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Proceedings of the second Kaon Factory Physics Workshop, Vancouver, August 10-14, 1981 Woloshyn, R. M.; Strathdee, A. 1981

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PROCEEDINGSOF THESECOND KAON FACTORY PHYSICS WORKSHOPVANCOUVER AUGUST 10-14, 1981Editors: R.M. W oloshyn and A. S tra thdeeMESON F A C I L I T Y  O F :U N I V E R S I T Y  OF A L B E R T A  S I M O N  F R A S E R  U N I V E R S I T Y  U N I V E R S I T Y  OF V I C T O R I A  U N I V E R S I T Y  OF B R I T I S H  C O L U M B I A TRI-81-4TRI-81-4PROCEEDINGSOF THESECOND KAON FACTORY PHYSICS WORKSHOPVANCOUVER AUGUST 10-14, 1981Editors: R.M. W oloshyn and A. S trathdeePostal address:TRIUMF4004 Wesbrook Mall Vancouver, B.C.Canada V6T2A3 December 1981PREFACEThe second TRIUMF Kaon Factory Physics Workshop was held August 10-14, 1981. The organizing committee consisted of J.R. Richardson (Chairman), M.K. Craddock, K.P. Jackson, J.N. Ng,A.S. Rosenthal and R.M. Woloshyn.A hundred physicists participated in the meeting which consisted of fifteen invited talks and four afternoon sessions. The invited speakers reviewed the present state of the art of kaon and neutrino physics. The workshop discussions centred on identifying the most important physics areas that could be studied with a machine that provided an increase in intensity of two orders of magnitude in primary proton beam over present accelerators in the energy range 8-25 GeV and on establishing some preliminary guidelines on the desirable properties of secondary beams at such a machine.Overall it appeared that a strong case existed for the con­struction of kaon/neutrino factories; 8-10 experimental set-ups could be identified, each of which would make possible a several- year programme of important experiments needing the extra beam intensity or purity which such a machine could provide. The main topics which would benefit are CP violation, rare kaon and hyperon decays, baryon spectroscopy, kaon-nucleus interactions and hypernuclei.The organizers wish to thank all those who contributed to the planning and running of the Workshop. Special thanks are due to A1 Rosenthal, who was involved in organizing all aspects of the meeting, and to Joan Haggerty, who looked after secre­tarial matters. The work of Anna Gelbart and Lorraine Gray in the preparation of these proceedings is also gratefully acknowledged.R.M.W.A.S.iiiC O N T E N T SPageIntroductionJ.R. Richardson ....................................................  1INVITED PAPERSExperiments with K-mesons testing models of CP-violationR.K. Adair .......................................................... 3The physics of CP violationsLing-Fong Li ........................................................ 12K° physics at FermilabG.B. Thomson ........................................................ 18Measuring |n00/n+_|K. Nishikawa .................................................   26Neutrino-nucleus interactionsT.W. Donnelly ....................................................... 30Neutrino electron elastic scattering and neutrino oscillation experiments at LAMPFH.H. Chen ........................................................... 44Survey of neutrino physicsA.K. Mann ........................................................... 54Hadron-nucleon interactionsD.V. Bugg ........................................................... 72Soft QCD: Light quark physics with chromodynamicsN. Isgur ............................................................ 82Search for dibaryonic states with strangeness -2 and -1 in the interactions of kaons and pions on deuteriumE. Pauli ............................................................ 99Kaon-induced nuclear reactionsC.B. Dover .......................................................... 107Kaon-nuclear scattering at medium energiesR.A. Eisenstein ....................................................  118Exotic atomsJ.D. Davies ......................................................... 136Progress report in hypernuclear physicsA. Gal ..............................................................  148Experimental hypernuclear physicsB. Bassalleck ....................................................... 167vREPORTS ON WORKSHOPSPageReport on kaon production and neutral kaons workshopD. Axen ......  177Report on neutrino workshopD.A. Bryman ......................................................... 183Report on hadron-nucleon interactions workshopK.P. Jackson ........................................................ 193Report on hadron nuclear interactions and hypernuclei workshopD.F. Measday ........................................................ 196SummaryD.V. Bugg ........................................................... 202List of participants .................................................  208viINTRODUCTIONJ. Reginald Richardson TRIUMF, Vancouver, B.C., Canada V6T 2A3 and University of California, Los Angeles, CA, U.S.A. 90024It is now four years since I gave my first seminar on the feasibility of adding a kaon and, possibly, a ~p factory to TRIUMF. Since that time several workshops have been held at TRIUMF and Los Alamos and elsewhere on the physics fertility and the possible characteristics of such a high intensity multi-GeV accelerator.We hope that the present workshop will give us at TRIUMF a clear-cut answer to the following question "Will the physics made possible by an increase in intensity of two orders of magnitude in the primary proton beam in the energy range 8-25 GeV justify the large amounts of money and scien­tific effort required for the design and construction of such an accelera­tor?" It should be borne in mind, of course, that increased intensity in the primary beam can be used to effect an improvement in the purity and momentum resolution of the secondary beams, lower the mass of the target, etc.An important question concerns the optimum energy for such a factory. Knowledge of the production cross sections of K+ , K“ and "p vs. incidentproton momentum is an essential ingredient of the answer to this question.Recent contributions to this knowledge from measurements at CERN and KEK will be presented at the session on Monday afternoon. From a preliminary examination of these data, however, it seems likely that there is no clear- cut preference in proton energy (above 8 GeV) for the production of kaonsof momentum ^ 1 GeV/c. For the production of kaons of higher momentum andfor p, however, it seems probable that a proton energy of at least 15 GeV would be desirable.The decision on the maximum energy of the kaon factory will thus be strongly influenced by the following factors:1. The relative importance of research using:a) kaons of momentum ^1 GeV/cb) kaons of momentum >1.5 GeV/cc) p (In this case an attempt should be made to include in the esti­mate the probability that LEAR will have been working for some7 years in p physics before the kaon factory comes on line.)d) neutrinos of varying energy2. Technical feasibility of the design— including the very important con­sideration of probable losses of the beam in the overall accelerationprocess3. Cost4. Design effort requiredWe hope that this workshop will go a long way towards the evaluation of the above factor number 1.Table I shows three sample combinations of accelerators which are presently being considered as possible kaon factories for TRIUMF. The first is a combination of two cyclotrons, one accelerating the beam to 3 GeV and the second taking it up to 8.5 GeV. Either the normal mode or the pulsed mode may be used. The second possibility is a single synchro­tron which would take the beam from TRIUMF and accelerate it to any energy up to a maximum of 15 GeV. The third possibility is a combination of two2Table I.Cyclotrons Synchrotrons3 GeV 8.5 GeVOne machine only 15 GeV maximum 3 GeV 20 GeVNormal modeProtons/pulse 6.4 x 107 6.4 x 107 1.2 x IO1" 1 x io1"* 8 x 1015Repetition rate 23 MHz 23 MHz 4 Hz 6 Hz 0.12 HzPulse length 0.3 nsec 0.25 nsec 125 msec 80 msec 8.5 secAverage current 250 p A 250 pA 75 pA 100 pA 80 pAMacro duty factor 100% 100% 50% 50% 50%Variable energy? Uncertain Uncertain yes yes yesPulsed modeProtons/pulse 3 x 1010 3 x 1010 1.2 x 1011* 1 x 10lt( 8 x 1015Repetition rate 40 kHz 40 kHz 8 Hz 12 Hz 0.12 HzPulse length 2.0 nsec 1.5 nsec 1.5 psec 1 psec 0.8 psecAverage current 250 uA 250 pA 150 pA 190 pA 150 pADuty factor 1/1.1 x 101* 1/1.5 x i o 1* 1/8 x 101* 1/8 x 101** 1/107*The addition of a superconducting storage ring could be considered for neutrino research.synchrotrons, the first being a 3 GeV booster and the main ring (possibly superconducting) giving a maximum energy of 20 GeV. These three possibili­ties are to be considered only as samples of classes of possible post­accelerators for TRIUMF.The efficiency of extracting beam from TRIUMF is close to 100%. The same is true for the cyclotron at SIN. However, detailed estimates cannot yet be made for the injection and extraction efficiencies for the acceler­ators shown in the table. They all have some technical problems affecting the expected efficiencies. For comparison purposes at this time, the rather unrealistic assumption has been made that each of these processes has an efficiency of 100%. A major task of the design study now under way at TRIUMF is to make realistic estimates of these efficiencies.An important consideration for neutrino research is the availabilityof a primary beam of very low duty factor, e.g. 1/106 at the BrookhavenAGS. The only sample accelerator shown in the table which has a comparable or better performance is the 20 GeV main ring at 1/107. This would make available a primary beam variable in energy from 3 to 20 GeV. The addi­tion of a superconducting storage ring to the cyclotrons would make a similar low duty factor available from those accelerators.For the 15 GeV single synchrotron, the addition of a storage ring would have two advantages: a) it would make possible a duty factor as low as 1/107 and (b) it would make possible a duty factor as high as 90% withan average beam output of 150 yA.In conclusion I would like to thank all the visitors who have come to the workshop in response to our mutual interest in intermediate energy physics.3EXPERIMENTS WITH K-MESONS TESTING MODELS OF CP-VIOLATIONR. K. AdairYale University, New Haven, Connecticut 06520 ABSTRACTThree experiments involving measurements of the decays of low energy K-mesons are described which provide important tests of models of CP- violation. In particular, two experiments conducted at Brookhaven National Laboratory were concerned with the measurements of the polarization normal to the plane of decay of muons produced in Ky3 decays; measurements were made on the decays of K+ and mesons. The techniques used, results, and meaning of the results of these measurements are presented. A third ex­periment, now in preparation and scheduled to run at BNL this winter, is designed to measure the difference in the charge ratios for the decay of Kl and Kg to two pions, thus determining the value of |e'/e|- Each of these three measurements is important, each measured quantity should be measured with the highest possible accuracy, and each of these measurements might well be done best at a Kaon factory.INTRODUCTIONThe scores of experimental measurements made in the period —  almost two decades —  which followed the discovery of CP-violation by Christenson et al.1 resulted in the important, though disappointing, conclusion that the only CP-violating phenomena observed can be described by a model in which there is but one free parameter defined by the experiments; |n| = 2.3*10“3, the portion of Kg state in the Kl amplitude. In the past, lack­ing a credible model of the strong and weak interactions, it was convenient to describe CP-violation models in terms of a perturbation theory "super- weak" |AS|=2 interaction with a strength of about 10-9Gf acting in first order or a "milliweak" interaction acting in second order with a strength of about 10-3Gf. The superweak interaction, weaker than the weak interac­tion in second order, leads to CP-violating effects, outside of the K0- ^  system results which are known, which are unobservable with present techniques.With the maturation of quantum chromodynamics (QCD), it is now more use­ful to consider CP-violation within the framework of QCD models. Though CP-violation cannot be introduced into the minimal standard SU2 x Uj model with only four quarks and one Higgs doublet, more extensive models can admit CP-violation through the introduction of more than one Higgs doublet, or through an extension to the six quarks which are now suggested by experi­ment, or through the introduction of a larger group structure. In particu­lar, it is attractive to consider CP-violation as resulting, phenomenologi- cally, from phase differences between the six or more quark amplitudes2 or phase differences between two or more Higgs doublets.3 ,t+Weinberg3 has pointed out that if CP-violation derives from CP-violat­ing phases in the Higgs sector, one should expect small muon polarizations in the direction normal to the plane of decay in K^3 decays. Zhitnitskii1* has shown, for a particular model of CP-violation in the Higgs sector, that such CP-violating muon polarizations of the order of 5*10-3 can be expected. We discuss here measurements of K+ decays and K^ decays which lead to interesting limits on the magnitude of such polarizations.4If CP-violation derives from intrinsic phase differences between the quark amplitudes, there will be no sensible CP-violating polarization of muons from the Ky3 decays inasmuch as only one quark transition is involved in those decays and CP-violation is only evident in the introduction of a phase difference, other than 0 or ir, between two amplitudes. However, Gilman and Wise5 and others have shown that the six quark, Kobayashi- Maskawa2 model of CP-violation leads naturally to a substantial direct production of two pions from Kl decays (in addition to the two pions pro­duced through the Kg impurity in the Kl state), and the charge ratio for these direct two-pion decays will not be the same as for Kg decays and hence the charge ratios for two-pion decays from Kl and Kg decays will differ.We note that neither the Higgs sector calculations nor the quark sector models of CP-violation are without serious theoretical problems. Deshpande6 and Sanda7 have shown that, for a broad set of plausible models, CP-violation in the Higgs sector sufficient to explain the K^ ->■ 2n transi­tions will result in a difference between the 2ir charge ratios from Kl and Kg decays beyond the measured limits. Similarly, Branco8 has demonstrated that, under rather general conditions, one should not expect CP-violating phase differences in the six-quark system.MEASUREMENTS OF MUON POLARIZATIONS FROM K^3 DECAYSOur measurements9 were made at Brookhaven National Laboratory on K+ meson decays from a non-separated, short, 3.95 GeV, positive beam of par­ticles produced in the forward direction by the interaction of 28 GeV pro­tons on a platinum target. The momentum acceptance of the beam, dp/p, was about 0.10 and the acceptance in solid angle was about 4*10“5 sr.A diagram of the muon-polarization detection equipment is shown inFig. 1. Of the K+ mesons passing through the 5 m drift space, about one in25,000 decays through the Ky3 mode such that the y+ is focused by the 1.2 m diameter toroidal magnet through a further steel absorber to stop in the 1500-kg aluminum polarimeter while a gamma ray from the decay of the tt0 converts in the Pb-glass counter array located on the beam axis. The path of acceptable muons is defined by the hodoscope arrays, V, A, B, M, F, and I while the direction of the polarization of the muons which stop in the polarimeter is, determined by a measurement of the direction of emission ofthe e+ from the y+ decay through analyses of signals generated in theG-counters.Various anti-coincidence counters reduce the two backgrounds which constrain the event rate by accidental counts in the polarimeter muon decay (positron) detector counters, G, and by accidental coincidences between gamma rays from the tt0 7t+  K-decay mode and muons from K^2 decays. The data handling was directed and the data was collected through a Fastbus10 elec­tronic logic system with a data transfer capability near 109 bits/sec and the analysis of this data was conducted on-line so that the results of the measurements were known at any time as the experiment proceeded. The results presented here, derived from the analysis of 2*107 events, were available within minutes of the termination of the experimental run.In our design, we detect the possible existence of the CP-forbidden polarization normal to the plane of decay by measuring the polarization of the muons in the laboratory system in the direction p^x for a selected class of events where the direction of the K-beam lies in (or at a very small angle to) the plane of decay. The lower diagram of Fig. 1 suggests,5Fig. 1. The central figure shows the experimental apparatus where the different hodoscopes are designated by capital letters.The upper diagram presents an exploded view of a polarimeter element showing the vector polarizations of a stopped muon and the lower drawing presents a schematic view of the relationship between the momentum and spin vectors of the K^3 decay products in the center-of-mass and laboratory systems.schematically, the character of the accepted decays in the center-of-mass system and in the laboratory system for the type of events selected by the hodoscope counter system, the Pb-glass array, and the associated trigger logic. Through the requirement that events are to be accepted only if more than 1.2 GeV energy is deposited in the Pb-glass by a photon nominally derived from the decay of the ir° , events are selected such that the tt° must travel in the forward direction (along the K-beam line). Since the it0 and K+ momenta are then (nearly) collinear, the condition that the K- beam must lie in the decay plane is satisfied.The upper diagram of Fig. 1 shows a section of the polarimeter together with vectors representing the components of polarization of the stopped muons. The component Pn , present if CP-invariance is violated, lies in the direction Pk x Py 5 the component Pt is perpendicular to the beam and lies in the decay plane, while the third component, Pl , is in the direc­tion of the beam. The polarization component P^ is determined by measur­ing the U-D decay asymmetry as a function of time as the muon precesses in a 60 G axial magnetic field produced by a current which passes through windings about the polarimeter circumference. Here, U represents counts recorded in the clockwise counter, looking downstream, and D the counts in the counterclockwise counter. For each of the 32 counters, clocks are started upon recording the set of counter hits which signifies that an ac­ceptable muon stops in the polarimeter; the clock is stopped when a decay positron passes through the counter. As the muon precesses, the ratio A=(U-D)/(U+D) will vary sinusoidally with the precession frequency. The6(CP-allowed) transverse polarization will produce an amplitude of the form At(t)=At sin mt and the normal (CP-violating) polarization will pro­duce an amplitude of the form An (t)=An cos mt. The frequency, to, deter­mined by the sign and magnitude of the axial field, is reversed every pulse (every three seconds). This results in a cancellation of the CP- conserving amplitude, A^ -(t) , so that the magnitude of any CP-nonconserving amplitude, An(t), can be selected without interference from the large CP- conserving amplitude. Conversely, the addition of the signed amplitude, pulse-by-pulse, measures At (t).We note that the existence of a CP-violating polarization defines a screw direction. Conversely, systematic errors can simulate a CP-violat- ing effect only if those uncertainties effect a screw direction. Recog­nizing this, the apparatus was designed and constructed to avoid deviations from cylindrical symmetry. This symmetry, together with the selection of a well defined Fourier component of An (t), serves to reduce systematic uncertainties to a level less than 10"3 in the polarization, a level ap­preciably below that of the statistical uncertainties.The results of the experiment are shown in the graphs of Fig. 2. The dashed curve shows the best fit to cos wt, the measure of CP-violating polarization. The amplitudes for the two classes of events are At=-0.0692010.00043 and An=-0.00029±0.00046 where the signs reflect the conventions used. The ratio of these polarizations An/At=(4,2±6.7)•10”3 is just the phase difference (modulo it) between the muon amplitude with positive helicity and the amplitude with negative helicity. In the absence of time-reversal violation (or CP-violation assuming CPT invariance) this phase must be 0 (or it) hence the error in the null result is an excellentmeasure of the sensitivity of the experiment.Fig. 2. The upper graph shows, at the left, the variation of At as a function of time and the bottom graph shows similar data for A ^  The plots to the right show the same data with the background subtracted plotted modulo 1.2 psec, the preces­sion cycle time. Note the different ordinate scales.7We can calculate Py(lab) knowing the systematics of Ky3 decays and the acceptance of our apparatus over the Dalitz plot of the decay kinematics. From such a calculation, accurate to a few per cent using Monte Carlo methods, we find Pt(lab)=0.857 and, then, Pn (lab)=(-3.6±5.7)•10~3. Again, from the Monte Carlo calculation, we find Pn (c.m.)