail. The proposal consists of an accumulator ring with large acceptance which can store antiprotons produced at the PS; these antiprotons can be cooled stochastically and can be decelerated or accele­rated to give antiprotons of momenta in a range of 300 MeV/c p <2 GeV/c. During the accumulation and cooling period tt impurities decay away, so that a clean beam with high energy resolution (6p/p 10-3) can be obtained. A beam of more than 106 p/sec is envisaged. The quality of the beam allows one to plan experiments such as pp ones in a gaseous hydrogen target 10 cm long and at atmospheric pressure.Not all the work is on the drawing-boards. There are lower-energy and lower-intensity K* and/or antiproton beams available at the Brookhaven National Laboratory (from the AGS), at CERN (from the PS), and perhaps at the KEK in Japan. To demonstrate that actual data exist, I show you in Figs. 1 and 2 some experimental results obtained by the Carnegie-Mellon/ Houston/Brookhaven group and presented by R.A. Eisenstein on the elastic scattering of K+ and K- by 12C. The various curves are optical model anal­yses which were discussed at the same session. You might note that the fit to the K+ elastic scattering cross section is remarkably good. I believe that we are likely to see an increasing emphasis on investigations with K~ and p prior to the next conference in this series.Fig. 1. K+ + 12C elastic scattering differential cross Some optical model fits are shown.sectionFig. 2. K + 12C elastic scattering differential cross section Some optical model fits are shown.219II. DIFFERENCES OF PROBESWhat is it that makes kaons and antiprotons interesting probes for nuclear studies? It is primarily the differences of their interactions with nucleons which appeal to the nuclear physicist. The K+ has strange­ness +1; since there are no baryons with such strangeness, the K+ cannot be absorbed in nuclei to form hyperfragments. For both K^, the long-range single-pion exchange force with nucleons is absent. The K+ is the weakest known hadronic probe of the nucleus. It may scatter only elastically or inelastically, except for forming "exotic" Z* resonances at momenta above ~800 MeV/c. In the quark language, which is becoming "de rigeur" at these conferences, such resonances are thought to be 5-quark objects (q4q}; they are narrow resonances. From the above considerations, it follows that the mean free path of K+ particles in nuclei below ~800 MeV/c is large,^5 fm.In contrast to K+ particles, the K- interacts strongly with nucleons. Because its strangeness is -1, it can be absorbed readily by single nucleons to form hyperons. It thus differs from pions which are absorbed primarily on two nucleons. This difference, alone, makes K- studies more sensitive to the nuclear surface than pions. Moreover, it is this absorp­tion mechanism which permits us to study hypernuclei, a subject which was presented earlier at these sessions by B. Povh. The AN force is quite different from the NN one. As we heard, there is some evidence that the spin-orbit force is very weak. The one-pion exchange force is absent, except through isospin mixing of the A0 and E°, but K and K* exchanges are allowed [see Fig. 3(a)]. Because of the long range of the pion exchangeFig. 3. Contributions to (a) a AN force, (b) a K-^ N force.220force, charge symmetry-breaking, via A°-E° mixing, may be relatively large in the A-N system. The K-N force, illustrated in Fig. 3(b) , also differs considerably from the ttN  force. The K-N system can and does form reso­nances; close to threshold there are the A (1405)— actually slightly below threshold— and the A(1520)3/2- , which has a small width of only ~15 MeV. Again, it is this difference from the much shorter-lived A (1232) formed by pions which is being accentuated by physicists. Can one profitably use the small width of the A(1520) as a tool to study the effect of the nuclear medium on a resonance? What are the effects of the Fermi motion, of collisional broadening, and of new decay channels unavailable to the free A(1520)? We heard several talks on these matters.Of course, studies of the free particles are useful for testing and limiting proposed basic theories of particle physics. Recent gauge theories which do not conserve muon number predict a small branching ratio (10“12-10-16?) for Kl -*■ e1^  ; the present experimental limit is 2 x 10-9. This ratio already sets limits on the mass (>30 TeV) of the gauge boson