/Pn (lab)=1.17 and, for the set of events selected by the apparatus, we have Pn(c.m.) = (-4.2±6.7) • IO-3.The above numbers are relevant to the sub-class of decays selected by the specific character of the experimental design and a more universal expression of the results is necessary. For the kinematic region such that py*pv=0, we have Pn=(-3.0±4.7)•IO-3. Another useful, and more gen­eral, parametrization is expressed in terms of the value of £, the con­ventional ratio of form factors used in discussion of Ky3 decays; taking Re £ =0, we find Im £ =-0.016±0.025.According to Zhitnitskii, CP-violation in the Higgs sector leads to a polarization, for Pn where Py*pv=0 and Ty is of the order of 100 MeV such that:pn = (^ T~(v 2/v I) = 63* 10"3 (v|/v§)where the value of mg is set at 2 GeV by the measured K°-K° CP-violating effects and (v^/vj) is a real number defined by the gauge transformation properties of the Higgs doublets and not otherwise determined experimen­tally: Zhitnitskii expects this number to be of the order of one. We note that for this K+ experiment the limits set are of the magnitude ex­pected and serve to constrain the value of the free parameter to be less than two.MEASUREMENTS OF MUON POLARIZATIONS FROM Ky3 DECAYSThe equipment used for the measurements of the transverse polariza­tion of the y+ from the Ky3 decay mode is similar to that shown in Fig. 1 used for the K+ decay measurements. (Indeed, the neutral K measurements were made before the charged K measurements.) The primary difference in equipment is found in the replacement of the Pb-glass counters on the beam axis with scintillation counters designed to register the charged it” particle. There was also a difference in selection inasmuch as two categories of events were accepted. Aside from events such that the pion trajectory was nearly in the direction of the beam (labeled here, P- events), events were selected such that the pion trajectory lay close to the muon trajectory and then nearly in the plane defined by the muon and the beam line. These (M) events were also selected by the hodoscope system and the trigger logic and measurements of the muon polarization normal to that plane were used in the final analysis of CP-violation as well as for the P-events with the pion directed along the beam line. Both the CP-conserving transverse polarization and the CP-nonconserving polar­ization lay in opposite directions for the two classes of events.For these measurements, the mesons, produced at an angle of 6° from the interactions with a platinum target of 28 GeV protons from the Brookhaven AGS, travel about 7 m through clearing magnets and collimators into the 5 m drift space shown in Fig. 1. Aside from the somewhat dif­ferent selection of events and the detection of charged pions through scintillation counters, rather than the detection of the neutral pions through the interaction of the pion-decay photon in the Pb-glass counters,8Fig. 3. The top curve shows the variation of as a function of time and the bottom curve, An . Note the different scales.The curves to the right show the same data, modulo 1.2 ysec, the precession cycle time, with the background subtracted.the measurements of the CP-violating polarizations were conducted in a manner quite similar to that described for the K+ experiment.The curves of Fig. 3 show the data for the most important results. The amplitudes are summed over both classes of events where the M ampli­tudes are multiplied by -1 to take into account the different signs of the polarization which were expected and observed. The amplitudes of the two classes of events, evaluated by least-squares analyses, are At=0.054310.00063 and An=0.0002810.00063. This leads to a value of Pt=0.42, consistent with Monte Carlo calculations of the polarizations expected for these classes of events, and a value of Pn=0.0021+0.0048 for the CP- nonconserving component of polarization. From the Monte Carlo calcula­tions, we find that Im5=Pn/0.18=0.01210.026 to be compared with the value of Im£;« a « 0 .008 to be expected from final state electromagnetic interac­tions of the p+ and ir- . With a more careful correction for the electro­magnetic final state effects, we find, for the CP-violating part of the form factors: lm£=0.00110.030.Stronger constraints can be invoked if we compound the results of the measurements of the charged and neutral K-decays. The experiments are similar and the statistical handling of the data is nearly identical for the two measurements inasmuch as the uncertainties are almost wholly statistical. Therefore, it is permissible to add the results of the two measurements to derive a value of Im?=-0.01010.019 and, Pn= (-1.8513.60)• 10~3. Although this null result cannot exclude the possibility that the CP-violating effects, known from observations of the K°-K° system, derive from CP-violating phases in the Higgs sector, we conclude that such mech­anisms do not make unusually large contributions to Ky3 decays.MEASUREMENTS OF Ks -> 2ir AND Kl -> 2tt CHARGE RATIOS AND e'/eThe dominant mechanism responsible for the CP-violating transition Kl -+ 2tt is the presence of a small Kg amplitude impurity in the Kl state. Writing e = <Ks |Kl >, |e|=0.00228 and the phase, determined wholly by CP-9conserving parameters, is: 0=Atan(2AM/rs)=43.8°, where AM is the Kl~Ks mass difference. If superweak models of CP-violation hold, this will be the only sensible contribution to the two-pion decay of the Kl. However, less restrictive models of CP-violation, such as the Kobayashi-Maskawa description of CP-violation through phase differences between the six quarks, lead to a direct transition, Kl -*■ 2tt, which may show a different charged/neutral 2n-decay ratio than for Kg decays. In superweak models, the 2ir-charge ratio will be the same for Kl and Ks decays even as the Kldecays solely through the Kg part of the Kl amplitude. Therefore thedetection of any difference between the 2tt charge ratios in Kl and Ks de­cays would demonstrate the existence of a direct CP-violating transition of the Kl to the two-pion final states and exclude any superweak descrip­tion of CP-violation. At the present time the charge ratios are known to differ12*13 by no more than 15%.A two-pion state can be separated into I-spin 0 and I-spin 2 parts; I-spin 1 is forbidden by g-parity conservation. For pure I-spin 0 states, the intensity of tt+tt- will be twice that for the 7r°ir0 state while thatratio will be one-half for an I-spin 2 state. Since the I-spin 0 and I-spin 2 states must be orthogonal, the different two-pion charge amplitudes which make up the I-spin 2 states must have different signs if the signs are chosen to be equal for the I-spin 0 state. The charged to neutral de­cay ratio of about 2:1 for Kg decays indicates that the Ks decays almost wholly to an I-spin 0 state of the two-pion system. If direct transitions, Kl -*■ 2tt, take place solely to the I-spin 0 also, there will be no differ­ence between the Kl and Kg decay charge ratios, but if transitions take place to the I-spin 2 state, the charge ratio for the direct transitions will be different from that which takes place through the Kg impurity in the Kl amplitude and, hence, there will be a difference between the charge ratios for the decay of Kl and Kg.The phases, though not the signs of the direct amplitudes, are knownfrom general considerations; the I-spin 0 phase will be tt/2, characteris­tic of a weak CP-violating amplitude; the phase <f> of the I-spin 2 ampli­tude e' will be cj>=7r/2+62—<So=37° where 62 and 60 are the final state two-pion scattering phase shifts for the I-spin 2 and I-spin 0 states.The diagrams of Fig. 4 show the relevant complex amplitudes for the charged and neutral 2tt decays. The amplitudes Aq and e r for the direct transitions are exaggerated for clarity. Further, for convention, theFig. 4. An Argand diagram presentation of the amplitudes for the charged and neutral decays of the Kl 2tt .10amplitudes are normalized so that the intensity factors (Clebsch-Gordan coefficients) are absorbed in the neutral amplitudes. The neutral ampli­tudes for the I-spin 0 transitions are smaller by a factor of /l/2 than the similar charged amplitudes while the I-spin 2 neutral amplitude is larger by /2 and has the opposite sign. Noting that the direct amplitudes must be small compared to e, the ratio of the charged to neutral intensi­ties for Kg decay will be 2 while, for the Kl decay, that ratio will be 2*(1+6*|e'/e|)• Then a measurement of the relative charge ratios from Kg and Kt to an accuracy of 1% will result in a measure of the ratio of \ z ' l z \ to an accuracy of 1/600. Cronin and Winstein are preparing such measurements at Fermilab and we will commence preliminary measurements at BNL soon.Although it is the interference between the very small I-spin 2 amplitude z ' with the large I-spin 0 amplitude z which allows a sensitive search for a finite I-spin 2 direct transition, the magnitude of the dif­ference between the two charge ratios would be larger if the I-spin 0 amplitude were smaller. But this amplitude can be made smaller by the production of a coherent Kg amplitude such that that amplitude will inter­fere destructively with the Kg part of the Kl amplitude. The diagrams of Fig. 5 suggest the character of a particular, possible, exploitation of this effect so as to produce larger charge ratio differences and, possibly, allow more sensitive measurements.If we consider the production of K° mesons by protons, or ir mesons or K+ mesons, at sufficiently low incident particle energies, K° states will be produced in nucleon interactions rather than K° states. Then, at the target, Kg and Kl amplitudes will be produced equally and in phase.f ......— -..... *•----------@ ...........►beam which passes through a regenerator is shown at the top of the figure. The amplitude and phase (with respect to the Kl state) of the Kg amplitude is shown as a function of time below.11Downstream, the Kg phase will advance with respect to the Kl amplitude as a consequence of AM, the Kg-KL mass difference, and the magnitude of the Kg amplitude will decrease through the decay of that state to two pions. After a proper-time of about 7*10”10 sec, the Kg phase will be about 225° and interfere destructively with the Kg impurity amplitude which is at a phase of 43.8°. But the generated amplitude will be about five times as great as the impurity amplitude.However, if a Kl -* Kg regenerator (e.g. 50 cm of graphite) is placed in the beam properly, as suggested, quite schematically, by the diagram of Fig. 5, the regenerated amplitude, produced at a phase angle of about -40° with respect to the Kl , can be used to beat down the Kg amplitude from the target so that the impurity amplitude and the generated amplitude are of comparable magnitudes with opposite phases and the interference will be nearly complete. Then a small I-spin 2 amplitude will produce a large, more easily detected, difference in charge ratios. Indeed, it should be possible, through fine-tuning of the regenerator part of this interferom­eter, to produce either constructive or destructive interference between a direct I-spin 2 amplitude and I-spin 0 amplitude from the interferometer system facilitating identification of a direct k£ CP-violating decay amplitude.Since the regenerated amplitudes are small at large K-energies and since both K° and K° states are produced with comparable intensities at high hadron projectile energies, the exploitation of such interference techniques is limited to low energies such as found at a Kaon factory.REFERENCES1. J.H. Christenson, J.W. Cronin, V.L. Fitch, and R. Turlay, Phys. Rev. Lett. 13, 138 (1964).2. M. Kobayashi and K. Maskawa, Prog. Theor. Phys. 45), 652 (1973).3. S. Weinberg, Phys. Rev. Lett. _J7, 657 (1976).4. A.R. Zhitnitskii, Yad. Fiz. 31, 1024 (1980) [Sov. J. Nucl. Phys. 31, 529 (1981)].5. F. Gilman and M. Wise, Phys. Rev. D ^0, 2392 (1979).6. N.G. Deshpande, Phys. Rev. D 23, 2654 (1981).7. A.I. Sanda, Phys. Rev. D 23^, 2647 (1981).8. G.C. Branco, Phys. Rev. Lett. ^4, 504 (1980).9. M.K. Campbell et al., submitted to Phys. Rev. Lett.10. L.B. Leipuner et al., IEEE Trans. Nucl. Sci. NS-28 No. 1, 333 (1981).11. W.M. Morse et al., Phys. Rev. D 21, 1750 (1980).12. M. Banner et al., Phys. Rev. Lett. 28^ , 1597 (1972).13. M. Holder et al., Phys. Lett. 40B, 141 (1972).12THE PHYSICS OF CP VIOLATIONS*Ling-Fong Li Physics Department, Carnegie-Mellon University,Pittsburgh, Pennsylvania 15213ABSTRACTVarious mechanisms for the CP violations are discussed in the frame­work of the gauge theories of the weak and electromagnetic interactions. Their experimental implications on the K0 -»■ 2n decay, electric dipole moment and K0 -*■ 3ir decays are illustrated.1. INTRODUCTIONEver since the CP violation was first observed in the Kq-Kq system seventeen years ago,1 it has remained to be a challenge to understand the source of the CP violations. The progress in the seventies has led to the gauge theory description of the weak and electromagnetic interactions, which can explain a great variety of different weak interaction processes. In particular, the success of the standard Weinberg-Salam-Glashow model2 based on the SU(2) x U(l) gauge group in the neutral current phenomen­ology3 has been very impressive. In spite of its great success, there are still many aspects of the standard model which have yet to be tested experimentally. This leads to many variations of the standard model which are still consistent with the present experiments. In particular, the present experiments on CP violations can accommodate many other models besides the standard model. In this talk, I will discuss various mechan­isms for the CP violations within the framework of the gauge theories. Hopefully, future experiments will be able to distinguish these different mechanisms.2. THE MECHANISM OF CP VIOLATION IN GAUGE THEORIESPhysically, CP violation comes from the interference between two amplitudes with different CP phases. In the framework of gauge theories, there are basically three different mechanisms for the CP violations.(A) Hard CP violationIn this case, the CP violation is present in the Lagrangian even before the spontaneous symmetry breaking. This can be realized by having the Yukawa coupling constants complex and violating CP symmetry.Since the weak eigenstates are not the same as the mass eigenstates, the CP violations in the Yukawa couplings will be fed into the couplings of the gauge bosons to the fermions through the diagonalization of the mass matrices which are proportional to the Yukawa coupling. The character­istic feature of this hard CP violation is that it will persist even to energies much higher than the onset of the spontaneous symmetry breaking, which is determined by the vacuum expectation values of the scalar fields.One particular realization of this mechanism is the standard SU(2) x U(l) model with three generations of quarks.11 These quarks have the*Work supported in part by U.S. Department of Energy13following structuredoublets UR » CR » tR dR » SR » bRsinglets ,where(1)and C is the Kobayashi-Maskawa mixing matrix1* which is just the general­ization of the Cabibbo mixing to the case of 3 generations of quarks. In the standard parametrization, it has the formwhere Cj[ = cos0j[, = sin0i and 6 is the CP violating phase. Note that in general C is a 3x3 unitary matrix which has 9 parameters that can be taken to be 3 angles and 6 phases. However, not all 6 phases are physi­cal because some of them can be removed by redefining the phases of the quark mass eigenstates,without changing any physics. It turns out that there is only one CP violating phase left over after the redefinition in the case of 3 genera­tions of quarks. In general, for n left-handed doublets in SU(2) x U(l) theory, there are l/2(n-l)(n-2) numbers of CP violating phases.Note that in the form given in Eq. (2), the CP violation is present only in c- and t-quark sectors, but not in the u-quark sector. This is purely convention, because one can move the CP violation phase 6 to the other sectors by redefining the phases of the quark fields. Since the physical CP violating effects always involve two amplitudes with differ­ent CP phases, all different conventions will give the same results.In the standard model, it turns out that due to the simple structure of the scalar fields, the CP violations in the Yukawa coupling disappear in the process of diagonalizing the mass matrices and reappear only in the gauge couplings to the quarks.(B) Soft CP violationThis mechanism was first pointed out by T.D. Lee.5 In this scheme, the Lagrangian is CP invariant before spontaneous symmetry breaking and the CP violation is generated after spontaneous symmetry break­ing. This will happen when the scalar fields (Higgs fields) develop complex vacuum expectation values. This soft CP violation requires at least 2 sets of scalar multiplets so that the relative phase between vacuum expectation values of different scalar multiplets can have physi­cal meaning. This implies that the scalar sector is more complicated than the standard model which only requires 1 set of scalar multiplets, the SU(2) doublet.(2)(3)14In contrast to the hard CP violation, the soft CP violation will go away at energies much higher than the vacuum expectation values of the scalar fields which set the scale for the spontaneous symmetry breaking.The simplest example of the soft CP violation5 is to have two doublets of scalar fields in the SU(2) x U(l) model such that their vacuum expectation values have different phases.<<h>0 = (vi)’ ^ 2>0 = (v2ei6) ’ (4)where 6 is the CP violating phase. In this case, the fermion mass matrices are complex and there is also CP violation in gauge couplings to the quarks just like the standard model. In addition, there is CP viola­tion mediated by the scalar fields through the Yukawa couplings. This particular model has the feature that the Yukawa coupling of the neutral scalar particle changes the quark flavors. The smallness of the AS = 2 KL-KS mass differences will imply a rather large mass for this neutral scalar particle. This can be avoided by enlarging the scalar sector to three doublets with some discrete symmetries to prevent the neutral flavor changing effects.6(C) 6-vacuum in QCDThe non-trivial topological properties of QCD give rise to the ex­istence of the instanton, which modifies the structure of the vacuum (6-vacuum). It turns out that this non-perturbative effect generates an additional effective interaction of the form,7withLeff = payVFyv = 3yA$ - 9vAy + fabcA|]Acv a,b,c=l ... 8F S v  = W F a ° 6  ( 5 )In Eq. (5), Ay is the gluon field of QCD, fa^c the structure constants of SU(3) and 6 is an arbitrary parameter. This effective interaction vio­lates the P and CP symmetries. From the estimate of the neutron dipole moment,8 the 6 parameter has to be rather small,6 < IO"8 , (6)and will make its contribution to all other CP violating effects too small to be of experimental interest.One way to avoid this strong CP violation is to introduce an extra axial U(l) symmetry9 so that we can have 6 = 0 .  But, this U(l) symmetry is broken and leads to the existence of a rather light pseudo-scalarmeson,10 the axion. However, this very light axion could have very smallcoupling to the fermions so that it is very difficult to detect.3. THE PHENOMENOLOGY OF CP VIOLATIONThere are three types of CP violating quantities which are of direct interest to the present or future experiments.(1) The CP violation parameters n+- and n0o tlie K -* 2ir decays. They are defined by15A(KL TT+TT~) _ A(Kl -*■ Tr°TT°)n+“ ~ ACKg^TT+TT-) ’ n°° ~ A(Kg -*■ Tr°Tr°) * ^In the usual parametrization, they can be written asn+- = e + e' , n00 " e - 2e' (8)where e comes from the CP violation in the Kq-Kq mass matrix and e f. measures the CP violation in the K -*■ 2tt decays. The present experi­ments11 give1 3oo= 1.00 ± 0.06 (9)n + -and the future experiments12 can get to a fractional percent of accuracy.(2) The electric dipole moment of the neutron. The present experimental upper limit13 is Dn - 10~2k e-cm and can be improved by two orders of magnitude in the near future.(3) The CP violating parameter in K -*■ 3ir decays;A(Ks-*ff+Tr_TT0) n+ 0 A(Kl ->■ ir+ir-Tr°)  ^ ^The present experimental limit on n+_0 is rather poor, but the ex­periments in the future might be able to measure the difference (n+_0-h+_)/n+_ to an accuracy of order of 25%.We will now discuss the theoretical predictions for both hard and soft CP violations. For the hard CP violation we will concentrate on the popular standard model while for the soft CP violation we will illustrate the situation for one of the many alternatives. One should keep in mind that to various degrees all these theoretical calculations suffer from the strong interaction effects which are not under control.(A) Standard model (hard CP violation)As we have discussed, in the standard model the CP violation is present only in the gauge coupling to the quarks involving angles 0i which are not very well known experimentally.For the K0 ■+ 2tt decays, generally, the ratio j e r/e | is not very sen­sitive to the mixing angles and is predicted to be very small because of the Al = 1/2 property of the CP violating part of the interaction.15 Various theoretical calculation16 gives| e f/e| ~  0.003 - 0.02 (11)in agreement with the present experimental limit. The range for this ratio is due to various different mechanisms for calculating the non- leptonic decays. The upcoming experiments which can determine this ratio to a fractional of percent level might be able to distinguish these mechanisms.In the Kq -*■ 3tt decays, one can use the usual soft-pion technique to relate the parameter n+-o to the Kq -* 2ir parameters n+- and q00 to give the approximate relation17 *n+-o - n+- =  n00 - n+- ■ (12)This indicates the difference | n + - o  - n+-| is also of few percent level.16As for the neutron electric dipole moment, the standard model yields rather small value because the electric dipole moment of the quark van­ishes in the lowest order in this model. Various calculations18 give values of Dq between IO-30 and 10“ 32 e-cm, which are too small to be seen in the near future.(B) Soft CP violationOne of the interesting features of the soft CP violation models based on the SU(2) x U(l) group is that the electric dipole moment can be very near the present experimental upper bound. Thus the forthcoming improvement on the measurement of the electric dipole moment8 will be able to tell whether this is the right mechanism for the CP violation.For the K0 -*• 2tr decays, we will discuss a particular realization of the soft CP violation for illustration. The example is a SU(2) x U(l) model with 3 doublets of Higgs scalars with a discrete symmetry to guaran­tee the flavor conservation.6 The CP violation is in the Higgs coupling to quarks but not in the gauge couplings. Then it turns out that with reasonable assumptions, the ratio |e'/e| is predicted to lie in the rather narrow range190.048 < |e'/e| < 0.050 (13)which is in conflict with the present experimental limit. One possible way out of this difficulty is to drop the requirement of the flavor con­servation at the expense of having rather heavy Higgs particles (~250 GeV).4. DISCUSSION _Up to now the CP violation has been observed only in the Kq-Kq system. This makes it rather difficult to pin down the origin of the CP  violations. The observation of CP violations in any other system would be very helpful. Even though we discuss the soft and hard CP violations separately, they are not mutually exclusive. It is very likely that some quantities can be attributed to the hard CP violations while others are dominated by the soft CP violations.15It is interesting to note that CP violation is also needed for pro­ducing the excess of the baryons over the anti-baryons in the universe in the context of the grand unified theories. But the theoretical calcula­tion is too crude at present time to shed any light on the right mechan­ism for the CP violations.REFERENCES1. J.H. Christenson, J. Cronin, V.L. Fitch and R. Turlay, Phys. Rev.Lett. 13, 138 (1964).2. S. Weinberg, Phys. Rev. Lett. Ij), 1264 (1967);A. Salam in Elementary Particle Theory, ed. N. Svartholm (Almqvist and Wiksell, Stockholm, 1967) p. 367;S.L. Glashow, Nucl. Phys. 22^ , 579 (1961).3. See for example, J.E. Kim, P. Langacker, M. Levine and H.H. Williams, Rev. Mod. Phys. 53, 211 (1981).4. M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 4£, 652 (1973).5. T.D. Lee, Phys. Rep. 9C, 143 (1974).6. S. Weinberg, Phys. Rev. Lett. _37, 657 (1976).7. G. ’t Hooft, Phys. Rev. D J.4, 3432 (1976);17C.Callan, R. Dashen and D. Gross, Phys. Lett. 63B, 334 (1976);R. Jackiw and C. Rebbi, Phys. Rev. Lett. 37_ 172 (1976).8. V. Baluni, Phys. Rev. D19, 2227 (1979);R. Crewther, P. Di Vecchia, G. Veneziano and E. Witten, Phys. Lett.88B, 123 (1979).9. R. Peccei and H. Quinn, Phys. Rev. D lb, 1791 (1977).10. S. Weinberg, Phys. Rev. Lett. 40, 223 (1978);F. Wilczek, ibid 40, 279 (1978).11. Particle data group, Phys. Lett. 75B, 1 (1978).12. B. Winstein et al., Fermilab proposal;R.K. Adair £t al., Brookhaven AGS proposal.13. N. Ramsey, private communication.14. G. Thomson et al., these proceedings, p. 18.15. This has been emphasized by L. Wolfenstein, Proc. of Neutrino 79 Con­ference (Univ. of Bergen, Bergen, 1979), p. 155.16. F. Gilman and M.B. Wise, Phys. Lett. 83B, 83 (1979);B. Guberina and R.D. Peccei, Nucl. Phys. B163, 289 (1980);L. Wolfenstein, Nucl. Phys. B160, 501 (1979).17. L.-F. Li and L. Wolfenstein, Phys. Rev. D_21, 178 (1980).18. D.V. Nanopoulos et al., Phys. Lett. 87B, 53 (1979).B.F. Morel, Nucl. Phys. B157, 23 (1979).19. A. Sanda, Phys. Rev. D 23, 2647 (1981);N. Deshpande, Phys. Rev. D 23, 2654 (1981);See also: J. Donoghue, J. Hagelin and B. Holstein, Harvard Univ. pre­print (1981) and D. Chang, Carnegie-Mellon Univ. preprint (1981).18K° PHYSICS AT FERMILABG.B. ThomsonRutgers University, Department of Physics and Astronomy,New Brunswick, NJ 08903A discussion of the topic, K° physics at Fermilab, would be impossibly long, as can be seen from Table I, a list of the K° experiments done at Fermilab since the lab turned on in 1972. The first four, finished by 1977, were studies of the strong interactions of the K°, T£° system, and the rest, with the possible exception of the particle search were studies of rare kaon decays. What I really will spend my time on today is two of these experiments: E-533, the Pi-Mu Atoms experiment, and E-621, a Measurement of the CP-Violation Parameter, n+-o.Table I. K° physics at Fermilab.E-82 Carbon regeneration Chicago, Wisconsin,E-420 H2 regeneration San DiegoE-486 A-d ep end enc e Chicago,E-226 K° charge radius WisconsinE-533 Pi-Mu atoms Wisconsin, Stanford,E-584 Particle search ChicagoE-617 CP violation: noo/u+- Chicago, StanfordE-621 CP violation: n+-o Rutgers, Wisconsin, Michigan, MinnesotaPi-Mu ATOMS EXPERIMENTThe persons responsible for the Pi-Mu Atoms experiment are listed in Table II.Table II. Pi-Mu atoms personnelSam Aronson, Dave Hedin, Gordon Thomas,U. of Wisconsin Greg Bock, Bob Cousins, John Greenhalgh, Mel Schwartz,Stanford U.Bob Bernstein, Bruce Winstein,U. of ChicagoIn a rare decay mode first predicted by Nemenov^ and observed by Coombes jit al.^, the k£ will occasionally decay into a pi-mu atom and a neutrino. We report herewith a measurement carried out in an intense, high energy k£ beam at Fermilab in which we have observed 303 examples of these atoms and determined the branching ratio:Rate [Kl -* (iry) atom + v] 7R = r -------- 3.77 ± 0.62 x IO"7RateLKt ir y vj19Theoretical calculation of this ratio is straightforward and is carried out by regarding the decay KL = (Trp)atom + v as a weak two body process. The matrix element can be normalized to the decay mode Kl -* Tryv, and because of the pointlike nature of the weak interaction will depend directly upon the square of the pi-mu atom wave function at the origin, |iJj(0)[2„ The theoretical value of R depends somewhat upon the form factors involved in Kl Tryv and has been determined^ to be Rtheory = (4.52 ± 0.12) x IO"?.In calculating this value of R, it has been assumed that no inter­actions other than the normal Coulomb interaction are significant in determining |i|j(0)p. If any such anomalous interaction were present, it might lead to a change in the wave function at small distances and affect the anticipated branching ratio into atoms.To implement the experiment, we constructed an intense high energy Kl° beam at Fermilab. After the 400 GeV/c proton beam struck a beryllium target, a succession of magnets and collimators swept all charged particles from the flux of secondaries emerging in the forward direction. A sheet of lead placed before the collimators and sweeping magnets removed the gamma rays from the Kl° beam, which then consisted of about 100 neutrons for each Kl°, with an average Kl° momentum of about 75 GeV/c.The precise arrangement of the various elements in the detection apparatus is shown in Figure 1. The decay products which were of interest to us were those which had risen sufficiently out of the beam region to clear the bottom of the detector system. The remainder of the beam passed underneath the detector, in vacuum, to a concrete dump considerably downstream.The distinguishing characteristic of a pi-mu atom is the fact that it is a neutral object which is quite easily ionized by passing it through a very thin foil. Indeed, we have calculated that approximately .01 inch of aluminum is sufficient to ionize the atom. After ionization, the two charged particles will be travelling co-linearly with essentially the same velocity - a characteristic which is basic to our detection procedure.However, before we allow the atoms to be ionized, we must be able to reject those unbound ir-y pairs which happen to be nearly colinear and ofequal velocity. Were they to reach the foil unperturbed, then they would sub­sequently provide a thoroughly confus­ing background to the ionized atoms.To eliminate these "pseudo-atoms" we introduce a region of horizontal magne­tic field prior to the foil; the conse­quent vertical separation of the pion and muon serves to remove them from further consideration.The ionizing foil follows, still within the vacuum tank but above the k £ beam itself. After ionization, theFigure 1. Pi-Mu Atoms Spectrometer20pion and muon are parallel and have momenta in the ratio of their masses. They next enter a region of vertical magnetic field which serves to separate them horizontally, giving each an equal and opposite 165 MeV/c impulse. At the end of this magnetic region they leave the vacuum system through a thin window.The pion and the muon now pass, in sequence, through the following: a plane of thin horizontal scintillation counters (W) which just over­lap the window; a magnetic spectrometer consisting of: three pro­portional wire counters, an analyzing magnet whose field is set so as to precisely cancel out the effect of the magnetic field region which followed the foil, and two additional proportional wire counters; three hodoscopes of vertical scintillation counters (A, G, and B) and one of horizontal scintillation counters (H); an array of shower counters; and a 15 foot steel wall to stop all charged particles except muons, followed by a hodoscope of scintillation counters (M) to detect the penetrating muons.In the analysis of the data, unbound Ky3 decays were separated from TT-y atoms by the pattern of hits the pion and muon made in the propor­tional counters: the atoms showed an apparent "V" with vertex withinthe magnetic field region following the foil, while the Ky3 triggers did not. Also the projection of the struck wires onto a vertical plane showed two clear tracks for every Ky3 because of the perturbation the pion and muon suffered in the magnetic field just before the foil.Since the (neutral) atoms did not feel this perturbation the pion and muon tracks from an atom coalesced into an apparent single track in this vertical projection.In Figure 2, we show a histogram, for all the remaining events, of the quantity a = (p7r_Py) / (p-rr+Py)» where p-n-(py) is the pion (muon) momentum. For atoms, the pion ana muon have the same velocity, hence a should be the difference over the sum of the pion and muon masses, equal to 0.14. Figure 2 shows an extremely clean peak at a = 0.14 containing 303 7T-y atoms.By choosing the complementary data set for analysis, we can count the number of conventional Tryv decays observed by the detector during the time we collected the 303 ir-y atoms. All that remains is calculating the efficiency of our apparatus for observing these decays. We performed this calculation by making a Monte Carlo simulation of the experiment.The simulation contained a Ky0 momentum spectrum consistent with that measured by Edwards et al_., ^  the Ky3 decay parameterization measured byDonaldson et al., and the geometry of the beam and detection apparatus.To judge the accuracy of the simulation we plot in Fig. 3, a histogram of the longitu­dinal coordinate of Ky3 de­cay vertices. Both data and the Monte Carlo simula­tion are shown, and they agree closely. We also sim­ulated pi-mu atom events using the same Monte Carlo method.-3 -2 -IALPHA FOR FINAL DATA SAMPLE Figure 2. Alpha Histogram21Calculating the efficiency of our detector for pi-mu atom and un­bound Tryv decays, and using these numbers to calculate the branching ratio, we obtain R = (3.77 ± 0.62) x 10“7 . This agrees very closely with the theoretical prediction.In conclusion, we have collected 300 examples of the rare decay k£ -> TT-y atoms + v, and have measured the ratio of ir-y atom decays to k £ -* iryv decays. The theoretical expectation for this ratio is cal­culated on the assumption that the interaction between the muon and the pion at very small distances is just the Coulomb interaction. The close agreement between theory and experiment lends weight to this assumption; i.e., that there is no anomalous interaction between the pion and the muon.Table III. E-621 personnelA. Beretvas, T. Devlin, R. Whitman and G. Thomson Rutgers UniversityR. Handler, L. Pondrom, M. Sheaff U. of WisconsinO.E. Overseth- U. of MichiganK. Heller U. of MinnesotaFigure 3. Decay VerticesA MEASUREMENT OF n+-oExperiment 621, a measurement of n+-o, is a collaboration of the physicists listed in Table III.I. IntroductionWe have proposed to measure the CP violation parameter,r | | q  =  A m p ( K g -*■ 7T+ TT- 7 r ° ) / A m p ( K L -> Tr+ Tr—r r ° )by studying the interference between Kg and decays near their pro­duction target. The proper time, t, dependence of 7r+7r-ir° decays in an incoherent K°, K° beam is:M  ^  {e- ^ L  + I ^ , 2 e- c /xs + 2D|n+. 0 |x cos(Amt + <j>) e-t^ TS} (1)22where Nl is the number of K^’s exiting from the target, B is the Kl Tr+7r~Tr° branching ratio, t^Ct s) is the K-^Kg) lifetime, AM is the Kl~Ks mass difference, <j> is the phase of n+-0 > an<i D is the dilution factor (to be discussed later).The only 3tt final states that contribute are those with 1=1. There are two such states, with the Tr+ir- isospin equal to 0 or 2. If we define two amplitudes for decays to these final states,<3ir;I3ir-l, I71+ Tr-«0| T |K°> = iA x eiSl ,Iand <3Tr;I37r=l, 1 ^ = 2  | t|k°> = ±a [  ei6l ,then the CP violation parameter is:n = e + i 12^1 _ A . i<6i-«l) ImAi ( 2 )H— o  R e A i  / J  R e A x  K }The prediction of the superweak theory"* is that A^ and a { are both real, and ri+_0 = £. Other theories predict that there should be a direct CP violation; i.e., Im Al and Im Al are not zero. They have arguments on the order of 1 mrad. If this is true then the direct CP violation could contribute to ri+_0 as much as e does!So, the theoretical prejudice is that |ri+_0 | is between about lxl0“3 and 4x10-3, with considerable uncertainty in that range. If |ri4_ 0 | < lxl0“3 were the case, perhaps a cancellation in Eqn. 2 or a separate £l anc* (with could explain it. The latter caseviolates CPT however^. If |TVf_0 1 were found to be > 4x10-3, that would be very interesting indeed. So an experiment with a sensitivity in the 10~3 range could make a significant contribution to the understanding of CP violation.II. The ExperimentPast experiments shed little light on the subject. The one with best statistics, Metcalf et al.