exchanged, and the experimental limit can undoubtedly be improved. Other rare decay modes are also of interest.The relationship of the study of the static properties of strange particles and resonances to their underlying quark structure, to confine­ment and to (perturbative) QCD was also discussed. The presence of the strange valence quark brings in a new degree of freedom which enriches the spectroscopy and may give us new insights into the mechanism of quark con­finement and how to apply QCD to this problem.The antiproton, in contrast to the K+ , is perhaps the most strongly absorbed hadronic probe of nuclei. It is therefore exceedingly sensitive to the nuclear surface; this is, in fact, one feature which makes the study of {T-atoms of interest. In addition, as we heard in a report byH.-M. Chan, the NN resonances (baryonium) exhibit rather striking features, which may give one insight into the underlying quark structure of nucleons. Are the narrow resonances near threshold an indication of a q2q”2 system?Are there bound pp states, and if so what is their character? Can p ab­sorption be used to form nuclei far from the region of stability through multipion emission processes?III. SOME PHYSICS QUESTIONSLet me summarize some of the physics which becomes accessible with kaon and antiproton probes by posing a series of questions. The questions, as such, were not raised at the workshop, though many of them (but not all) were discussed there.K+ Meson1) Can the K+N (primarily K"*~n) force be determined with sufficient precision to allow one to use K+ scattering as a tool to extract neutron densities and particularly neutron radii of nuclei? It is the lack of such information which at present prevents the use of K+ beams to determine neutron radii. The isospin 1 K+N force appears to be repulsive in low partial waves. Some contributions to the force are shown in Fig. 3(b).2) Does the K+ meson preferentially excite simple modes of motion of the nucleus, e.g., the giant isoscalar resonances? In other words, is it a useful as well as new probe of nuclear structure? It appears that such is the case.2213) What is the nature of "exotic" Z* resonances? Can one study the effects of the nuclear medium on these resonances in inelastic K"^  scatter­ing measurements?K~ Meson1) What is the nature of the K-N force? Some contributions are sketched in Fig. 3(a). How well can one determine the AN, the EN, and the EN forces with K~ beams? Considerable information has already been obtained on the AN force.2) It seems that a study of the A (1520) in the nucleus may help us understand the effect of the nuclear medium on a narrow resonance. Will such studies help us to sort out what happens to a broader resonance such as the A (1232)? To what extent will it help us understand what happens at higher energies where overlapping Y* resonances occur?3) Can kaonic atoms be used to study the nuclear surface, or are such studies spoiled by our lack of knowledge of the K-N force and the role of the A(1405)? What can we learn from E- atoms?4) Is the recoilless formation of hyperons (pK- ~  550 MeV/c for A0 , Pj(- ~  300 MeV/c for E°) an important mechanism in the formation of hyper­nuclei?5) The study of hypernuclei has already been a rich source of new information. It is from these studies that features of the AN force have been deduced. At the workshop, the start of a table of A-hypernuclear iso­topes was shown. How far will we be able to extend this table and what surprises will we find?6) Does the A really behave like a spinless strange neutron in hyper­nuclei? What kinds of new information can we extract from detailed high resolution (K- ,tt-) and from (K- ,Tr-y) spectroscopic studies of A hyper­nuclei? This is clearly a rich field of study, in which the A can be con­sidered as a strange probe or "impurity". What are the structural changes brought about by the presence of this impurity in the nuclear medium? Can one, for instance, study core polarization in this way?7) Do strangeness analog resonances exist in heavy nuclei? These SU(3) generalizations of the SU(2) isobaric analog resonances have been predicted, but not yet observed. They are states with the same antisym­metric space-spin structure as the nucleus with a neutron instead of a A, even though the Pauli principle does not restrict the A orbitals as it does those of neutrons.8) What is the nature of SU(3) symmetry-breaking forces at low energies? Studies of the EN and