^ collected only 384 events in the reaction K+p ->■ K°pTT+ using a 2.4 GeV/c K+ beam, giving a result|n| Q | = .21 ± .24. Their apparatus consisted of a wire chamber spectro­meter looking at the bare target, and was limited by the integrated flux of K+ mesons. To get better statistics, one must go to a magnetic channel, such as the one in the M2 beam, and give up the knowledge of whether the initial state was a K° or a K°. This introduces the dilution factor into Eqn. 1,D = [1-K°/K°]/[1+KO/k°] .K~/K+ production ratios have been measured at high energies, and agree with fits done for K°'s (see ref. 3). The K°/K° ratio for this experi­ment is small, and is shown in figure 4.Figure 5 shows the apparatus: following the sweeping magnet is a24 meter long evacuated decay region, three drift chambers, the spectro­meter magnet, three MWPC's, counters, and a lead-glass wall. Above and23Figure 4. K/K Ratio. below the magnet aperture are additional gamma detectors, the A counters, consisting of scintillator anti-counters,2 xD of Pb, and an MWPC, giving accurate position resolution for gamma-ray hits. In front of the lead-glass is a similar Pb/MWPC combination to improve the position resolution of the 4" x 4" lead-glass blocks.Integrated over momentum, the acceptance is 95% for the charged particles, and 83% for the gamma-rays, 2/3 of the time both hitting the lead-glass.-20mf tOm 6mt30mt44 mGXD c h a m b e rs  0 0  MWPC0  SCINTILLATOR 0  LEAD GLASS 0  A-CO UN TER SFigure 5. Apparatus, Elevation ViewIII. Acceptance in zThe crucial question about the acceptance is its variation with z, the longitudinal vertex position. Although the z-dependence is quite flat, Monte Carlo simulations can predict it only to the 1% level, while the experiment requires an order of magnitude better knowledge. There­fore we propose to measure the acceptance by using a second target. If we target the proton beam 20 m upstream of the usual target position, the falling exponential will kill off the interference term for K^'s in the decay region. We will then see only the Kl -»■ tt° decays, which have the same distribution as the Kl term of the main target data: thedifference in z distributions of the two data sets (main and upstream targeting) will be due to the interference term. The highest precision is achieved with equal numbers of events in the two data sets, collected24simultaneously in a double beam geometry, switching the roles of the beams frequently.IV. Sensitivity and ResolutionTo estimate the sensitivity of this experiment let us assume that n+_0 = £ in magnitude and in phase. A Monte Carlo calculation using the measured resolution of the spectrometer tells us the acceptance as a function of momentum and proper lifetime (or z of the decay). Then an analytic calculation of proper time distributions allows us to "generate" as many events as we care to, the number Nj(p,z) coming from the main or interference target, and the number Nn (p,z) coming from the upstream or normalization target. If we form the ratio Nj(p,z)/Nn (p,z) for the same z bin, the acceptance cancels and, summing over momentum, the proper time distribution of this ratio is shown in Fig. 6. The errors shown in the figure are statistical errors that come from the double beam flux calculation given below. Using these values and errors, generating poisson fluctuations thereby, and fitting to the known dis­tribution yields standard deviations of about 10 degrees in the phase and about 25% in the magnitude n+_0 .The other two curves in Fig. 6 illustrate these same results, if ImCA^/ReCAi) in Eqn. 2 were +e and -e respectively; i.e. u^ q = e(l±i), and show the experimental response to these cases.V. Rates and BackgroundProduction rates expected from each target are listed in Table IV. At modest beam intensities, hundreds of detected K^/pulse result, and the flux of charged particles in the spectrometer is reasonable.Figure 6. Sensitivity of the ExperimentTABLE IV PRODUCTION RATESVI. Plan for Data CollectionWe propose to split the data collection into two phases. In phase 1 we would use the present spectrometer modified in two ways: drift chamberswould be added, and the beam line would be modified so that the present beam could strike one of two targets that could be placed in the beam by remote control. The rates of Table IV are directly applicable to this case. If we collected 100 K^/pulse, a week's running would yield about 3 M events,Target Interference NormalizationCollimator hole .4 x .4 =a2 .•4 x .4 cm2Thickness 24 cm Tungsten 7 cm TungstenLocation z-0 z— 20 mBeam intensity 1 x 10i0 ppp 1 x lO1^  pppDecay length 14 m 14 mS 3 200/pulse 180/pulse»° 170 k 60 kS3 70 k 5 kn 7.5 M 1.5 MY 10 M 2 Mn interactions 75 k 15 kY conversions 6 k 1 kTotal decays and interactions 500 k K^/1000 hr run*}with 24 m decay S length82 M)74 M25which we would split equally between the two targets. With this data sample we would achieve a statistical accuracy of .003. In performing this phase 1 test we would learn the following:1) how to trigger most efficiently on K^'s. Past experience in the M2 beam shows that collecting 100 events/pulse is possible, but no attempt has ever been made to increase the rate above that.2) the best way to handle systematic errors. With 1/3% accuracy to shoot for, Monte Carlo calculations should be an excellent guide to understanding the data.3) how best to do the second phase of the experiment, collecting 150 M events with controlable systematic errors.The result of this phase 1 test would be some excellent physics: we would decrease the experimental error (or upper limit) on |n| | bytwo orders of magnitude, pushing it down to the level where we might see something. In other words, we would answer the question, is |r)+_0 | anomalously large.Phase 2 of the experiment would build on all that we learned from phase 1. We would require a double beam setup, faster data-collection capability, and a 6250 bpi tape drive. We would also lengthen the decay region to 24 m to make better use of higher momentum K ^ ’s.VIII. ConclusionWe have proposed an experiment to detect the difference between and Kg by measuring the CP violation parameter U+-o* would do this in two phases: in phase 1 we would make the minimal modifications toour existing apparatus (the hyperon spectrometer in the M2 beam line), and run for 200 hours. We will measure U+-o with an error of about .003.With the knowledge gained from phase 1, we will undertake phase 2, collecting enough data to decrease the phase 1 error by a factor of 6,We will achieve a precision of 1/2 x 1 0 - 3 in the measurement of U+_0 in 1000 hours of running.References1. L. L. Nemenov, Sov. J. Nucl. Phys. 16, 67 (1973).2. R. Coombes et a l ., Phys. Rev. Lett. 37_, 249 (1976); also Anne Hall, Ph.D. Thesis, Stanford University, 1977 (unpublished).3. R. T. Edwards jit al., Phys. Rev. D18, 76 (1978).4. G. Donaldson et al., Phys. Rev. D9, 296Q (1974).5. L. Wolfenstein, Phys. Lett. 1J, 562 (1964).6. K. Kleinknecht, Ann. Rev. Nucl. Sci. 26, 1 (1976).7. M. Metcalf et al., Phys. Lett. 40B, 703 (1972).26MEASURING |n00/n+-|K. NishikawaEnrico Fermi Institute, University of Chicago, Chicago, Illinois 60637ABSTRACTIn this talk, we review the experimental situation of the measure­ment of CP violation parameters in decays. The discussion is based onthe Kobayashi-Maskawa model. It is extremely important to test this against the superweak hypothesis.THE MIXING PARAMETER e AND ITS MEASUREMENT1The mass eigenstates of the KO,K° system are|KS> = { (1+e) |k o > + (1-e) |K°>}/A+|e|2 |KL> = {(1+e)|K0> - (1-e)|K°>f//l+|e|2where e is a paramete_r for the mixing of CP eigenstates. Defining \p a=K° amplitude and a=K° amplitude, the time development of the state ip is given by- m- & ) +Hf”  ©  •Unitarity requires Mjj, 1^22* ^ll ancl ^22 to t>e real, and Mi2=M2i » and ri2=r2i. CPT invariance requires that M n = M 22 and rn = r 22* CP invariance requires that M 12 and T^i are real. Assuming CPT invariance, the rela­tion between the mass matrix and z isz =-Im Mini ilm ri2/2i(ms-mL) + i/2(rs-rL) *where mg(l )> rS(L) are KS(L) mass and decay width, respectively. Studies of leptonic decays2 show Im T12/2 << Im Mi2* Then, using the measuredvalues of mg-mL, II and Tg,<f>e =  (43.7 ± 0.2)° .The parameters which are actually observed in experiments are n+- = amp(KL -*■ /amp(Kg ->n00 = amp(KL -> ir°ir0)/amp(Kg ->• it0tt0)and charge asymmetry in Kj^ 3 decay. u N+ - N~= N+ + N" ’For the 2ir decay mode we define27e 'v2 a owhere a2,a0 and 62*^0 are amplitudes of the decay and phase shifts of final state interaction in 1=2,0 states.Thenn+- =  e + £'0oo - E - 2e'6 =  2 Re e .EXPERIMENTAL VALUESMany measurements have been done on CP violation parameters since they were first observed by Christenson et al.3 in 1964. Here I will list the most recent results.From charge asymmetry of charged leptons in K£3 decay,46 = (3.41± 0.18) x io~ 3 (Ke3)6 = (3.13 ± 0.29) x IO-3 (Ky3) .Taking the average,6 = 2Ree = (3.27 ±0.16) x 10-3 .Using<j»e = (43.7° ± 0.2°)gives|e| = (2.27 ± 0.08) x 10“ 3 .This number should be compared with the world average of U+-, obtained by the interference experiments,U+- = (2.279 ± 0.026) x 10-3 9°± 1. 3°) #Direct measurement of the ratio |noo/l+-I yields1000/1+- | = 1.03 ± 0.07 (based on 124 tt0tt° events) (Ref. 5)|n0o/o+- I = 1-00 ± 0.06 (based on 167 Tr°ir0 events) (Ref. 6) .All the above measurements are consistent with e '= 0 and can be combined togive the upper limit |e'/e| <0.02. However, because the phase of e' isArg e' = j  + (S2-<50) >we can deduce its value. Using experimental data from tt production by low energy pions, K+ and K° decay, and analysis, <52-^c ■'-s determined to be7’862-<50 = -53° ± 6 °28Therefore Arg e' ~  37°, which is close to that of e. This is a potentialdifficulty for observing e', even if e'^0. If we can measure | tl0o /  12to 1%, we can measure e '/e to 0.002%, since2—  1 +  6 e '/e •ooU + -THE0RETICAL MOTIVATIONThe discovery of x, T states and the success of SU(2) * U(l) gauge theory as a theory of weak interactions motivate the modification of Cabibbo theory to six quarks. The most notable feature, as pointed out by Kobayashi and Maskawa,9 is that the theory naturally includes a CP- violating phase. In this framework, |e f|/ |e| has been estimated by Ellis et: al_.10 to be ^1/450. Recently, in order to try to explain AI=l/2 rule in strange particle decay the so-called "Penguin diagram" (QCD short distance effect) was introduced and | e  ' | / | e | was recalculated. Although the value depends on the top quark mass and gluon corrections, the esti­mates are=1/50 ~  1/150 , Gilman and Wise11 = 1/250 ~ 1/500 , Guberina and Pecci.12If these estimates are true, there is a good chance to see these QCD effects by measuring |n0 o / ri + - |2 to 1% accuracy.NEW EXPERIMENTAL MEASUREMENTS ON e 1The two most precise experiments quoted previously were plagued by low statistics and high backgrounds (from the dominant -*■ 3tt° decay) .In order to separate background and correctly normalize by coherently re­generated Kg -y 2tr, it is absolutely necessary to have excellent energy and angular resolution.Two new experiments have been approved and will run during the next year; some details can be found in the experimental proposals.1 3 >1 ** Both groups aim for high statistics (~50 K 2tt° events) and good mass and angle resolution.The Chicago-Stanford group13 will convert one of the four gamma rays in the 2 tt° mode, tracking the resultant e+e” pair by drift chambers for good vertex resolution. The other three gammas are identified in a finely segmented 804-element lead glass detector. In addition, many systematic effects such as efficiency of detector and Kl flux will be eliminated in the data taking as both decays of Kl 2 tv° (in one beam) and those of Kg -* 2tt° (in another nearly parallel beam in which a regenerator is placed) are simultaneously recorded.The BNL-Yale group114 plans to study the time dependence of 2ir decays downstream of the regenerator. The tttt decay proper time distribution after a regenerator can be written asAitit « p e :^ mt-t:/ 2 T s 4 . r)+_ s( 00 )where p is the regeneration amplitude which depends on momentum of Kl and29the properties of the regenerator. Suppose that we could adjustp  eiAmt -t /2ts —  _ e at t = t ' ,in principle we then enhance the e' contribution. By measuring bothand near minimum, the ratio of the two decay modes will show a greatdeal of structure if eVO.Both of the above experiments are aiming for a 1% measurement on the ratio of the directly measured quantity R=|n00/ — I 2 * This then would yield a determination of e f with an uncertainty of 0.0017 e. Thus the true sensitivity of the experiments is at the level of—  ^ 0.004 .REFERENCES1. K. Kleinknecht, Ann. Rev. Nucl. Sci. 26_, 1 (1976).2. F. Niebergall et^  jil., Phys. Lett. 49B, 103 (1974).3. J.H. Christenson, J.W. Cronin, V.L. Fitch and R. Turlay, Phys. Rev. Lett. 13, 138 (1964).4. C. Geweniger et al., Phys. Lett. 48B, 487 (1974).5. M. Banner et al., Phys. Rev. Lett. J28, 1597 (1972).6. M. Holder et al., Phys. Lett. 40B, 141 (1972).7. G. Barbiellini et al^ ., Phys. Lett. 43B, 529 (1973).8. M.J. Losty jit ad.., Nucl. Phys. B69, 185 (1974);CERN-Munich Collaboration in Int. Conf. on Meson Spectroscopy IV, Boston, 1974.9. M. Kobayashi and T. Maskawa, Prog. Theor. Phys. _49, 652 (1973).10. J. Ellis, M.K. Gaillard and D.V. Nanopoulos, Nucl. Phys. B109, 213(1976).11. F. Gilman and M.B. Wise, SLAC-PUB-2341 (1979).12. B. Guberina and R.D. Pecci, Max Planck Inst, preprint (1979).13. R. Bernstein et al., Fermilab report 617.14. R.C. Larson et al., BNL report 749.30NEUTRINO-NUCLEUS INTERACTIONS*T.W. Donnelly Center for Theoretical Physics Laboratory for Nuclear Science and Department of Physics Massachusetts Institute of Technology Cambridge, MA 02139ABSTRACTA brief overview of the subject of electroweak interactions with nuclei is presented and the inter-relationships amongst the various processes of interest discussed, specifically insofar as the underlying nuclear many-body problem is concerned. Using these ideas predictions may be made for charge-changing and neutral current neutrino reactions in nuclei. A selection of examples is given and several conclusions are drawn on assigning priorities for future work in this field.INTRODUCTIONThe subject of electromagnetic and weak interactions is discussed in many places including several review articles1-1* which I have used in preparing this talk on nuclear physics with neutrinos. In particular I have drawn heavily on the material presented in Ref. 4 in which both charged and neutral current interactions are discussed and have employed the notation used in that work. The basic processes discussed here are indicated diagrammatically in Fig. 1. These include: inFig. la, electromagnetic interactions, namely, electron scattering and the special^subclass, real-photon reactions (the former has q _> to, where q = |q| is the three-momentum transfer and to is the energy transfer, while the latter are restricted to the real-photon line q = oj); in Fig. lb, the "conventional" weak interaction processes, 3-decay and charged lepton capture; in Fig. lc, charge-changing neutrino reactions; in Fig. Id, neutral-current neutrino scattering; and in Fig. le, electron scattering via the neutral current weak interaction (which produces a V-A parity violating effect in interfering with diagram la). These interactions are mediated by exchange of the bosons y , and Z°. As we believe we understand the interaction of the leptons with these bosons, the focus of such studies of semi-leptonic electroweak interactions in nuclei is on the hadronic side and is contained in the initial state, |i>, to final state, |f>, matrix elements of the appropriate operators'*', specifically, Jy, the electromagnetic current, > the charge-changing weak interaction current, andthe neutral weak interaction current. Note that the same current operator, J^, enters in electromagnetic electron scattering and in real photon reactions (i. e. the same physics is involved); however in the*Work supported by the U.S. Department of Energy (DOE) under contract number DE-AC02-76ER03069. A similar version of this talk also appears as part of the Los Alamos Neutrino Workshop, June, 1981.^Following the notation of Refs. 1-4 a second-quantized nuclear operator is indicated with a caret.31former it is possible to fix to, for example to excite a given state in the nucleus, and to vary q over all values such that q >_ co (i. e.Figure 1. Electro­weak interaction processes. The heavy lines indicate a nucleus proceeding from an initial state i to a final state f.In the neutral current processes (a,d,e) the same nuclear system is involved; in the charge-changing reactions (b,c), neighboring nuclei differing by one unit in charge are involved.(c)(d)(e)to map out an electromagnetic form factor F(q)), whereas in the latter only one point on the form factor is measured, namely the q = w point.So also in the processes shown in Figs. lc-e, in principle it is possible to map out complete weak interaction form factors at fixed i d .  However, as for the real-photon processes, under the conditions in which most of our present understanding of weak interactions in nuclei has been obtained, that is via the "conventional" weak processes shown in Fig. lb, the available range of momentum transfer q is severely limited. In g-decay, the four-momentum transfer is time-like, qy = q2 - u>2 0,so q _< a). Now even a very high energy nuclear 3-decay reaction has co < 20 MeV whereas a measure of when the momentum transfer is large or small is some typical nuclear value, Q, say the Fermi momentum Q 'v- kF ^ 200 - 250 MeV. So in 3-decay we are restricted to the low-q limit (or long wavelength limit, LWL) in which q/Q << 1. In charged lepton capture the momentum transfer q : - u; where m^ is thelepton mass (electron or muon). In electron capture we again have q/Q << 1, while in muon capture typically q ^ 80-100 MeV. Thus in the "conventional" weak interaction processes only two separate momentum transfer regions are explored, the low-q long wavelength region32and the region around 80-100 MeV. Neutrino reactions (at least in principle) have the potential to explore the complete weak interaction form factors and not just these restricted, rather low-q regions.Let us begin a discussion of the complete class of electroweak processes in nuclei by considering transitions between states |i> and |f> which are characterized by angular momentum J, parity ir, and isospin T, as well as by discrete energies and Ef (specific examples are considered below). The differential cross sections (i. e. differential in the lepton scattering angles) are given bydodft = oQ F2(q,m,0), (1)where 0 is the scattering angle (say between the incident neutrino and the exiting muon in the reaction (Vy,y )), where Oq is the elementary cross section (for example, the Mott cross section in electron scattering), and where F2(q,to,0) is a nuclear form factor. Expressions of this type may be obtained for all of the electroweak processes discussed here1 .The form factors may be expressed in terms of matrix elements of specific angular momentum and isospin multipole projections of the currents (see Ref. 4 for the general discussion):F(q,u),0) 'V' <f I {projections of J 5(±)« y or « y (2)Ignoring the isospin content for a moment we have two basic types of currents to deal with here, a vector (V) current, (for all of the processes) and an axial-vector (A) current, (for the weak interaction, but not for the electromagnetic interaction; the "5" indicates the extra Y5 in the elementary axial-vector current, see Eq. (5b) below). As we are dealing with four-vectors, we then have the eight basic types of multipoles listed in Table I.Table I. Multipole OperatorsN = natural parity, (-)^; U = unnatural parity, (-)^+1The details of such multipole decompositions of the currents are given in Refs. 1-4. In particular we usually assume that the vector current is conserved as in the case of electromagnetic interactions and, through the Conserved Vector Current (CVC) hypothesis, that the vector part of the weak interaction current is conserved. With this assumption theV Parity A Parityy = 0 ("charge") y = 3 (longitudinal)y = 1,2 (transverse)N£.el*•*!1L5l - * t  u-el 5ulT v * *  N33longitudinal multipole, L, may be related to the "charge" multipole,M, and so dropped from the list, leaving seven basic types of multipoles. Including the isospin content we must deal with multipoles labelled X K y, where 7  = M j = 0 for isoscalar transitions (electromagnetic and neutral current weak interactions); J  = 1, = 0 for isovectorneutral current processes (electromagnetic and weak); and 7 = 1 ,*«r = ±1 for isovector charge-changing weak interaction processes (see Ref. 4 for the general isospin content).As a specific example for orientational purposes consider an electromagnetic transition from the ground state of 12C, J^T = 0+0 to the 15.11 MeV excited state in 12C having JWT = 1+1, where both states have Mj = 0. Only one multipole contributes, T”J^ g. with j  -  1, T  = 1, <My = 0, that is, we are discussing an*Ml transition.Now the ground states of *2B and also have J^T = 1+1, however now with = -1 and +1 respectively. Thus in the charge-changing weak interaction processes we have the multipoles .g-,** * >anc* ’ wit^ $ = ^  = = an<* resPectivefy.' * * Furthermore, in the neutral currentweak processes we have againmt = - i 015.11+ 1l+lthese same four multipole operators, but now with ►*> = 0. The relationship amongst these electro­weak processes is illustrated in Fig. 2. We shall return to this important example a little later.Now these multipole operators may be decomposed in the following way:T = X,(l) + f(2) (3)Figure 2. Electroweak interaction processes in the A = 12 system. where T stands for any one of theseven (or eight) basic operators in Table I with X labelling the angular momentum and isospin content. Here T-y1  ^ ^ a^Sj is a one-body operator (that is, it changes the quantum numbers of nucleons in the nucleus one-at-a-time from 1 to 2),Tj£2) ^ a ^ a ^ a ^ a ^ is a two-body operator (that is, it changes the quantum number from (1,2) to (3,4)), etc. (see Ref. 5). Usually the one-body contributions dominate over the two-body, etc. contributions, where the latter include the effects of meson exchange currents6*7 (see below for a brief discussion of MEC effects in electromagnetic interactions). Thus, for the present purposes we shall restrict our attention entirely to the one-body operators, T£17. For these an exact statement may be made:<f T.( 1) i> = aa <a,(l) a' > (aa') (4a)where on the left-hand side is the many-body nuclear matrix element required in the nuclear electroweak form factor. This in general involves initial and final nuclear states with arbitrarily complicated34many particle-many hole configurations. The right-hand side contains an expansion in single-particle matrix elements, where a ■*-*■ {nHjmj ,%mt} is a complete set of single-particle quantum numbers and where the c-numbers are one-body density matrix elements in which areburied all the complexities of the nuclear many-body problem. If we truncate the sums over a and a 1 to a finite model space (and we do this for example in performing shell model calculations for the nuclear states), then a finite (frequently quite small) set of numbers(aa') characterizes the nuclear dynamics content for this specific transition. In fact we shall assume that isospin is a good quantum number, in which case we may deal with matrix elements reduced in angular momentum and isospin spaces. Then the above equation becomes< f ! l  * y ! y ( q )  " i >  =  a a '  < a "  T j ; 7 ( q )  " & , >  * ^ y ( a a , )  ’  ( 4 b )where the symbols || denote the doubly-reduced matrix elements and where a-*-* (n£j;%}, that is, the single-particle quantum numbers other than mj and mt. Presuming that the single-particle matrix elements are known within some model space (we return to this below), then the following procedure may be tried:(1) For a well-studied process such as electron scattering measurements of cross sections lead to form factors (Eq. (1)) and hence to the many-body reduced matrix elements as functions of q for the appropriate operators (i. e. to the left-hand side of Eq. (4b)).(2) These may be expanded in a set of single-particle matrix elements within some model space with expansion coefficients being the one-body density matrices iJj.(3) Now the relationship may be turned around for less well-known processes such as the weak interaction reactions. The same set of density matrices are used, but now with the appropriate weak interaction operators and their single-particle matrix elements. This yields the many-body reduced matrix elements, the form factors and hence the weak interaction cross sections. In other words, the point of this procedure is to bury our lack of knowledge of nuclear dynamics in the minimum number of relevant quantities (the one-body density matrices) and to let a known process such as electron scattering determine them to the extent that this is possible. In a sense one is "calibrating a specific nuclear transition" by following these steps and by using all the good quantum numbers available by choosing appropriate nuclear transitions one uses the nucleus as a "filter" to selectively study different pieces of the electroweak interaction. Several examples of following these procedures are reviewed in Ref. 4 (see also the references contained therein).Let us return now to the form of the single-particle matrix elements in Eqs. (4). Using general principles such as Lorentz covariance, parity and time-reversal invariance and conservation of isospin we may write1*:for the free single-nucleon matrix elements of a vector (5a) and axial- vector (5b) current. Here the nucleon states are labelled by momentum It, helicity X and isospin projection mt = ±%. The isospin content of the operator is contained in1*The single-nucleon form factors Fj, F2, Fg, F^, Fp and Fp (Dirac, Pauli, induced scalar, axial-vector, induced pseudoscalar and induced tensor respectively) are all functions of four-momentum transfer qj]. 1 shall assume throughout that the vector current is conserved (see above), in which case Fg = 0. Furthermore we take only first-class currents to be non-zero, so that Fp = 0 as well. We adopt a strong form of CVC and assume that there is only one vector current for both electromagnetic and weak interaction processes. That is, we take only a single set of couplings {F^^, f | ^ , , F ^ ^ , 7 = 0,1} and constnthe physical currents through the relations:1 7 =0, Xy =0(6)(7a)(7b)(7c)for the electromagnetic, charge-changing weak and neutral weak interaction(5a)(5b)3536currents respectively. Here the neutral current couplings »7 =  0 , 1 ,  depend on the underlying gauge theory model of the electroweak interaction . In particular for the standard W-S-GIM model (see Ref. 4 for a brief introduction to gauge theory models) we havewithso that, for example, there is no axial-vector isoscalar neutral current weak interaction coupling. We return to this point below.As a final step in making the connection to nuclear physics one takes the non-relativistic limit of the single-nucleon expressions (Eqs. (5)) and employs the appropriate single-particle wave functions (not plane waves as in Eqs. (5), but more commonly harmonic oscillator wave functions8 or Hartree-Fock wave functions or some approximation to them). This yields the single-particle matrix elements needed on the right-hand sides of Eqs. (4) in terms of the elementary single­nucleon couplings Fj , F2, F^ and Fp.Let us return briefly to the question of meson-exchange currents8*7. If they are included in the analysis, then, in addition to operators T^1  ^ in Eq. (3), one also has two-body operators and mustemploy two-body nuclear density matrices (see Fig. 3).Figure 3. One- and two-body contributions to electromagnetic interactions.Calculations have been performed8 using shell-model wave functions for the states involved to obtain one- and two-body density matrix elements and applied to electromagnetic interactions with selected37nuclei. Some examples are shown in Figs. 4 and 5. As may be seenFigures 4 and 5. Electron scattering from 6Li and 7Li showing the one-body contributions only (solid lines) and the one- plus two-body MEC contributions (dashed lines). The figures with reference to the data are taken from Ref., at momentum transfers below about 500 MeV no large effects are introduced when MEC contributions are included. In particular, the A = 6 case (to be discussed in the following section) appears to be safely represented to perhaps the 10% level by one-body density matrixanalyses as described above. This is not always the case, however;specifically, the deep-inelastic region7 may contain significant MEC effects.NEUTRINO REACTIONS: SELECTED EXAMPLESLet us now turn to several examples of these concepts and the resulting predictions for neutrino reactions, (v£,£“), (v£,£+ ), where £ = e or y, and neutrino scattering, (v£,V£'), (v£,V£'). The A = 6 example (see Fig. 6) constitutes a much-studied simple case where these ideas have been explored9. The adjustment of the density matrixelements ^ (in this case,re-expressed in terms of wave function amplitude coefficients, see Ref. 9) permits an excellent fit to the electron scattering data to be made (a fit including high-q ee1 data is shown in Fig. 7). Having determined the required one-body density matrix elements it is possible to predict the analog weak interaction rates. In fact the 3-decay and y-capture rates predicted are in agreement with the measuredMt = -I 0 +1Figure 6. Electroweak interaction processes in the A = 6 system.38Figure 7. Electron scattering form factor for the l+0 -*■ 0+l (3.56 MeV) transition in ^Li (from Ref. 10). The fit is obtained as described in the text.values9’11, giving us confidence that the neutrino-induced processes can be predicted with good precision (to perhaps 10-15% in this case).The charge-changing and neutral current neutrino cross sections are shown in Figs. 8 and 9 respectively.Figures 8 and 9. Charge-changing and neutral current neutrino reactions in the A = 6 system (from Refs. 9 and 12 respectively). For the neutrino scattering calculations = 35° was employed in Ref. 12, whereas 29° is the currently accepted value.y(MeV)CVJEoVo&b*NEUTRINO ENERGY (MeV)39Another classic example is the A = 12 system (see Fig. 2); here a one-body density matrix analysis of the type described above yields the neutrino cross sections shown in Figs. 10 and 11.(Tr  ( x ICT*0cm 2 )1.2.--------------------------------------------------------------------------------------Figures 10 and 11. Charge-changing and neutral current neutrino reactions in the A = 12 system (redrawn from the work of Ref. 13 and from Ref. 12 respectively). For the neutrino scattering calculations 0W =35° was employed in Ref. 12, whereas 29° is the currently accepted value.CMEoOXAb*NEUTRINO ENERGY (MeV)Other examples show a similar behavior (see Ref. 4 for discussion several other cases). Two such worth mentioning in passing are the 7Li case (ground state and 0.478 keV first-excited state, see Fig. 12)which may serve as an excellent neutral current excitation case for reactor anti-neutrinos12 and secondly, theofspecial case of 0+ 0“ transitions11*,as in the A = 16 system, where the neutrino reaction cross sections are sensitively dependent on the induced tensor second-class current coupling,Figure 12. Neutral current neutrino excitation of 7Li.40(see Eq. (5b)).An important general feature also worth mentioning at this point is to note the low-q or long wavelength behavior of the various multipoles (the allowedness in usual 0-decay terminology). This is discussed in Refs. 4 and 15 in some detail. The important point here in the present discussion is that for inelastic neutrino scattering the axial-vector dipole dominates whereas for elastic neutrino scattering (because of the coherence in this case) the vector monopole dominates. These are the analogs of the familiar Gamow-Teller and Fermi g-decay allowed multipoles15. Thus, at not too large momentum transfer (say q/Q < 1, using the above estimate of Q *v< kp 'v* 200-250 MeV), one has a special situation: for inelastic scattering an Ml transition ispredominantly axial-vector; for elastic scattering the vector current dominates. In the former case, by selecting the isospin quantum numbers1**15 we may selectively study the isoscalar axial-vector and isovector axial-vector couplings, g^°) and in Eqs. (7c and 8).Note that in the standard model (see Eq. (9)> the former vanishes: such an isoscalar Ml transition could provide a sensitive test of the underlying gauge theory model couplings 1+»15.Turning to the other allowed multipole, the vector monopole or "Fermi" matrix element, we see that the cross section for elastic neutrino scattering1* is proportional to A2 (just as elastic electron scattering1’1* is proportional to Z2). On the other hand the target recoil energy is proportional to A-1 and for A too large becomes too small (for given neutrino energy) to detect. Thus, while very heavy targets have relatively speaking very large neutrino cross sections (and this is relevant in astrophysics in collapsing massive stars), at the neutrino energies of interest here the interest in elastic scattering centers on rather light nuclei. In particular the case of ^He seems to be of special experimental interest16’17. The elastic neutrino cross section is proportional to (g^° }2 = (oty0  ^ - 2sin20y)2 (see Eq. (8) and Refs. 4, 17) and so provides still another test of the underlying gauge theory model (in the standard model, ct^ °) = 0; see Eq. (9)). It would be very nice to see the nuclear coherence effect demonstrated for the neutral current weak interaction. This constitutes a test of isoscalar CVC.As a final example here let us turn from discussions of exclusive reactions in which the kinematic variables are presumed to be well enough known that only a single discrete nuclear transition is involved to inclusive reactions where a range of nuclear excitations is integrated over to obtain the measured cross section. With a spectrum of neutrino energies from a pion decay-in-flight neutrino facility this will be the case in fact. In Fig. 13 the A = 12 situation is indicated schematically. To obtain the total neutrino cross section it is necessary to sum over the giant resonance excitations and also the higher energy quasi-elastic region. This is just the situation that occurs in inelastic electron scattering at these energies (see Fig. 13). The problem is that the models used for the quasi-elastic region (usually the Fermi gas model) are known to be rather poor at these values of q and u> for electron scattering. Thus while the giant resonance41Figure 13. Inelastic, electroweak interactions in the A = 12 system.The 1+1 15.11 MeV state ofand its analog, the ground state of12N are shown. The region in whichparticle-hole states are excited, the giant resonance (GR) region is shown, as is the quasielastic (QE) region. These have analogs in the charge-changing neutrino reactions which connect *2C to excited states of 12N.excitation region (see Fig. 14) is probably quite well accounted for by the ODW calculation13 (that is, to perhaps 20-30%) the higherFigure 14. Charge-changing neutrino reactions in the A = 12 system (redrawn from Ref. 13). Here the strength has been summed for the particle-hole states in the giant resonance region (roughly the first 15 MeV of excitation energy in 12N). The one-body density matrices adopted here have been adjusted to produce a good fit to the (e,e') data.a ,  (x K ) cm  )excitation energy region is not so well understood. As this inclusive reaction is the one used for neutrino detection in a class of neutrino oscillation experiments it is important to do the best job possible on predicting the cross section.42CONCLUSIONSIn conclusion, there are many examples of exclusive nuclear neutrino reactions which test specific parts of the electroweak current. The primary use of nuclear targets, as against the nucleon ,, is likely to be this ability to select or "filter out" specific pieces of the interaction. Two exceptions, however, come to mind: (1) Itwill be of interest to demonstrate the nuclear coherence seen in elastic neutrino scattering as discussed above, and likely the ^He case is the one favored; and (2) There may be a time when questions of axial-vector meson-exchange current effects (many-body nuclear effects) can be addressed, perhaps in the case of deuteron neutrino-disintegration (see Fig. 15).The following is a condensed summary of the conclusions reached at the Los Alamos Neutrino Workshop in June, 1981, under the heading "Nuclear Physics with Neutrinos":(1.) First Priority Reactions(a.) p(v,p)v, elastic neutrino scattering to test the vector and axial-vector, isoscalar and isovector parts of the weak neutral current. Although this really falls under "Particle Physics with Neutrinos" it is of course fundamental in discussions of nuclear physics.(b.) neutrino reactions with 2Hd(v,d)v, elastic neutrino scattering to test the vector andaxial-vector, isoscalar parts of the weak neutral current (the latter is zero in the W-S-GIM model). d(v,p)vn, d(v,n)vp, d(v,pn)v, inelastic neutrino scattering, including potentially the last coincidence reaction.There is heightened sensitivity to the axial-vector, isovector weak neutral current here. d(v£,£“)pp, d(v£,£“p)p, Si = e or y, charge-changingdeuterium neutrino-disintegration, including potentially the latter coincidence reaction to test the q-dependence of the charge-changing weak interaction.(2.) Second Priority Reactions(a.) Inelastic neutrino excitation (v,v') followed by de-excitation of the nucleus by Y,p,a, . . . decay. For example the (v,v') excitation of the 15.11 MeV state of *2C followed by y-decay or the (v,v') excitation of the 12.71 MeV state of4312C also followed by y-decay. The former tests only isovector neutral currents while the latter is most sensitive to isoscalar neutral currents (there is a small amount of isospin mixing in the 12.71 MeV state). And, since at relatively low energies the axial-vector current dominates, again specific pieces of the weak neutral current may be studied.