AN forces and of E hypernuclei should be helpful in obtaining an answer to this question. Are E hypernuclei suffi­ciently stable and cross sections for producing them sufficiently largethat they can be studied? Are there strangeness - 2 5 hypernuclei?9) Can we understand the double charge exchange reaction for kaons sufficiently well to use it as a spectroscopic tool?10) The (K~,K+) reaction can be used to produce AA or E hypernuclei. What will studies of this reaction tell us about the AA force? Can the reaction be used to explore the underlying 6-quark basis for AA hyper­nuclei?11) The decays of Y*'s and Z*'s may be amenable to quark-parton and QCD model studies. Will such work be fruitful in teaching us about the connection of the quark and meson physics approaches?12) How useful are K° beams for studying nuclear structure? Althoughbeams of K° or and Kg mesons were not raised in the study, past222regeneration experiments suggest that studies with them can yield informa­tion on nuclear densities.13) Will studies with kaon beams help us to understand better the connection between the quark and meson pictures of hadrons and their forces?14) Can the rare decay modes K^/g y±e+ and K-*- -* TT± y ± e + be observed? If so, they may revolutionize, eliminate or tie down some of the ambitious gauge theories of weak, electromagnetic and strong interactions which continue to be proposed. Note that both strangeness and muon number are broken in these decays, whereas only muon number conservation is spoiled in y ey.15) Can weak interactions be studied usefully with kaon beams? For example, there have been suggestions that the Cabibbo angle reduces to0° in strong electromagnetic fields. Can this prediction be tested?The above questions refer to only parts of the issues raised by the speakers in the workshop. It is clear that one can use kaons, much like pions, to probe nuclear spectra and other nuclear properties. I thought it more helpful to stress the difference of the physics questions that can be explored with kaons rather than pions. Although I have presented the physics in terms of questions, I should point out that I believe the answer to quite a few questions is simply "Yes". Kaon beams do^  open new and interesting avenues with which to explore nuclei and hadronic properties.AntiprotonsAlthough there was considerably less emphasis in the workshop on anti­protons than on kaons, studies with this probe can be a rich source of new insights. We heard about some of these possibilities from H.-M. Chan.1) What is the relationship of the NN force to that of two nucleons?In a single-boson-exchange model, the real parts of these potentials are related by G-parity. The short range w-exchange potential, for instance, becomes strongly attractive. But what is the effect of the absorption?2) Are there bound states of the pp system, and if so what are their quantum numbers and other properties? Are these q2q”2 or q3q“3 bound quark states?3) How many narrow resonances are there close to threshold of the pp system? What is their structure? Are they q2cf2 states or are they simpler "molecular" type states? What causes their small decay widths?Why do they decay predominantly to BB" rather than to pions?4) The pd reaction may be used to explore pn states. Likewise the charge exchange of antiprotons might be used to study np states and reso­nances. What surprises await us there?5) The annihilation of p by p presumably occurs inside the quarkbag. The antiproton thus appears to be a prime candidate to tell us some­thing about the underlying quark structure of nucleons, of the size and character of the bag, and of the connection between quark and meson physics. Will this goal be realized?6) The study of p-nucleus scattering shows a total cross section larger than 2tt (5/3)<r2>, twice the geometric area of an object with uni­form density of rms radius <r2>1/2 . Will the expectation of using "p atoms to study the extreme outer edges of the nuclear surface be realized?7) With p" beams one can form AA, EA and other exotic systems such as 2NN. What are their properties?223The charge exchange reaction of p can give n beams. These open yet another field of study.Again, I have not discussed p nucleus scattering to study spectroscopy. Polarized p" beams open up yet new horizons.IV. CONCLUSIONSThe workshop demonstrated that a new and exciting realm of physics would be opened by a higher-energy accelerator, euphemistically called a Kaon Factory.Finally, on behalf of all of the participants in the workshop, I would like to thank the organizers: Harold Fearing, J. Reginald Richardson, and especially Michael K. Craddock who did most of the work, for organizing a very stimulating set of sessions.Table I. Kaon Factory WorkshopOrganizers: M.K . CraddockH. FearingJ.R . RichardsonPhysics I: Chairman, D.V. BuggJ.R. Richardson Opening remarksC.B. Dover IntroductionM. May Physics for a new kaon facility at the AGSR.R. Silbar Report on the Los Alamos Kaon Factory WorkshopR.A. Eisenstein Experimental elastic and inelastic kaonscatteringF. Tabakin Kaon-nucleus interactionS.R. Cotanch Can K+-nucleus scattering accurately determineneutron radii?G.N. Epstein Kaon-nucleon interactions in the A (1520) regionPhysics II: Chairman, E. BoschitzP. Herczeg Symmetry-violating kaon decaysN. Isgur Hyperon physics and chromodynamicsU. Gastaldi Physics with a low energy antiproton ring (LEAR)at CERNA. Deloff Kaonic hydrogenM. Soyeur Quark model description of the radiative decayof the resonance A3/2~(1520)224DISCUSSIONBUGG: I have a technical comment on a point not discussed at the workshop,but I think it is relevant. Beam intensity is important, but beam quality is also vital. Ten years ago, y beams of 10^/sec were available. Nowadays many experiments restrict themselves to 5 x 10^/sec, but they have very much improved beam quality. With kaons an intensity of 106/sec will be adequate for most experiments. But separation of K± from rubbish is the major difficulty. I suggest that this is a strong reason for preferring an isochronous ring cyclotron over a synchrotron, because of the availability of time of flight. The RF in a cyclotron is at fixed frequency, and can be much higher in voltage than at a synchrotron, where a large frequency swing is required. Experience at TRIUMF is that time of flight with respect to cyclotron RF is an enormous asset in separating particle types. At a kaon factory, one might even take advantage of RF separation, rather than electrostatic separation. I believe this is a fundamental reason why kaon physics cannot economically be mopped up at existing accelerators, and why a dedicated facility is required. If one wants to study K°s, time of flight will be essential in separating them from neutrons. If one wants to excite Y*s by tickling A°,Z- in a foil, time of flight is again an essen­tial requirement; in this case intensity is not the issue, since the par­ticle lifetime requires that the experiment be done within 1 m of the production target, and the experiment is intensity limited anyway.As regards energy, one can cover the interesting range of KN reso­nances with 3 GeV/c K“ , and this is adequate for K-nucleus studies, too. Hence I conclude that 8 GeV beam energy is adequate if one is strapped for money.SINGER: Was there any discussion on the beam energies considered for thekaon factories?RICHARDSON: The question of the energy of a kaon and/or p factory mustdepend on good knowledge of the production cross sections. The curves for both the K and p" production show knees at about 10 GeV, but it must be realized that knee is based upon unpublished results from a single laboratory. For a pure kaon factory perhaps 9-10 GeV would be sufficient, but for a combination K and p factory energies from 16 to 30 GeV have been suggested.SCHIFFER: Since secondary kaon beams are heavily contaminated with pions,and one normally has to count every particle in the beam to tag it, how would this be done with the very intense beams from a 100 yA proton beam?RICHARDSON: In response to the question of the handling of intense kaonbeams I would simply remark that the new kaon beam at Brookhaven has approximately 10 times the expected pion/kaon ratio. Until this difficulty is understood it is too early to discuss the handling of even more intense kaon beams.225ROBERTS: The current situation with p atoms is roughly the same as K~atoms, viz. a number of X-ray strong interaction shifts and widths have been measured for a range of nuclei. The best one can do with the data is to obtain some sort of phenomenological optical potential as with K - atoms. Secondly, the Rutherford Lab group reported two years ago at Zurich (and subsequently published) that £~ strong interaction widths and shifts have been measured and they indicate that the Z~-nucleus interaction is considerably weaker than either the p-nucleus or K~-nucleus interaction.226PROGRAMMEMonday