(b.) Coherent elastic scattering, the prime example being ^HeCv,l+He)v to (i) see the coherence demonstrated and (ii) measure the vector, isoscalar weak neutral current coupling. This constitutes a test of the extension of the usual isovector CVC hypothesis to include the isoscalar weak neutral current.REFERENCES1. T. deForest, Jr. and J.D. Walecka, Adv. in Phys. JL5, 1 (1966).2. T.W. Donnelly and J.D. Walecka, Ann. Rev. Nucl. Sci. 25, 329 (1975).3. J.D. Walecka, in "Muon Physics", Vol. 2, ed. V.W. Hughes and C.S. Wu (Academic Press, N.Y., 1975) p. 113.4. T.W. Donnelly and R.D. Peccei, Phys. Reports fiO, 1 (1979).5. A.L. Fetter and J.D. Walecka, "Quantum Theory of Many-Particle Systems", (McGraw-Hill, N.Y., 1971).6. J. Dubach, J.H. Koch and T.W. Donnelly, Nucl. Phys. A271, 279 (1976).7. T.W. Donnelly, J.W. Van Orden, T. deForest, Jr. and W.C. Hermans,Phys. Lett. 76B, 393 (1978); J.W. Van Orden and T.W. Donnelly,Ann. Phys. 131, 451 (1981).8. T.W. Donnelly and W.C. Haxton, Atomic Data and Nucl. Tables 23,103 (1979); 25, 1 (1980).9. T.W. Donnelly and J.D. Walecka, Phys. Lett. 44B, 330 (1973).10. J.C. Bergstrom, U. Deutschmann and R. Neuhausen, Nucl. Phys. A327,439 (1979).11. J.B. Cammarata and T.W. Donnelly, Nucl. Phys. A267, 365 (1976).12. T.W. Donnelly, D. Hitlin, M. Schwartz, J.D. Walecka and S.J. Wiesner, Phys. Lett. 49B, 8 (1974).13. J.S. O'Connell, T.W. Donnelly and J.D. Walecka, Phys. Rev. C6,719 (1972).14. T.W. Donnelly and J.D. Walecka, Phys. Lett. 41B, 275 (1972).15. T.W. Donnelly and R.D. Peccei, Phys. Lett. 65B, 196 (1976).16. H. Chen and R. Reines, UCI-Neutrino Report No. 31 (1979).17. T.W. Donnelly, separate contribution to the Los Alamos NeutrinoWorkshop, June, 1981.44NEUTRINO ELECTRON ELASTIC SCATTERING AND NEUTRINO OSCILLATION EXPERIMENTS AT LAMPF*Herbert H. Chen Department of Physics University of California, Irvine, California 92717ABSTRACTA UCI/LASL experiment (E225) is currently being installed at the LAMPF beam stop neutrino facility. Goals of this experiment are: to study neutrino electron elastic scattering; to search for ve 's from the beam stop, e.g. Vy -> ve oscillations, y+ -* e+ veVy allowed by the multi­plicative law; to study the inverse beta reaction on 12C; to search for neutrino decays; etc. Many other experiments are being planned to search for neutrino oscillations both via appearance, e.g. Vy -* ve (E559, E609, E645), Vy -> ve (E638), and disappearance, e.g. ve -*■ ve (E645) , Vy -*■ Vy (E638).INTRODUCTIONA program of research in neutrino physics has been under way for a number of years at LAMPF using a beam stop neutrino facility. Several feasibility studies and an experiment have been completed. An experiment is currently being installed and many more are being planned both for the beam stop and for a new decay in flight facility. The current list of experiments is shown in Table I. Results from E31 have been published,1*2 and results from E148 are available in a number of UCI internal reports and conference reports. 3 Therefore, the present report will focus on E225 which is being installed in the LAMPF beam stop neutrino facility, and will summarize the many planned experiments on neutrino oscillations.LINE A BEAM STOP NEUTRINO SOURCE5The LAMPF accelerator now delivers a 0.6 mA proton beam at 800 MeV. This beam passes through a sequence of meson production targets and iso­tope production targets before ending at the beam stop. The residual pro­ton current at the beam stop is in the range 0.33 mA to 0.60 mA with pro­ton energy in the range 730 MeV to 800 MeV, depending on the particular target(s) inserted upstream.The LAMPF accelerator operates at a macro duty factor between 6% and 9%, i.e. it delivers 120 macro pulses per second with each macro pulse duration in the range 500 ys to 750 ys. The macro pulse consists of micro pulses which are 0.25 ns wide separated by 5 ns.Neutrinos are produced in the beam stop from decays of stopped u+,s and stopped y+,s. Due to the pion and muon lifetimes, the neutrino source duty factor follows LAMPF1s macro duty factor. The neutrino types and spectra are shown in Fig. 1. Note that the LAMPF beam stop is a unique source of ve 's, since reactors are copious sources of ve's, and high energy accelerators are copious sources of Vy's and Vy's. Stopped*Research supported in part by the National Science Foundation and by the Department of Energy.45Table X. Neutrino experiments at LAMPF.NumberInstitutions(Spokesman)Title StatusE313 Yale, LASL (Nemethy)A Neutrino Experiment to Test Muon ConservationCompleted(1979)E533 BNL(Davis)Observation of the Electron- Neutrino at LAMPFFeasibility StudyInactiveCompleted(1977)E148a UCI(Chen, Reines)Neutrino Electron Elastic Scat­tering (A Feasibility Study)Completed(1977)E225a UCI, LASL (Chen)A Study of Neutrino Electron Elastic ScatteringInstallingE225A3 UCI, LASL (Chen)A Search for Neutrino OscillationsProposedE2543 Harvard-Smithsonian(Fireman)Feasibility Study for Measure­ment of the Inelastic Neutrino Scattering Cross Sections in 39KCompleted(1977)E5593 Rice, Houston, LASL (Minh, Phillips)Search for Neutrino OscillationsProposedE609a LASL(Kruse)Anti-Neutrino Oscillation Experiments at LAMPFConstructingE638b LASL, Maryland (Dombeck)A Search for Oscillations Using Muon NeutrinosDesigningE645a Ohio, ANL (Ling, Romanowski)A Search for Neutrino Oscillations at LAMPFDesigningNotes:aline A beam, stop source line D decay in flight source (proposed)tt"'s and stopped y-,s are absorbed so that few y s decay. Because of this, the ve flux is suppressed by a factor of at least 103. The neutrino flux from the beam stop has been determined from a measurement of the rate of stopped tt+  decays per incident proton in an instrumented copper beam stop.6 Recently, this flux has been enhanced 40% by the addition of a20 cm thick water degrader' upstream of the beam stop. Details concerning this flux are shown in Table II.Protection against the beam stop is provided by a 6.3 m Fe shield. The Fe thickness was chosen to reduce backgrounds from the beam stop to a level well below anticipated neutrino signals. The 6% duty factor poses a severe problem in that the rejection factor it provides against cosmic ray backgrounds is relatively small. Furthermore, cosmic ray backgroundsFig. 1. Neutrino types and spectra from stopped tt+  and y+ decay at the LAMPF beam stop. NEUTRINO ENERGY (MeV)46Table II. Neutrino fluxes and calculated rates for E225.Beam at A6 Full Beam A5 Out A5 In (Al & A2 targets in)Proton energy (MeV) 800 770 730Proton current (pA) 1,000 760 575Stopped tt+ decay/proton3 0.072 0.067 0.059Stopped tt+ decay rate (10llf sec'1)4.5 3.2 2.1ve flux at 9 mb (1012 cm'2 day'1)3.8 2.7 1.8Qenhanced ve flux (1012 cm'2 day'1)5.4 3.8 2.5Rv-A^day'1)^ 5.2 3.7 2.4Rcl2(day'1) 11.9 8.4 5.6R c ^ C d a y ' 1) 1.09 0.77 0.51Rp(day'1) 228 161 107Notes:aThis was measured for a Cu beam stop (Ref. 6).^The additive lepton number conservation law and the absence of neutrino oscil­lations are both assumed. The Vy and Vy fluxes are identical to the ve flux.cThe 20 cm H 2 O insert is estimated to increase the neutrino flux by ~40% (Ref. 7).^14 metric ton detector consisting of 10 tons PVT (CH-^ and 4 tons polypropylene (CH2 ).are severe at these low energies. Therefore, the walls and roof of the LAMPF neutrino facil­ity consist of Fe 1.0 m and 1.2 m thick, respec­tively. This Fe thick­ness was chosen to reduce backgrounds from the hadronic component of the cosmic rays to a level below that arising from the muonic component. Figure 2 shows a sche­matic of the line A neutrino facility.Fig. 2. LAMPF Neutrino Facility.47UCI: R.C. Allen, G.A. Brooks, H.H. Chen, P.J. Doe, H.J. Mahler,A.M. Rushton, K.C. Wang LASL: R.L. Burman, R. Carlini, D. Cochran, Minh Duong-van, J.S. Frank,V.D. Sandberg, R.L. Talaga (MP); T.J. Bowles (P)Detector SystemThe E225 detector system occupies the entire volume inside the LAMPF neutrino facility. The detector system layout is shown in Fig. 3. An active anticoincidence, consisting of 4 layers of MWPC, is used to reject charged cosmic ray events with very high efficiency, i.e. inefficiency less than about IO"5 . Inside this MWPC is an additional 5-1/4" thick Fe shield which absorbs neutrals (gammas) generated by muons. This Fe shield is augmented by an additional 1" thick layer of Pb on the front and back walls, and on the roof.The central target/detector system has a sensitive mass of about 15 tons. It contains 40 layers of NE114 plastic scintillator (10' x 10' x 1") alternated with plastic flash chamber modules (5x and 5y alternating layers/module). The scintillation counters8 measure energy as well as dE/dx (particle identification). The flash chamber modules9 measure posi­tion as well as angle within each module.To identify cosmic ray backgrounds, activity in each of the 600 MWPC's and in each of the 160 scintillation counters is stored for 32 ps before a trigger. This time duration is dictated by the muon lifetime, and the anticipated cosmic ray stopping muon decay rate of ~107 day-1.To identify the inverse beta reaction ve12C -*■ e_12N^*^ , activity in each of the 160 scintillation counters is stored for 64 ms after a trigger. This time duration is dictated by the 11 ms half-life of 12N, and its anticipated rate which is shown in Table II.EXPERIMENT 225Fig. 3(a). Top view of the UCI/ LASL Neutrino Detector.Fig. 3(b). End view of the UCI/LASL Neutrino Detector.48Physics GoalsThe large fraction of ve's from the LAMPF beam stop makes it a unique source of neutrinos. The primary goal of E225 is to study neutrino elec­tron elastic scattering. The experiment was initially proposed10 several years before the proof of renormalizability of spontaneously broken gauge theories (G. t'Hooft, B.W. Lee et al.) that led to the reexamination of Weinberg/Salam-Ward (WS) electromagnetic-weak unification theories and the discovery of weak neutral current interactions. In the absence of a weak neutral current interaction there is no ^v^,e“ elastic scattering, and V-A "theory" gave a well defined ^v^e- elastic scattering cross section. With WS theory, a weak neutral current interaction arises from Z° exchange.Thus (Vy,e“ and ^g,e‘ elastic scattering occurs at a rate governed bysin20w , the one free parameter in the theory. The 'Vy,e“ and ve ,e“ ratesfrom WS normalized to the V-A rate are shown in Fig. 4. The anticipated rates for E225 with a 20 MeV detection threshold assuming V-A are shown in Table II. With this rate, we believe that a 10% measurement of the elas­tic scattering cross section is possible. Thus, we may detect the inter­ference term between Z° and W-1 exchange diagrams.11To minimize ve12C -»■ e~12N ^  events as backgrounds for neutrino elec­tron scattering, this reaction is tagged via 12N -* 12C e“ve decay. Thus, the ve12C reaction can be identified as background and used to test the calculation of Donnelly et al.12With the suppression of ve 's from the beam stop (in the standard theory), the observation of ve*s at levels significantly higher than ex­pected would be clear evidence for new physical phenomena. ve 's can bedetected with relative ease using the vep -*■ e+n reaction. This led E31 totest the multiplicative lepton number conservation law which allows-+■ e+ veVy decay, and to search for Vy ve oscillations. Their pub­lished results, at the 90% confidence level, are1’2 :R <0.098 6m2 < 0.91 eV2where R is the y+ branching ratio for the multiplicative mode giving rise to ve , and 6m2 = |m2 - m2 | , and m2 are masses of neutrino eigenstates.This limit on 6m2 assumes maximal ^e »vp mixing. Its magnitude does not rule out the existence of Vy -*■ ve oscillations that might be suggested by evidence presented by Reines, Sobel and Pasierb.13 We anticipate that E225 can improve this limit on R by about an order of magnitude, and on 6m2 by about a factor of three.llf Curve 1 in Fig. 5 shows this limit on 6m2 as a function of sin220.The existence of neutrino oscillations could affect our measurement of the neutrino electron cross section. To examine the magnitude of this effect, we assumed Vy ■*-*■ ve oscillations only (the worst case possibility), and calculated the fractional change in detected rate as a function of 6m2 and sin220, with sin20w = 0.23. Figure 6 shows that the change in rate is small, i.e. <1%, over the region allowed by E31. Thus, the primary goal of E225 will remain unaffected if neutrino oscillation exists.StatusInstallation of the E225 detector system is in progress. At present, 26 of the 40 layers in the central detector are in place. The remainder will be installed by August. The MWPC anti installation has started. We49Fig. 4. Neutrino Electron Elastic Scattering Rates normalized to the V-A rate as a function of sin20w .Fig. 5. Limits on 6m2 as a func­tion of sin226 for Vy ve ap­pearance at the 9 m position (curve 1), at the 36 m position (curve 2) , and for ve -*• ve disap­pearance at the 36 m position (curve 3). These limits are dominated by neutrino backgrounds, cosmic ray backgrounds, and neu­trino rate, respectively.anticipate completion of this by early fall. The detector checkout and calibration is beginning. This process should occupy us to the end of this calendar year. We hope to begin data acquisition with the full de­tector system when the LAMPF beam becomes available next March.NEUTRINO OSCILLATION EXPERIMENTS AT LINE AInterest in neutrino oscillation experiments is very high at LAMPF. Table III shows in greater detail the oscillation experiments listed in Table I. Most experiments use the Line A neutrino source described earlier. E638 would use a new neutrino source in Line D which will be described in the next section. The experiments in line A are briefly summarized in numerical sequence.Fig. 6. The fractional change in detected neutrino electron elastic scattering with sin20w = 0.23 is shown as a function of 6m2 and sin220 assuming ve Vy oscilla­tions (the worst case possibility). Over the region allowed by E31, the change is small, i.e. <1%.50Table III. Neutrino Oscillations Experiments at LAMPF.Type(Source)Proponent Reaction Detector(tons)6 m2vy - ve E225A vep -*• e+n plastic scint. + flash chamb. (15)0.18(Line A Beam Scop)E559 vep -*• e+n with e+n coinc.liquid scint. + drift chamb. (5)0.08E609 vep -*■ e+n with n delayed coinc.gadolinium loaded liquid scint. (4.5)0.12E645 v ep -*• e+n H 2 O C planes + drift chamb. (5 + 15)0.06ve ve E225A ve12C - e- 12N (*} with 12N delayed coinc.plastic scint. + flash chamb. (15)0.5E645 veD -*• e'pp D2 O C planes + drift chamb. (5 + 15)0.3vp -  ve (Line D Decay in Flight)E638 ve 12C -*• e“X liquid scint. + drift chamb. (50)0.025vp -*• vp E638 Vy12C ■* p"X liquid scint. + drift chamb. (50)0.2E225AThe UCI/LASL collaboration is proposing to move the E225 detector system with its shielding after the approved program is completed. Moving the detector system to a second position will allow an improved limit on Vy -*■ ve appearance, as well as providing a limit for ve -* ve disappearance. Curves 2 and 3 in Fig. 6 show these limits on 6m2 as a function of sin226. Data for both channels are taken simultaneously via vep -»■ e+n (with 35 MeV detection threshold) and ve12C -*■ e-l2N ^  (with 12N -*■ 12C e+ve delayed coincidence).E559A Rice/Houston/UCLA/LASL collaboration is proposing to search for Vy -»■ ve appearance. The detector would be modular with 3" thick liquid scintillation planes alternated with x-y drift chambers. The detection reaction is vep -*■ e+n with fast delayed coincidence between a backward going e+ and the forward neutron. The neutron signals its presence by scattering with a proton in an adjacent scintillation plane. The electron equivalent energy deposited by the proton is small, i.e. 0.1 to 0.5 MeV. Figure 7 shows their Monte Carlo simulation for this coincidence measurement.E609A Los Alamos group is planning to place a large pot of liquid scintil­lator in a hole 30 m from the beam stop to search for Vy -* ve appearance. This pot of liquid scintillator is loaded with gadolinium so that the vep -*■ e+n detection is a prompt e+ with a delayed neutron signal via cap­ture by Gd. This produces several gammas totalling about 9 MeV. The capture time is a function of Gd loading. Figure 8 shows their Monte Carlo results on capture time versus Gd loading. A Gd content of 0.5% is favored.51Fig. 7. Monte Carlo simulation of e+n (vep -> e+n) coincidence measurement in E559.40  6 0Time (/is )Fig. 8. Probability of neutron capture as a function of time in a tank of 4200 liters of scintil­lator for various percentages of Gd in E609.