afternoon PHYSICS I (Chairman: D.V. Bugg)SpeakerOpening remarksNuclear physics with kaonsPhysics for a new kaon facility at the AGSReport on Los Alamos Kaon Factory Workshop:PhysicsKaon elastic and inelastic scattering at 800 MeV/c Kaon-nucleus interactionsNeutron density studies through K+-nucleus scatteringKaon-nucleus interactions in the A (1520) regionJ.R. Richardson C.B. Dover M. MayR.R. Silbar R.A. EisensteinF. TabakinS.R. CotanchG.N. EpsteinTuesday morning ACCELERATORS AND BEAMS (Chairman: J.R. Richardson)An improved kaon beam and spectrometer for the AGSThe Fermilab booster as a kaon factory Possible kaon and antiproton factory designs for TRIUMF A LAMPF kaon factory Future plans for SINA low energy kaon beam with superconducting combined function magnets Measurement of K±-nucleus elastic scattering at forward angles: An experiment to be done at KEKE.V. Hungerford III B . BrownM.K. Craddock D.E. Nagle J.P. BlaserA. YamamotoI. EndoTuesday afternoon PHYSICS II (Chairman: E. Boschitz)Symmetry-violating kaon decays Hyperon physics and chromodynamics Physics possibilities with LEAR, a low-energy antiproton facility at CERN Kaonic hydrogenQuark model description of the radiative decay of the resonance A3/2“(1520)P. Herczeg N. IsgurU. Gastaldi A. DeloffM. SoyeurPoster session227WORKSHOP PARTICIPANTSR. ABEGG, University of Manitoba, Winnipeg, Manitoba, CanadaG.S. ADAMS, Los Alamos Scientific Laboratory, Los Alamos, NM, USA K. AHMAD, University of Surrey, Guildford, Surrey, EnglandM. ALBERG, University of Washington, Seattle, WA, USA Y. ALEXANDER, Hebrew University of Jerusalem, Jerusalem, Israel R. ALLARDYCE, CERN, Geneva, Switzerland J. ALSTER, Tel-Aviv University, Ramat Aviv, IsraelC. AMSLER, University of New Mexico, Albuquerque, NM, USAH.L. ANDERSON, Los Alamos Scientific Laboratory, Los Alamos, NM, USAF. ANDO, Shinshu University, Matsumoto, JapanD. ASHERY, Tel-Aviv University, Ramat Aviv, IsraelI.P. AUER, Argonne National Laboratory, Argonne, IL, USA N. AUERBACH, Tel-Aviv University, Ramat Aviv, IsraelD. AXEN, University of British Columbia, Vancouver, B.C., CanadaG. BACKENSTOSS, Universitat Basel, Basel, SwitzerlandJ.M. BAILEY, Instituut voor Kernphysisch Onderzoek, Amsterdam, The NetherlandsF. BALESTRA, INFN, Torino, ItalyR.C. BARRETT, University of Surrey, Guildford, Surrey, England J. BARTKE, Joint Institute for Nuclear Research, Dubna, Moscow, USSRB. BASSALLECK, Carnegie-Mellon University, Pittsburgh, PA, USAG.A. BEER, University of Victoria, Victoria, B.C., Canada P. BENNETT, TRIUMF, Vancouver, B.C., CanadaJ.L. BEVERIDGE, TRIUMF, Vancouver, B.C., Canada0. BING, Centre de Recherches Nucleaires, Strasbourg-Cedex, FranceE.W. BLACKMORE, TRIUMF, Vancouver, B.C., CanadaJ.P. BLASER, Schweizerisches Institut fur Nuklearforschung, Villigen, SwitzerlandM. BLECHER, Virginia Polytechnic Institute and State University,Blacksburg, VA, USAD. BOAL, Simon Fraser University, Burnaby, B.C., CanadaB.E. BONNER, Los Alamos Scientific Laboratory, Los Alamos, NM, USAE. BORIE, Inst, fur Theoretische Kernphysik, Universitat Karlsruhe,Karlsruhe, Federal Republic of GermanyE. BOSCHITZ, Inst, fur Exp. Kernphysik, Universitat Karlsruhe, Karlsruhe, Federal Republic of Germany J.D. BOWMAN, Los Alamos Scientific Laboratory, Los Alamos, NM, USA J. BREWER, University of British Columbia, Vancouver, B.C., CanadaB. BROWN, Fermilab, Batavia, IL, USAD. BRYMAN, TRIUMF, Vancouver, B.C., CanadaD.V. BUGG, Rutherford Laboratory, Chilton, Oxon., England J. CARROLL, Lawrence Berkeley Laboratory, Berkeley, CA, USAA.L. CARTER, Carleton University, Ottawa, CanadaB.C. CLARK, Ohio State University, Columbus, OH, USAA.S. CLOUGH, University of Surrey, Guildford, Surrey, EnglandM. COMYN, TRIUMF, Vancouver, B.C., CanadaS.A. COONy University of Arizona, Tucson, AR, USAS.R. COTANCH, North Carolina State University, Raleigh, NC, USAM.K. CRADDOCK, University of British Columbia, Vancouver, B.C., CanadaK.M. CROWE, Lawrence Berkeley Laboratory, Berkeley, CA, USAW. DAHME, Schweizerisches Institut fur Nuklearforschung, Villigen,Switzerland P. DALPIAZ, INFN, Torino, Italy228H. DANIEL, Tech. Universitat Munchen, Garching, Federal Republic of GermanyA. DELOFF, University of Guelph, Guelph, Ont., CanadaM. DEUTSCH, Massachusetts Institute of Technology, Cambridge, MA, USA V. DEVANATHAN, University of Washington, Seattle, WA, USAB. DIETERLE, University of New Mexico, Albuquerque, NM, USAM. DILLIG, Universitat Erlangen-Nlirnberg, Erlangen, Federal Republic of GermanyJ. DOORNBOS, TRIUMF, Vancouver, B.C., CanadaC.B. DOVER, Brookhaven National Laboratory, Upton, NY, USAJ.F. DUBACH, Los Alamos Scientific Laboratory, Los Alamos, NM, USAG. DUTTO, TRIUMF, Vancouver, B.C., CanadaV.P. DZHELEPOV, Joint Institute for Nuclear Research, Dubna, Moscow, USSRM. ECKHAUSE, College of William & Mary, Williamsburg, VA, USAP. EGAN, Yale University, New Haven, CN, USAJ.M. EISENBERG, Tel-Aviv University, Ramat Aviv, IsraelR.A. EISENSTEIN, Carnegie-Mellon University, Pittsburgh, PA, USAI. ENDO, Hiroshima University, Hiroshima, JapanG.N. EPSTEIN, Massachusetts Institute of Technology, Cambridge, MA, USA K.L. ERDMAN, TRIUMF and Univ. of British Columbia, Vancouver, B.C., CanadaG.T. EWAN, Queen's University, Kingston, Ont., CanadaH.W. FEARING, TRIUMF, Vancouver, B.C., CanadaE. FERREIRA, Pontificia Universidade Catolica, Rio de Janeiro, Brazil A. FUJII, Sophia University, Tokyo, JapanA. GAL, Hebrew University of Jerusalem, Jerusalem, Israel U. GASTALDI, CERN, Geneva, SwitzerlandJ .V . GEAGA, Lawrence Berkeley Laboratory, Berkeley, CA, USAD. GILL, TRIUMF, Vancouver, B.C., CanadaC. GLASHAUSSER, Rutgers University, Piscataway, NJ, USAC.D. GOODMAN, Oak Ridge National Laboratory, Oak Ridge, TN, USA K. GOTOW, Virginia Polytechnic Institute and State University,Blacksburg, VA, USAD. GURD, TRIUMF, Vancouver, B.C., CanadaC.K. HARGROVE, National Research Council, Ottawa, Canada R. HARTMANN, College of William & Mary, Williamsburg, VA, USAA. HAYNES, TRIUMF, Vancouver, B.C., CanadaR. HEFFNER, Los Alamos Scientific Laboratory, Los Alamos, NM, USAE.M. HENLEY, University of Washington, Seattle, WA, USAP. HERCZEG, Los Alamos Scientific Laboratory, Los Alamos, NM, USA R. HESS, University of Geneva, Geneva, SwitzerlandF. HIBOU, Centre de Researches Nucleaires, Strasbourg-Cedex, FranceC.M. HOFFMANN, Los Alamos Scientific Laboratory, Los Alamos, NM, USAE.W. HOFFMANN, Los Alamos Scientific Laboratory, Los Alamos, NM, USAG.W. HOFFMANN, Los Alamos Scientific Laboratory, Los Alamos, NM, USAM.G. HUBER, Universitat Erlangen-Niirnberg, Erlangen, Federal Republic ofGermanyV. HUGHES, Yale University, New Haven, CN, USAE.V. HUNGERFORD III, University of Houston, Houston, TX, USAR. HUTSON, Los Alamos Scientific Laboratory, Los Alamos, NM, USAG. IGO, University of California, Los Angeles, CA, USAN. ISGUR, University of Toronto, Toronto, Ont., CanadaK. ITOH, University of Saskatchewan, Saskatoon, Sask., CanadaD.F. JACKSON, University of Surrey, Guildford, Surrey, England K.P. JACKSON, TRIUMF, Vancouver, B.C., CanadaB.K. JAIN, Bhabha Atomic Research Centre, Bombay, India229R.R. JOHNSON, University of British Columbia, Vancouver, B.C., CanadaG. JONES, University of British Columbia, Vancouver, B.C., CanadaT. KAMAE, University of Tokyo, Tokyo, JapanA.N. KAMAL, University of Alberta, Edmonton, Alberta, CanadaR. KEELER, University of British Columbia, Vancouver, B.C., CanadaB.D. KEISTER, Carnegie-Mellon University, Pittsburgh, PA, USA J. KENNY, Bradley University, Peoria, IL, USAF. KHANNA, Atomic Energy of Canada Ltd., Chalk River, Ont., Canada R. KIEFL, University of British Columbia, Vancouver, B.C., CanadaW.W. KINNISON, Los Alamos Scientific Laboratory, Los Alamos, NM, USAK. KLINGENBECK, Universitat Erlangen-Niirnberg, Erlangen, Federal Republic of GermanyW.M. KLOET, Rutgers University, Piscataway, NJ, USA W. KLUGE, Inst, fur Theoretische Kernphysik, Universitat Karlsruhe, Karlsruhe, Federal Republic of Germany J.D. KNIGHT, Los Alamos Scientific Laboratory, Los Alamos, NM, USAC.J. KOST, TRIUMF, Vancouver, B.C., CanadaS. KOWALSKI, Massachusetts Institute of Technology, Cambridge, MA, USAS. KULLANDER, Gustaf Werner Institute, Uppsala, Sweden R. KUNSELMAN, University of Wyoming, Laramie, WY, USA R.H. LANDAU, Oregon State University, Corvallis, OR, USAH.C. LEE, Atomic Energy of Canada Ltd., Chalk River, Ont., Canada T.S. LEE, Argonne National Laboratory, Argonne, IL, USAM. LEON, Los Alamos Scientific Laboratory, Los Alamos, NM, USA K.F. LIU, University of California, Los Angeles, CA, USAD.L. LIVESEY, University of New Brunswick, Fredericton, N.B., Canada V.M. LOBASHEV, Institute for Nuclear Research, Academy of Sciences USSR,Moscow, USSRD.E. LOBB, University of Victoria, Victoria, B.C., Canada J.A. MACDONALD, TRIUMF, Vancouver, B.C., CanadaR.J. MACEK, Los Alamos Scientific Laboratory, Los Alamos, NM, USAG.H. MACKENZIE, TRIUMF, Vancouver, B.C., Canada R. MADEY, Kent State University, Kent, OH, USAJ. MAHALANABIS, Saha