—t 4ft N- SFig. 9. Tunnel construction for E645.E645An Ohio State/ANL/Caltech collaboration is proposing to search for ve -*■ ve disappearance and vy ve appearance. They plan to use a modular detector with 1" thick H2O or D2O Cherenkov planes, and 1-1/2" thick x and y proportional drift chamber planes. The detection reactions_are veD -+ e"pp for ve -> ve disappearance, and vep -*■ e+n for Vy -> ve appearance. They would set up two detectors, 5 tons and 15 tons, with the smaller one stationary at 25 m and the larger one moveable up to 60 m. This system would be set up in a tunnel as shown in Fig. 9.LINE D NEUTRINO SOURCES (PROPOSED)A new neutrino facility is proposed for line D at LAMPF. A proton beam of 100 yA will be used to generate V y ' s  from pion decay in flight as well as neutrinos from a beam stop. Several ideas are also being considered to store muons so as to produce higher energy ve 's, e.g.Lobashov bottle, muon storage ring, etc. This facility is designed to make use of the proton storage ring (PSR) now under construction, which will reduce the duty factor to 3.6 x  10“6 for V y ' s  from tt+  decay in flight, and52to 6 x IO-5 for neutrinos from y+ decay at rest. The layout of this facility is shown in Fig. 10. Pion focussing devices, e.g. horn, dipoles, etc., are being considered to enhance the neutrino flux. The neutrino spectrum from tt+  decay in flight, with a bare target, a 30 m decay tunnel, and detector at 50 m is shown in Fig. 11.E638A Los Alamos/Maryland group is proposing to search for Vy -*■ Vy disap­pearance, and Vy -*■ ve appearance using the bare target Vy beam. They pro­pose to begin the experiment before the PSR becomes operational in 1986.A 50 ton modular detector of liquid scintillator and drift chamber planes would be used to detect y“ and the decay e- in delayed coincidence from V y 1 2 C  -*■ y“X, and to detect e" from ve12C -*■ e“X. The detector would be moveable in the 200 m long tunnel shown in Fig. 10.0 100 200 500 FEETS  A*Fig. 10. Layout of proposed neutrino facility in line D at LAMPF.Fig. 11. Neutrino spectrum from a bare target decay in flight source.SUMMARYWithin the next year, the E225 detector will become operational, and the E609 detector will be installed at LAMPF. Within another year, the other detectors may begin installation. We presume that this arsenal of detectors will contribute to our knowledge about neutrinos.REFERENCES1. S.E. Willis et al., Phys. Rev. Lett. 44, 522 (1980); errata, ibid. 45, 1370 (1980).2. P. Nemethy et al., Phys. Rev. D 23^, 262 (1981).3. H.H. Chen and J.F. Lathrop, UCI-Neutrino No. 11 (1975); also, Neutrino175, Balatonfured, Hungary (1975) Vol. 1, p. 92.4. G.A. Brooks, H.H. Chen, and J.F. Lathrop, UCI-Neutrino No. 19 (1977) also, Neutrino '77, Baksan, USSR (1977) Vol. 2, p. 376.5. LAMPF Users Handbook.6. H.H. Chen, J.F. Lathrop, R. Newman, and J.C. Evans, Nucl. Instrum. Methods 160, 393 (1979).7. R.L. Burman (MP, LASL), private communication.8. K.C. Wang and H.H. Chen, IEEE Trans Nucl. Sci. NS28, 405 (1981).9. R.C. Allen, G.A. Brooks and H.H. Chen, IEEE Trans. Nucl. Sci. NS28, 487 (1981).10. LAMPF proposal No. 38 (1971).11. B. Kayser, Neutrino '78, Purdue, USA (1978), p. 979.12. T.W. Donnelly, AIP Conference Proceedings 26_, 454 (1975).13. F. Reines, H.W. Sobel, and E. Pasierb, Phys. Rev. Lett. 4f>, 1307 (1980).14. H.H. Chen, UCI-Neutrino No. 44 (1980).54SURVEY OF NEUTRINO PHYSICSAlfred K. Mann Department of Physics,* University of Pennsylvania Philadelphia, Pennsylvania 19104ABSTRACTA survey of recent advances in neutrino physics is given which is in­tended to illustrate the breadth, and also the unity, of neutrino physics. The emphasis is on experimental data and is two-fold: (i) on data that use the neutrino as a probe of matter and test the unified gauge theory of weak and electromagnetic interactions, and (ii) on data that bear on the properties of the neutrino itself as a fundamental particle.I. INTRODUCTIONThe last decade has seen significant advances in the study of leptons, both in their intrinsic properties and in their interactions with other elementary particles. This is especially true of the study of neutrinos to which improvements in accelerator technology and developments in mas­sive, highly instrumented detectors have contributed importantly. Indeed, in the evolution of the now accepted unified gauge theory of weak and electromagnetic processes, the study of neutrino interactions, particular­ly weak neutral current interactions, played a leading role. It is natu­ral, then, in a workshop on a prospective neutrino and kaon "factory", to assess recent and present progress in neutrino physics, and thereby to establish goals and criteria for the factory.In this talk I have tried to illustrate the breadth, and also the unity, of neutrino physics by discussing experiments that use the neutrino as a probe of other matter and of the properties of the weak interaction, and by mentioning data that bear on the properties of the neutrino itself as a fundamental particle. Section II of the talk is concerned with weak neutral current (WNC) phenomena, Sec. Ill with weak charged currents (WCC), Sec. IV with some intrinsic properties of neutrinos, and, finally, for the purposes of this workshop, Sec. V discusses some present neutrino experi­ments with emphasis on lower-energy neutrino physics at BNL.II. WEAK NEUTRAL CURRENTSA. GeneralOne of the results of the successful unification of weak and electro­magnetic interactions is the establishment of the single parameter of that theory, sin20y, as a new fundamental constant. This is further emphasized by recent attempts to develop grand unified theories in which the standard model of strong, weak and electromagnetic interactions, SU(3)C * SU(2)L x U(l), is embedded in an underlying, simpler gauge group. Here, the idea is that additional symmetries may restrict certain features which are arbitrary in the standard model. One result which is worthy of remark is that, at very large Q2 , the coupling constants of each of the constituent*Research supported in part by Department of Energy, Contract DE-AC02-76-ERO-3071.55interactions in the standard model, when properly arranged, yield a numer­ical value of sin20w which corresponds to the observed value of sin20w when rough allowance for the Q2-dependence is taken into account. Accord­ingly, precise measurements of sin20y in as many WNC phenomena as possible are of primary importance to further development of unified theories.The present status of such measurements is indicated in Table I which is taken directly from the review article by Kim e£ a^.1 One sees that the WNC deep inelastic scattering measurements and also the asymmetry measurement in polarized e + D scattering have yielded relatively precise data. On the other hand, measurements of WNC exclusive processes, partic­ularly the purely leptonic processes, are seen to need significant improvement if they are to constrain the theory as much as is desirable.B. Leptonic WNCInterest in purely leptonic WNC reactions is high because their theoretical interpretation is so direct. Thus the cross sections for Vy(Vy) + e” Vy(Vy) + e“ are given by(1)where, in the Weinberg-Salam model,and, e.g.( 2)(3)Statistically precise measurements of ov and Oy would as a consequence give a very precise determination of sin20^, and one in which many of the possible systematic errors would cancel.The world data on these reactions as of August, 1981 are shown in Table II, which bears out the need for additional experiments.Because of the difficulty in obtaining intense beams of ve and ve, data on the reactions ve (ve) + e” -*■ ve(ve) + e” are even more sparse. Special interest is present in these reactions due to the expected inter­ference between the WNC and WCC amplitudes through the exchange of neutral and charged intermediate vector bosons, respectively. At the moment, the cross section for ve + e" -* ve + e" is determined to be (7.6 ± 2.3) x IO"46 cm2 for Ee < 3 MeV and (1.9 ± 0.5) x IO-46 cm2 for Ee > 3 MeV, using reactor antineutrinos.2 These data do not yet permit clear identification of the interference term since the cross section is dominated by the WCC amplitude. An experiment now in construction at Los Alamos by Chen and his collaborators3 should soon yield improved results.The situation with respect to the couplings gy and g^ is shown in Fig. 1, again taken from Kim et al.,1 which makes clear that general agreement with the Weinberg-Salam model is present but substantial improve­ment is wanted.56Table I. Weak neutral current experimental data taken from Kim ^t al., Ref. 1.ReactionQuantitymeasured Data ± la ReferenceWS theory sin20w = 0.233(1) vN -*• vX Rv 0.307 ± 0.008 Geweniger et j d . , 1979 0.305(2) 0.30 ± 0.021 Mess al., 1979 0.312(3) 0.30 ± 0.04 Wanderer ^  al., 1978 0.326(4) 0.28 ± 0.03 Merritt e£ al., 1978 0.304(5) vN +  vX Rv 0.373 ± 0.025 Geweniger e£ jil., 1979 0.386(6) 0.39 ± 0.024 Mess al., 1979 0.374(7) 0.33 ± 0.09 Wanderer et al., 1978 0.365(8) 0.35 ± 0.11 Merritt £t al., 1978 0.399(9) vN -*■ vX 8L 0.32 ± 0.03 Deden £t^ al., 1979 0.297(10) vN ->-vX 8r 0.04 ± 0.03 Deden ^  al., 1979 0.030(11) vp -*-vX R? 0.52 ± 0.06 Blietschau ^  al., 1979 0.447(12) 0.48 ± 0.17 Harris et a l ., 1977 0.414(13) vp -*■ vX R* 0.42 ± 0.13 Derrick et al., 1978 0.383(14) vn ->-vXPRn/p 1.22 ± 0.35 Marriner, 1977 1.12(15)(16)v11-*-vX PvN -*• vii±XRn/pV*$'■1.06 ± 0.20 0.77 ± 0.14Bell et al., 1979 Kluttig £t al., 19770.9350.84(19)-(17)(18) -(23)vM ■+■ vn-^X vp-»- vp4 /_do/dq21.65 ± 0.331.27 +  °-36 - 0.27See Ref. cKluttig et al., 1977 Roe, 1979Entenberg et al., 1979; Kozanecki, 1978; Strait , 19781.161.01(24)'-(28)(29)(30)(31)Vp + v p vpe - vu edo/dq2o/ESee Ref. c +  1.2a2 4- 0.9 1.8 ± 0.8a1.1 ± 0.6aEntenberg et^ al., 1979; Kozanecki, 1978; StraitArmenise et al., 1979Cnops et al., 1978Faissner et al., 1978, 19781.521.521.52(32)(33)(34) V ee(low E)o/E02.2 ± 1.0a + 1.3a1 01,0 - 0.67.6 ± 2.2bFaissner e£ al., 1978 Blietschau ^t al.. 1976 Reines, Gurr and Sobel, 19761.321.32 6.37(35) "vee(high E) 0 1.86 ± 0.48b Reines, Gurr and Sobel, 1976 1.21(36) -(46) eD -*• eX Asymm. See Ref. d Prescott jit al., 1978, 1979funits of IO”1*2 E^ , (cm2GeV-1).Units of IO"1*6 cm2 .The data include measurements at 5 values of q2 for vp and vp.We fit directly to the 11 measurements at different values of y.57ALLOWED BY V -HADRON +  e-HADRONALLOWED BYves in 2 0 W 0 . 0Table XI. Numbers of observed events from various experiments on Vy(Vy) + e" -*■ Vy(vy) + e” , as of August 1981.e Vy + e~ •» Vy + e~ Vy + e~ -+ vy + e~obs bkgd obs bkgdGGM-PS <1 0.3±0.1 3 0.4±1ACH-PAD-PS 32 21 17 7.4+1.0C0L-BNL-FNAL 11 0.7±0.7GGM-SPS 9 0.4±0.4CHARM-SPS 11 4.5±1.5 72±16 —VPI-MARY-OXF-FNAL 46 12BEBC-SPS <1 0.4+0.2Fig. 1. Situation with res­pect to the leptonic coup­lings gy and gj[, taken from Kim et al., Ref. 1.Table III. Number of events obtained in various experiments on Vy(Vy) + p -*■ Vy(Vy) + p, as of August 1981.+ P ^  + p Vy + P -+ v y + pobs bkgd obs bkgdHPB-BNL 379 134 209 84CIR-BNL 117 15 125 21ACH-PAD-PS 217 155GGM-PS 100 62C. Semileptonlc WNC and WCCThe semileptonic elastic scattering reactions Vy(v^) + p -* vy (vy) + p(i) serve as a probe of the WNC hadronic couplings e^Cu), ej^d), eR(u),e^(d), and (ii) yield values of sin 0^ from measurements of da/dQ ando(vu + p -* vu + p) , ,R. = y «  0.1; 0.3 < Q2 < 0.9 GeV2^ o(vy + n -* \i~ + p)Rrj = + p ^ VP + «  0.2; 0.3 < Q2 < 0.9 GeV2 .^ a(vy + p -> y+ + n)The world data as of August 1981 are given in Table III, and representa­tive differential cross-section measurements11 are shown in Fig. 2. These results are superior to those so far obtained for the lepton reactions because the cross sections are in the ratio of mp/me, but improvements in semileptonic elastic scattering would also provide stringent, model- independent tests of the present theory.It is of interest to note recent improvement in the quality of WCC elastic scattering data. This is shown in Figs. 3 and 4 which summarize results from the 7-foot bubble chamber5 at BNL on vy + D -> p” + p + ps. In Fig. 5 is a summary of world data on M^, the axial vector mass in thedipole expansion of the Q2-dependence of the WCC elastic scattering crosssection.Taken in conjunction with the known value of My, the results in Figs. 3-5 are indicative of a relatively satisfactory understanding of WCC elastic scattering, and of the validity of using WCC rates to normalize58Fig. 2. Measurement by the Harvard- Pennsylvania-Brookhaven group of the differential cross section for vp+vp and vp-vp. The curves show the pre­diction of the WS-GIM model. Plots are from Ref. 4.Fig. 3. Q2-dependence of v^+D y” + p + ps. Plot is from Ref. 5.Fig. 4. Observed energy dependence and calculated cross section for V y + D  y" + p + ps, taken from Ref. 5.1 1 1 1—  I  -r ' f l d . f l N  lTHIS EXP.G6M(PR0PANE)ANL 1 2 ftGGM (FREON)BUDAGOVKUSTOMORKIN-LECOURTOm nt'u1 1 1 ------------ 1---------------1--------------0 .4  0 .6  0 .3  1.0 1.2 1.4 1.6MA (G tV )Fig. 5. Summary of world data on M^, taken from Ref. 5.59the WNC leptonic and semileptonic elastic scattering measurements.In the interest of brevity we omit any discussion of neutrino-induced single-pion production processes. If measured in sufficient detail, these should uniquely determine the I-spin properties of the hadronic weak current. At the moment, the data indicate a mixture of I = 0 and 1 = 1 ,  but definitive quantitative information is lacking.D. Chiral couplingsFor completeness, we show in Table IV, which is reproduced from Ref. 1, a summary of WNC chiral couplings determined from an analysis of the experimental data in Table I, and compared with the predictions of the Weinberg-Salam model, using sin20w = 0.233, and assuming p = M^/m| cos20y = 1. Solved for sin20y, the data yield 0.233 ± 0.009, where we should note that radiative corrections, if made, would reduce that value by about 0.01.Table IV. Summary of WNC chiral couplings from the analysis in Ref. 1 using all data in Table I and assuming p = 1.Experiment W-S(sin20y=O.233)£l (u) 0.339 + 0.033 0.345eL(d) -0.424 + 0.026 -0.423£r (u> -0.179 + 0.019 -0.155eR (d) -0.016 + 0.058 +0.077§V 0.043 + 0.063 -0.0368R -0.545+ 0.056 -0.50P 1.01 + 0.21 1.0E . WNC structure functionsMeasurements of deep inelastic scattering using narrow band neutrino beams have recently produced preliminary data on WNC structure functions. In one plot of Fig. 6 are shown WNC y-distributions for v and v from the CHARM collaboration6 which may be compared with their WCC y-distributions in the adjacent plot. Distri­butions in x and y for v for WNC and WCC scattering obtained by the Columbia- Rutgers-Stevens Institute collaboration7 at BNL are shown in Fig. 7. These•r*Eto.ill.6 0 04 0 0Fig. 6. Distributions in y for v and v for WNC and WCC inelastic scattering from the CHARM collabora­tion at CERN, Ref. 6.Xf- 200CC CHARMprelim.i/ ■-  -W- -N-V '___ 1___ 1 . t .0 0.2 0 4  06y0 8  I60cc NCcoHZUJCVIob)T\1 1 1-------- S a n d  o r  P V - A— - W e i n b e r g -  \  S a l a m  >0.2 0.4 0.6 0.8 1.0rFig. 7. Scaling variable distributions for charged-current events: (a) x distribution, (b) y distribution; scaling-variable distribu­tions for neutral-current events: (a) x distribution, (b) y distribu­tion (the flat V-A prediction is virtually identical to the Weinberg- Salam curve). Data from Ref. also confirm, albeit in a rough way, the Weinberg-Salam-Glashow model.III. WEAK CHARGED CURRENTSA. QPM and QCDThe principal information conveyed by deep inelastic WCC scattering is (i) the remarkable accuracy of the predictions of the quark-parton model (QPM) of the nucleon, and (ii) the indication of definite departures, small but not negligible, from that simplified, scale-invariant model.These departures constitute (with high-energy y-nucleon scattering data) much of the experimental evidence in support of quantum chromodynamics (QCD). We exhibit here both of these aspects of the data.In Figs. 8-11 are shown WCC distributions in Ey, py, 0y, and Ejj forv and v deep inelastic scattering as measured in the wide-band neutrino beam at FNAL by the HPWF collaboration.8 The solid curves are the results of a Monte Carlo calculation that assumes the QPM (and therefore scale invariance), approximate knowledge of the neutrino spectra, and detailed knowledge of the properties of the neutrino detector. The agreement between experiment and theory is seen to be excellent. We show in Fig. 12plots of o /Ev as a function of E^, for v and v, which, to a good61E „  (G e V )Fig. 8. Wide band neutrino energy distributions measured by the HPWF collaboration, Ref. 8.(G e V / c )Fig. 9. Muon momentum distributions measured by HPWF, Ref. 8.8 ^  (m ro d )Fig. 10. Muon angular distribu- Fig. 11. Hadron energy distributionstions measured by HPWF, Ref. 8. measured by HPWF, Ref. 8.NEUTRINO HADRON ENERGY DISTRIBUTIONANTINEUTRINO HADRON ENERGY DISTRIBUTION60 90E m (G e V )62-v,V [G e V ]Fig. 12. World data on v- and v- cross sections.Fig. 13. y-distributions measured by HPWF, Ref. 8.approximation, exhibit scale invariance above Ev «  10 GeV. Similarly, in Fig. 13 are given measured y-distributions for v and v which are compared with QPM predictions that include a small antiquark content (see below) of the nucleon. Again, the agreement between the model and the data is good.In contrast, we show in Fig. 14 the measured distributions in Q2 = 2mpEvxy for v and v, which are compared with the results of the Monte Carlo calculations described above. One sees that the calculated distri­butions which assume scale invariance, i.e., no explicit dependence of thenucleon form factors on Q2 , fail to describe the observed distributions at larger Q2. This is illustrated in another way by the plot of <Q2>/E vs. E in F i g .  15 w h i c h  s h o w s  an evident dependence on E.The dependence of the nucleon form factors on x and Q2 , which is indicated in Figs. 14 and 15, is shown explicitlymCO1-zUJ>UJ;o.o50.02“I— I— I I l l ' l l• a  HPWFR0IE3I0I 0 12' AN IA  SKAT• ■ COHS00 GGM/BEBC X I S ' F N A L  XH EP -ITEP   I i ■ l . ■ ..I— _  * T ^- j  i t - i - i  i  h i JL_Q 2  (G e V 2 )Fig. 14. Q2-distributions measured by HPWF, Ref. 8.10 20 E  (G e V )50 100 200Fig. 15. World data on <Q2>/E v s . E.63Q * ( G e V i )qKFig. 16. Data on F2 (x,Q2) taken from Ref. 8.Fig. 17. Data on xF3(x,Q2) taken from Ref. Figs. 16 and 17. The form factors F2 (x,Q2) and xF3(x,Q2) are seen to depend on both x and Q2 in a relatively complicated way that presents a challenge to thedescriptive power of QCD. The data in Figs. 16 and 17 are from two high statistics experiments,8’9 and represent a combined sample of more than 5 x IO14 deep inelastic events. The agreement between the two experiments is good; substantial improvement in the quality of the data will require very large statistical samples and careful attention to possible systemat ic errors.B. Fractional antiquark momentumThe QPM has succeeded in relating very different scattering pro­cesses. Thus, in Fig. 18 one sees the x-distribution of the fractional sea (anti-) quark momentum as obtained from deep inelastic v(v)-nucleus scattering10*11 and from dimuon production by inelastic p-nucleus scatter­ing.12 Taking into account the uncertainty in higher-order corrections necessary to interpret quantitatively the p-nucleus scattering, the agree­ment on antiquark content between these experiments is striking.Dimuon production by v and v provides the means to evaluate the strange antiquark magnitude and momentum distribution, and to make direct comparison with the valence quark momentum distribution. This is shown in Fig. 19 from the CDHS collaboration at CERN.11 As expected in the QPM, the strange antiquark distribution is peaked at a much lower value of x than is the valence quark distribution.C. Like-sign dimuonsOne possible inadequacy of the theory that bears comment concerns the production of like-sign dimuons by neutrinos. One anticipates that like-sign dimuons will result primarily from WCC-associated charmed64XFig. 18. Fractional sea quark momentum obtained from neutrino- induced dimuon data and proton- induced dimuon data, Refs. 10,11 and 12.particle production. The results of several experiments13 are shown in Fig. 20; the dashed line is a Monte Carlo prediction of associated cc production by gluon bremsstrahlung for py2 > 10 GeV/c. The discrepancy between the theoretical estimate and the data is obvious, but whether this is due to the approximate nature of the calculation or to some other, as yet unrecognized, effect is not clear.Fig. 19. Sea quark and valence quark momentum distributions ob­tained by the CDHS collaboration, Ref. 11.Fig. 20. World data on like-sign dimuon production taken from Ref. 13.IV. INTRINSIC PROPERTIES OF NEUTRINOSA. StatusThe intrinsic properties of neutrinos have been of interest to physicists and astrophysicists for many years. We show in Table V a sum­mary of known limits on the electromagnetic properties of neutrinos, reproduced from a paper by Bernstein eit al. in 1963. It is worth noting65Table V. Summary of the known limits for the electromagnetic interactions of neutrinos. Reproduced from Ref. 14.Property veCharge/e <4 x 10”17 from charge <10”13 from astrophysics,conservation if mVy < 1 keV<10”13 from astrophysics <3 x 10”5 from charge conservation<3 x 10”10 from electron- <3 x 10”5 from pionneutrino scattering production by neutrinosMagnetic moment <10”10 from astrophysics <10”10 from astrophysics,(in Bohr magnetons) if mvy < 1 keV<1.4 x 10“9 from neutrino- <10”8 from pion productionelectron scattering by neutrinosCharge radius <4 x 10”15 from electron- <10”15 from pion production(in cm) neutrino scattering by neutrinos<4 x 10”11* from astro­ <4 x IO”11* from astro­physics physics, if mVy < 1 keVthat a more recent compilation by Beg et al.15 in 1978 does not give limits that are different in any important way from those in Table V.A