Institute of Nuclear Physics, Calcutta, India V. MANDELZWEIG, Hebrew University of Jerusalem, Jerusalem, IsraelG. MARSHALL, University of British Columbia, Vancouver, B.C., CanadaG.R. MASON, University of Victoria, Victoria, B.C., CanadaS. MAVRODIEV, Joint Institute for Nuclear Research, Dubna, Moscow, USSR M. MAY, Brookhaven National Laboratory, Upton, NY, USAB. MAYER, CEN Saclay, Gif-sur-Yvette, FranceJ.S. MCCARTHY, University of Virginia, Charlottesville, VA, USA R.J. MCKEE, Los Alamos Scientific Laboratory, Los Alamos, NM, USAA. MEKJIAN, Rutgers University, Piscataway, NJ, USA R. MIKULA, University of British Columbia, Vancouver, B.C., CanadaG.A. MILLER, University of Washington, Seattle, WA, USAR. MISCHKE, Los Alamos Scientific Laboratory, Los Alamos, NM, USAA. MUSSO, INFN, Torino, ItalyD.E. NAGLE, Los Alamos Scientific Laboratory, Los Alamos, NM, USAA. NAKAMURA, Waseda University, Tokyo, JapanH. NAKAMURA, Aoyami Gakuin University, Tokyo, JapanH. NARUMI, Hiroshima University, Hiroshima, JapanC. NEWSOM, Los Alamos Scientific Laboratory, Los Alamos, NM, USA J.N. NG, TRIUMF, Vancouver, B.C., CanadaJ.R. NIX, Los Alamos Scientific Laboratory, Los Alamos, NM, USA230Y. NOGAMI, McMaster University, Hamilton, Ont., Canada J. OOSTENS, University of California, Los Angeles, CA, USAH. ORTH, Physikalisches Inst., Universitat Heidelberg, Heidelberg, Federal Republic of Germany J.Y. PARK, North Carolina State University, Raleigh, NC, USAG. PAULETTA, University of California, Los Angeles, CA, USA R.M. PEARCE, University of Victoria, Victoria, B.C., CanadaM.A. PEREZ, Centro de Investigacion del IPN, Mexico, D.F., Mexico W. PFEIL, Universitat Bonn, Bonn, Federal Republic of GermanyC. PICCI0TT0, University of Victoria, Victoria, B.C.H. PIEKARZ, University of Warsaw, Warsaw, PolandB. PIETRZYK, Max-Planck-Institut fur Kernphysik, Heidelberg, Federal Republic of GermanyH. PILKUHN, Universitat Karlsruhe, Karlsruhe, Federal Republic of Germany L. PINSKY, University of Houston, Houston, TX, USAH. PIRNER, Inst, fur Theoretische Physik, Universitat Heidelberg,Heidelberg, Federal Republic of Germany R.E. POLLOCK, Indiana University, Bloomington, IN, USAH. POTH, CERN, Geneva, SwitzerlandB. POVH, Max-Planck-Institut fur Kernphysik, Heidelberg, Federal Republic of GermanyR.J. POWERS, California Institute of Technology, Pasadena, CA, USAH.G. PUGH, National Science Foundation, Washington, DC, USAI.E. QURESHI, University of Surrey, Guildford, Surrey, England M. RAYET, Universite Libre de Bruxelles, Brussels, BelgiumR.P. REDWINE, Massachusetts Institute of Technology, Cambridge, MA, USA P.A. REEVE, TRIUMF, Vancouver, B.C., CanadaJ.R. RICHARDSON, University of California, Los Angeles, CA, USAP.J. RILEY, University of Texas, Austin, TX, USAB.L. ROBERTS, Boston University, Boston, MA, USAL.P. ROBERTSON, University of Victoria, Victoria, B.C., CanadaR. ROCKMORE, Rutgers University, Piscataway, NJ, USAL. ROSEN, Los Alamos Scientific Laboratory, Los Alamos, NM, USAM. SAKITT, Brookhaven National Laboratory, Upton, NY, USAJ.T. SAMPLE, TRIUMF, Vancouver, B.C., CanadaE. SATOH, Chiba-Keizai College, Chiba, JapanJ. SCHIFFER, Argonne National Laboratory, Argonne, IL, USAH. SCHMITT, Universitat Freiburg, Freiburg, Federal Republic of GermanyP. SCHMOR, TRIUMF, Vancouver, B.C., CanadaS.R. SCHNETZER, Lawrence Berkeley Laboratory, Berkeley, CA, USA R. SEKI, California State University, Northridge, CA, USA K.K. SETH, Northwestern University, Evanston, IL, USAYu.A. SHCHERBAKOV, Joint Institute for Nuclear Research, Dubna, Moscow, USSRE.B. SHERA, Los Alamos Scientific Laboratory, Los Alamos, NM, USAH.S. SHERIF, University of Alberta, Edmonton, Alberta, CanadaI. SICK, Universitat Basel, Basel, SwitzerlandR.R. SILBAR, Los Alamos Scientific Laboratory, Los Alamos, NM, USA P. SINGER, Technion-Israel Institute of Technology, Haifa, IsraelB. SLOWINSKI, Institute of Physics, Warsaw, PolandD. SMITH, University of California, Irvine, CA, USA V. SOERGEL, CERN, Geneva, SwitzerlandM. SOYEUR, CEN Saclay, Gif-sur-Yvette, FranceN.M. STEWART, Bedford College, University of London, London, EnglandG.M. STINSON, University of Alberta, Edmonton, Alberta, Canada231T. SUZUKI, University of British Columbia, Vancouver, B.C., CanadaF. TABAKIN, University of Pittsburgh, Pittsburgh, PA, USA N. TAMURA, Argonne National Laboratory, Argonne, IL, USAS. THEBERGE, University of British Columbia, Vancouver, B.C., CanadaH.A. THIESSEN, Los Alamos Scientific Laboratory, Los Alamos, NM, USA A.W. THOMAS, TRIUMF, Vancouver, B.C., CanadaV.D. TONEEV, Joint Institute for Nuclear Research, Dubna, Moscow, USSR P. TRUOL, Universitat Zurich, Zurich, SwitzerlandS. TURPIN, Rice University, Houston, TX, USAM. UHRMACHER, Max-Planck-Institut fur Kernphysik, Heidelberg, Federal Republic of Germany J.D. VERGADOS, University of Ioannina, Ioannina, Greece J. VETTER, Physikalisches Inst., Universitat Heidelberg, Heidelberg,Federal Republic of Germany J.S. VINCENT, TRIUMF, Vancouver, B.C., CanadaR. VINH MAU, Division de Physique Thdorique, IPN, Orsay, FranceR.D. VIOLLIER, Massachusetts Institute of Technology, Cambridge, MA, USAA.H. WAPSTRA, Instituut voor Kernphysisch Onderzoek, Amsterdam,The NetherlandsJ.B. WARREN, University of British Columbia, Vancouver, B.C., CanadaP. WATSON, Carleton University, Ottawa, CanadaH.J. WEBER, University of Virginia, Charlottesville, VA, USAD. WERBECK, Los Alamos Scientific Laboratory, Los Alamos, NM, USAW.R. WHARTON, Carnegie-Mellon University, Pittsburgh, PA, USAC.A. WHITTON, University of California, Los Angeles, CA, USAW. WILHELM, Schweizerisches Inst, fur Nuklearforschung, Villigen, Switzerland K.L. WOLF, Argonne National Laboratory, Argonne, IL, USA A. YAMAMOTO, National Laboratory for High Energy Physics, Ibaraki, Japan T. YAMAZAKI, University of Tokyo, Tokyo, Japan A.I. YAVIN, Tel-Aviv University, Ramat Aviv, Israel J. YOCCOZ, Inst. National de Physique Nucldaire et de Physique des Particules, Paris-Cedex, FranceV. YUAN, Los Alamos Scientific Laboratory, Los Alamos, NM, USA M. ZACH, TRIUMF, Vancouver, B.C., CanadaG. ZU PUTLITZ, Physikalisches Institut, Universitat Heidelberg, Heidelberg, Federal Republic of Germany232Ando, F., 166 Auerbach, N. , 128 Auld, E.G., 159Bailey, J.M., 159 Barrett, R.C., 155 Batty, C.J., 154 Bedjidian, M . , 133 Beer, G.A., 159 Bertlni, R., 65, 124, 136 Biagi, S.F., 154 Billiris, B., 105 Bing, 0., 124, 136 Birien, P., 65, 124, 136 Blaser, J.P., 202 Borie, E., 147 Bouyssy, A., 124, 136 Brown, B., 178 Browne, K. , 65 Bruckner, W . , 65, 124, 136Cain, M . , 66 Catz, H . , 124, 136 Chaumeaux, A., 124, 136 Chen, X.T., 63 Clough, A.S., 154 Cotanch, S.R., 92 Craddock, M.K., 185Davies, J.D., 154 Deloff, A . , 143 Descroix, E., 133 Dobbeling, H . , 65 Dover, C.B., 4 Dreher, B., 159 Drumm, H. , 159 Durand, J.M., 124, 136Eisenstein, R.A., 75 Endo, I ., 101 Epstein, G.N., 97 Eramzhyan, R.A., 141 Erdman, K.L., 159Faessler, M.A., 109, 124, 136 Fetisov, V.N., 141 Frey, R.W., 65Garreta, D., 65 Gastaldi, U. , 43, 159 Gibson, B.F., 121 Grossiord, J.Y., 133 Gugelot, P., 109 Guichard, A., 133 Gusakow, M. , 133Henley, E.M., 217 Herczeg, P ., 20 Hirabayashi, H. , 212 Hoath, S.D., 154Hojvat, C., 178 Hungerford, E.V., 171Isgur, N., 33Jacquin, M. , 133 Johnstone, J.A., 164Kalinowsky, H., 159Kass, R.D., 66Kaufmann, W.B., 160Ketel, T.J., 65, 124, 136Kilian, K . , 43, 65, 124, 136Klempt, E. , 159Ko, W., 66Kopeliovich, B.Z., 110 Kost, C.J., 185 Kudia, M.J., 133 Kumar, K.S., 150 Kurokawa, S., 212Lander, R.L., 66 Landua, R., 159 Lapidus, L.I., 110 Law, J ., 143, 164 Lehman, D.R., 121 Leon, M . , 147 Li, Y.G., 63 Liu, K.F., 74 Lowe, J ., 154 Lynen, U. , 109Maeshima-Petrini, K. , 66 Majling, L. , 141 Mandelkern, M . , 105 May, M . , 111 Mayer, B., 65, 124, 136 Merle, K . , 159 Michael, W.B., 66 Moniz, E.J., 67, 97Nagle, D.E., 197 Nakamura, H . , 59 Narumi, H. , 117 Neubecker, K. , 159 Niewisch, J., 109, 124, 136 Nogami, Y. , 150Ogawa, K. , 117Pearson, J .S ., 66Pellett, D.E., 66Piekarz, H., 133Piekarz, J., 133Pietrzyk, B., 65, 109, 124, 136Pirner, H.J., 140Pizzi, J.R., 133Pniewski, J., 133Poth, H . , 170Povh, B., 65, 109, 124, 136AUTHOR INDEXPrice, L.R., 105 Pyle, G.J., 154Qureshi, I.E., 155Rafelski, J., 70 Richardson, J.R., 1, 185 Ritter, H.G., 124, 136Sabev, C., 159 Sarkisyan, L.A., 203 Schroder, H. , 109 Schultz, J ., 105 Sharman, P., 154 Shoemaker, G. , 66 Siemiarczuk, T., 109 Silbar, R.R., 12 Smith, D.W., 105 Smith, J.R., 66 Sotona, M . , 141 Soyeur, M. , 67 Squier, G.T.A., 154 Sumi, Y . , 101 Sunami, Y., 117Tabakin, F., 82Uhrmacher, M . , 65, 124, 136Van Giai, N . , 128 Viollier, R.D., 70Walcher, T., 65 Walczak, R. , 65 Waltham, C.E., 154 Wang, W.W., 63 Warren, J.B., 159 Wendling, R.D., 159 Williams, M.C.S., 66 White, B.L., 159 Wodrich, W.R., 159 Wong, C.W., 74Yager, P.M., 66 Yamamoto, A . , 212 Yuan, T.N., 63Zhang, Y.S., 63 Zielinski, I.P., 109 Zofka, J., 141, 142


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