significant charge radius would lead to a contribution to WNC scat­tering process, e.g., Vy + p -»■ Vy + p. Such an effect is now recognized to be negligible with respect to the observed primitive WNC coupling, al­though it was speculated after the earliest observations of v-induced WNC events that an anomalously large charge radius might be the origin of those events. Continued searches for a non-zero neutrino magnetic moment are on a par in importance with searches for a non-zero neutrino mass.The latter quantity would be overwhelmingly indicated by a non-zero value of the former quantity.B. Structure of the neutrinoIt is of interest to note that a quanti­tative limit on the structure of the neutrino can be obtained from comparison of deep in­elastic neutrino-nucleus scattering with deep inelastic muon-nucleus scattering. The actual comparison is made by searching for differences in the Q2-dependence of the nuc­leon structure function F2(x,Q2) as determ­ined from V y - N  and y-N scattering. This is shown in Fig. 21 where, as expected, the Q2- dependence formed by the two different probes is seen to be very similar. If we write F2(x,Q2)vP-n/F2(x,Q2)1j-n = k(l ± Q2/A2 ) , we find the limit on Av  ^ > 30 GeV2 with 90%Fig. 21. Comparison made in Ref. 16 of the data on F2 (x,Q2) as obtained from Vy-N scattering and from y-N scattering.66confidence, which leads to a limit on the radius at which a departure from a point-like neutrino might obtain of 7 * 10-15 cm. The correspond­ing limits for the charged leptons are several times smaller but we can look forward to improvements in the neutrino limit as future experiments extend the Q2 regime available to experiment.C. Neutrino mass and neutrino oscillationsThe possibility that neutrinos of different types (ve , , vT , ...)may have non-zero masses, and also may have non-zero matrix elements con­necting different types (violation of separate lepton number conservation), has been considered since 1963. These would lead to oscillations of neutrino type. In the last few years preliminary experimental evidence has begun to accumulate, and an ambitious program of searches for neutrino oscillations is under way at reactor and accelerator centers throughout the world. A number of reviews of this subject are available, so that a detailed summary here is unnecessary. We do present in Table VI, however, a list of representative proposed accelerator neutrino oscillation experi­ments that is appropriate to the interests of this workshop. The time scale of these experiments is 2 to 5 years from now because of their complexity.V. PRESENT NEUTRINO EXPERIMENTSA. StatusIt is useful to look at a list of "retired" neutrino detectors which is presented in Table VII. All of them have made substantial contribu­tions to the progress in neutrino physics of the past two decades. In Table VIII is a list of "active" neutrino detectors located at accelera­tors, with their properties and primary interests.B . Example of a detector for moderate energy neutrinosOne of the detectors in Table VIII is located at the Brookhaven AGS, which produces neutrinos of mean energy just above 1 GeV. This detector, the result of a collaboration among physicists from BNL-Brown-KEK-Osaka- Pennsylvania-Stony Brook-Tokyo, is directed primarily toward the reactions shown in Table IX, and, of course, toward precision measurements of sin20y.A schematic representation of the detector is given in Fig. 22 whichincludes an outline of the data acquisition shower magnet system.17 The detector is divided intoL U U N I L n  \  j t •four sections as indicated; the properties of a single section, and the totals for the entire detector, are shown in Table X, which gives an idea of the fine-grained nature of the detector. Figure 23 is intended to emphasize the importance to a neutrino ex­periment of the beam bunch structure at the AGS. All of the timing data in Fig. 23 are obtained with neutrino events. TheFig. 22. Layout of the Brookhaven- B rown-KEK-Os aka-P ennsyIvan ia-S t ony Brook-Tokyo neutrino detector data acquisition system.U N IT1U N IT2U N IT3U N IT4microprocaaiormicroprocessormicroprocataormicroprocataorI boom I------I m on ito r! I CAMACP D P - I t / 3 4  -P O P - IO67Table VI. Representative proposed accelerator neutrino oscillation experiments.Source ProponentsEv/L A2sin2aMode(MeV/m) (eV2)Meson UCI, LASL 40/9 <0.25 (\>p->-Ve)FactoryLASL, Maryland 150/(40-280) 0.050.24(vp-»ve)(Vp + Vp)liq scint+PDT; (50 ton movable proton tgt)OSU, ANL, LSU, CIT 40/(20-250) <0.1 SO.2(vv + ve)(Vp +  Vp)D 2O+PD T ;  (5 ton at Lj +  15 ton at L 2)Rice, Houston, LASL 40/(10-100) <0.05 ( v p - v e)liq scint; 15 tonHighEnergyAcceler­atorCERN-BEBC, Padua, Pisa, Athens, Wise.1 SO.15 <0.75(Vp-*ve)(vy -»-vx)(1/4H2 + 3/4Ne) ; 13.5 ton at 900 m; norm: WCC/WNC; magnetic horn beamCERN-CDHS 1 <0.25<1.25(Vp+Vp)(Vp^-vT)Fe + s c i n  +drift chbr; 280 ton at 100 m,1140 ton at 900 m; norm: collim bare tgt beam, geomFNAL, Columbia, CIT Chicago, Rochester, Rockefeller*50 1 0 1 < A2 < 1 0 3 (Vp -*-Vp)Fe + sc in + chbrs; 100 ton at 740 m, 250 ton at 1080 m; narrow band beamBNL, Brown, KEK, Osaka, Pennsylvania, Stony Brook, Tokyo (INS), UCI1 <0.2<1.0<0-210!< A 2 <300(Vp +  Vp)(Vp -*• vT)(Vp +  ve)liq scint+ prop dr chbr; 80 ton at 120 m,80 ton at 800 m; obs: Vp+n -*• p'+p, v+p v+p; norm: WCC/WNC(Vp-*-Vp)Table VII. Retired or almost retired neutrino detectors at accelerators.Detector Accel Period RemarksCOL-BNL AGS 1962-64 sp ch, scintGarg BC-CERN PS 1963-75 propane; freon7' BC-BNL AGS 1977-80 hyd, deut12' BC-ANL ZGS 1977-78 hyd, deut15' BC-FNAL 400 1974- neon; hydHPWF FNAL 1972-78 sp ch, liq scint,toroidal magCITRRF FNAL 1972-78 toroidal magHPWBNL AGS 1974-78 segmented liq scint (dr ch)CIR AGS 1974-78 sp ch, scintYALE-LA LAMPF ~1976-79 6 ton H 20, D 20, cheren det68Table VIII. On-going active neutrino detectors at accelerators.Detector Accel Period RemarksCDHS CERN-SPS 1976- 0TOT(E); WCC struc fns; Rv> Rv (WNC); v-oscCOL-CIT-CHI-FNAL-Roch-RockFNAL 1978- Fe, scint, chbrs, toroids. NBBCHARM CERN-SPS 1977- WNC struc fns; Vy(Vy)+e -*■ Vp(vp)+e; WBBMarble, scin, prop dr chbrsMITNIF FNAL 1979- Fe (thin), scin, flashersBEBC CERN-SPS 1976- WCC struc fns; Vy+e -*■ vp+e;Garg CERN-SPS 1976- WNC struc fns; multi leptons (charm); v-osc15' BC FNAL 1974- Neon, hyd, TST. WBBUCI LA LAMPF 1981- ve+e -*■ ve+e; v-osc; scin, flashers; Tr-stop bmBBKOPSBT AGS 1981- Vy(vy)+e -*■ Vy(vy)+e Vy(Vy)+P ■+ Vy(Vy)+PWCC, WNC single pion prod; v-osc Liq scint, prop dr chbrs; WBBTable IX. Principal subjects of study of the BNL-Brown-KEK-Osaka- Pennsylvania-Stony Brook-Tokyo neutrino detector.1. Vye" -*■ Vye" and Vye" -*■ Vye" Higgs sector exploration;p “ hfy^/M^ 2  cos20^ = i?(3/day, 300/yr) (1.5/day, 150/yr)2. vpP "*■ vyP and ''pP Vyp Number of Z°; W±(100/day) (50/day) Direct test of e-p universality (with e+e“ -+ p+p“)Direct test of e-q universality hadronic matrix elements3. VyN -*■ VyNir and VyN -*• VyNir(1000/day) (500/day)Isospin structure4. Vyn -*■ u“p and Vyp -*■ p+n Second class currents?5. possibly vee” •+ vee“ and vee" -*■ vee"WCC - WNC interference, and above6. Neutrino oscillations Neutrino mass; separate LNC69Table X. Properties of a single unit.32 Liquid scintillator slabs Active area/slab Thickness/slab No. cell/slabCell sizeWt(liq & acrylic)/slab Tot wt (liq & acrylic) Total pm4.22 m x 4.09 m 7.9 cm 164 -1 m * sile cmEf^ii)5 (along beam) x 25 cm1.35 metric tons 43 metric tons 102431 PDT x-y (double) plane Active area/plane Thickness/plane No. cells/plane Cell size Skin thickness Total cells4.1 m x 4.1 m 7.9 cm54 x 24.1 m x 3.75 cm (along beam) x 7.50 cm 0.5 mm x 43348Totals for expt.Wt (liq & acrylic) Pm (S2212/A)PDT cells Vol172 metric tons4096133924 m x 4 l  x l 3  aEkindE/dxTiming (1) Timing (2)x,y,z,0RangeFig. 23. Beam bunch structure of the AGS exhibited in neutrino events observed in the BNL-Brown-KEK-Osaka- P enns yIvan ia-S tony Brook-Tokyo detector.RF COARSE TIME BSTRIBUTION or OURGEO CURRENT EVENTSE V E N T  T IM E  (/is)correspondence in bunch time of the Vy + p ■+ Vy + p events and the Vy + n->- y" + p events is an important part of the proof that the former are not neutron-indueed.In Fig. 24 is shown output data representing an observed event of the type Vy + n -> y“ + p. The beam bunch structure applied to this event makes clear that the cluster of sparks and energy depositions at the bottom of Fig. 24 are not related in time to the vee at the top. The particle identification capability of the detector is illustrated by Fig. 25, in which the pulse height data for the event in Fig. 24 are repro­duced; the range, total kinetic energy, and dE/dx pattern unambiguously identify the short prong in Fig. 24 as a proton. Similarly, identifica­tion of pions, electrons and photon showers has been demonstrated.This detector is now taking data, and should begin to yield physics results by the summer of 1982.70Fig. 24. Computer print-out of a view (y-z plane) of a neutrino-induced event in the prototype detector (y is in vertical direction, z is in longitudinal direction of the detector, see Fig. 5b). Each number shown is the energy in MeV deposited in a calori­meter cell. Each x is a PDC central wire that has received a charge deposition (magni­tude not shown). Neutrinos are incident from the left.71Fig. 25. Plots of energy deposi­tions AE in the PDC and calorimeter cells along the tracks of the event A shown in Fig. 10. a) for x-PDC, b) for y-PDC, c) for calorimeter cells, and d) comparisons of AE/AZ predicted for a proton and for a pion with data from c). In a) andb) AE is in arbitrary units.VI. SUMMARYThis review has necessarily been sketchy because it was aimed at giving a feel for the broad sweep of neutrino physics rather than a treatment in depth of a limited area. It should be clear that much remains to be done to provide firmer experimental tests and verification of the present, elegant theory of weak and electromagnetic interactions. The intrinsic properties of neutrinos and the validity of separate lepton number conservation present challenges to all who are interested in elementary particle physics. Perhaps your neu­trino factory— when it comes to pass— will respond successfully to these challenges. I hope so.REFERENCES1. J.E. Kim, P. Langacker, M. Levine and H.H. Williams, Rev. Mod. Phys. 53, 211 (1981) .2. F. Reines, H.S. Gurr and H.W. Sobel, Phys. Rev. Lett. ^7, 315 (1976).3. H.H. Chen ej: al., LAMPF experiment 225.4. A. Entenberg et al., Phys. Rev. Lett. 4_2, 1198 (1979).5. N.J. Baker et al., Phys. Rev. D ^3, 2499 (1981).6. M. Jonker et al., quoted in F. Sciulli, Proc. XX Int. Conf. on High Energy Physics (Madison, Wise., 1980) p. 1279.7. C. Baltay et al., Phys. Rev. Lett. 44, 916 (1980).8. S.M. Heagy et al., Phys. Rev. D 23^, 1945 (1981).9. J.G.H. deGroot et al., Z .  Phys. Cl, 143 (1979).10. See Fig. 36 in Ref. 8.11. J. Knobloch et al., quoted in F. Sciulli, Proc. XX Int. Conf. onHigh Energy Physics (Madison, Wise., 1980) p. 1279.12. See, for example, J.E. Pilcher, Proc. 1979 Int. Symp. on Lepton and Photon Interactions (Fermilab, 1979) p. 185.13. M. Jonker et al., CERN preprint EP/81-95, August 1981 (submitted to Phys. Lett.).14. J. Bernstein et al., Phys. Rev. 132, 1227 (1963).15. M.A.B. Beg^t^l., Phys. Rev. D 17_, 1395 (1978).16. A.K. Mann, Phys. Rev. D ^3, 1609 (1981).17. P.L. Connolly and D. Cutts, Proc. of Topical Conf. on the Applicationof Microprocessors to High Energy Physics Experiments, (CERN, Geneva, 1981) .11 16 21 2 6  2 -A X IS  MOD NUMBER72HADRON-NUCLEON INTERACTIONS D.V. BuggQueen Mary College, Mile End Road, London El 4NS, U.K.ABSTRACTExtensive and high quality data on branching ratios of Y* resonances are required to test quantitatively QCD-inspired models of the baryon spectrum. Several specific experimental configurations suited to this are discussed.THE BARYON SPECTRUMThe ground-state SU(3) multiplets are the jP^/* nucleon octet, con­taining N(940), A(1115), E(1185) and 5(1315), and the jP=3'2+ decuplet, con­taining A (1230), E*(1385), 5*(1530) and ft(1685). These are the spin s=V2 and s - ' i  configurations of three quarks with zero angular momentum L. Note that each_contains a E and the octet also contains a A, with the result that the KN baryon spectrum is expected to be more complex than ttN .  _ A 1 s o ,  whereas one can isolate A states in tt+ p ,  the most easily accessible KN channel, namely K~p, is a 1:1 mixture of 1=1 and 0.The spectrum of nucleon resonances is reasonably well established (largely from ttN  elastic scattering) up to about a mass of 2100 MeV/c2.From 1500 to 1700 MeV/c2, there is a band of negative parity states with jP=V2-,3/2_ From 1700 to 1950 MeV/c2, there is a band of positive paritystates with jP=V'2+ to ^2* Ami from 1900 to 2100 MeV/c2, there are several established negative parity states with JP up to V2 . This pattern of alternating parity and steadily increasing JP is characteristic of an L ex­citation spectrum. It is by now firmly established that the group symme­try is SU(6)®0(3), i.e. three spin V2+ quarks combined with angular momen­tum L. The most extensive quantitative model with this group structure is that of Isgur and Karl.1 The predictions of this model are in sufficiently good quantitative agreement with current data that one should nowadays design experiments as specific tests of the model.The first excitation is the [70,L=l]". It lies below 1 GeV/c in uN and KN lab momentum. The spectrum of known levels is shown in Fig. 1. For strangeness S=0 it is com­plete. For S=-l, four states are missing. Pre­dictions of Isgur and Karlare given in Table I, 1/2_____, _ )65Qtogether with tentative '/2-identifications. One of thefirst tasks of experiment SU(3Jsinglets A A_ IQ20is to complete this multi- 3/2~.L5.?° y~ '690 V2 ----plet in S=-l. Unfortunately, y-1405 / —  i670 /   3/z~there is some evidence that '/{ 1780there may be one Di3 reso­nance too many in this mass £ SFig. 1. The [70,1]" multi- plet for S=0 and -1.Table I. Missing members of the [70,l]- multiplet.73JP Prediction of Isgur and Karl ObservationsV A*(1880) -> Ett A (1815)?2 A (1890)?3w E*(1650), octetV E*(1815), octet -* Ett,Attw E*(1810), decuplet E(1925)2 ’3range. Litchfield4 claims the existence of a E(1580), and there is some corroboration.5 The mass range is further complicated by the fact that it overlaps with radial excitations [56,0]+ of the ground state; the experi­mental picture of these excitations in S=~l is still very confused.3 It is also complicated by substantial mixing between members of the octets and the decuplet having the same JP; this mixing is a delicate test of theoretical models such as that of Isgur and Karl.A crucial feature of theirFig. z. N and A members or the low­est positive parity excitations.model is that it predicts the first positive parity excitations will consist of [56,2]+, [56,0]+ ,[70.0]+ , [70,2]+ and [20,l]+ multi­plets; the [56,0]+ and [70,0]+ are radial excitations of the ground state. The status of N* and A ex­citations, which experimentally lie below 1.5 GeV/c, is shown in Fig. 2. The [56,2]+ is almost complete, one[56.0]+ is established, and there are signs of a second. In the strangeness = -1 system a few states are established, but the picture is very incomplete.WHY GO ON?The SU(6)®0(3) character of the spectrum is reasonably well estab­lished, although the symmetry is ob’/iously badly broken in mass (and by mixing of s=^ and 3<^ ). We know the N,A spectrum up to about 1900 MeV/c2. Couldn't we stop there?The current fashion is to try to examine the substructure of hadrons,i.e. quarks and gluons, through experiments at very high energy accelera­tors. To some extent this is novelty, to some extent it is guided by the theoretical notion (asymptotic freedom) that quark interactions become weak and therefore more manageable at high q (although high enough q seems beyond the range of tractable accelerators and cross sections). The first flush of interest in spectroscopy has waned to some extent because experi­ments are hard without major improvements in intensity and quality of beams and complexity of detectors. Ultimately, the spectroscopy of nuc­leons and mesons is a basic fact with which Nature confronts us, and if we understand strong interactions quantitatively this spectroscopy has to be unravelled at least up to L=2 excitations, at which level the essential74qualitative features should all be operative.Present theories of spectroscopy are guided largely by mass values. However, it is well known that energy eigenvalues are readily perturbed by (i) small changes in the potential, (ii) inelastic thresholds, without the basic symmetry group being destroyed. In atoms, the spectrum of the hydro­gen atom is reproduced in Li, Na, etc., but the inner cores of electrons perturb the eigenvalues. Likewise, in the s-d shell in nuclei, one cannot calculate the spectrum of eigenvalues from the NN interaction; an empiri­cal effective interaction is used. In baryon spectroscopy, it is remark­able that many resonances appear at inelastic thresholds (e.g. Nq, Np, Nm, Eq, NA?), and one wonders whether these new channels do not distort the mass spectrum substantially. Hence, if we are to learn anything quantita­tive about the Hamiltonian beyond its approximate symmetry, we need to have a complete picture of wave functions, hence matrix elements, i.e. branching ratios, which relate directly to eigenvectors of the Hamiltonian.A major open question below beam momenta of 2 GeV/c is whether the [70,0]+ , [70,2]+ and [20,l]+ multiplets, which are a crucial prediction of the model of Isgur and Karl, exist. The present evidence for any states belonging to these multiplets is tenuous. An N*(1970), J^=7/2+, is tenta­tively established,6 and this is a candidate for the [70,2]+ ; however, it could be fitted into a [56,4]+ . A knowledge of its branching ratios would be decisive in choosing between the two. Other than this state, there are no good candidates for the missing multiplets. Isgur and Karl have shown that a general feature of these multiplets is that they couple weakly to ttN and KN, so one obviously needs to study other more strongly coupled channels. Nevertheless, it is remarkable and worrying that such extensive multiplets should have escaped detection almost completely. Conversely, there is a quite well-established6 A (1915) with jP=5/2 which can only be fitted into an anomalously low-lying [56,l]-. So it is clear that in the 1-2 GeV/c momentum range we are still ignorant not only of the quantita­tive features of the spectrum (branching ratios), but also its qualitative features.DISPERSION RELATIONSA cornerstone of strong interaction theory is the belief that scatter­ing amplitudes are analytic functions, hence satisfy dispersion relations of the general formIm f(s ')ds 'Re f(s) = Pole terms + i fThis has two importance consequences.Firstly, it halves the number of scattering experiments one has to do. In ttN  and KN scattering, there are two complex amplitudes, spin non-flip and flip. In the absence of analyticity, one would need to do four experi­ments to determine their magnitudes, phase difference, and phase relations between partial waves. Analyticity, in the form of dispersions relations, connects real and imaginary parts of the amplitudes, and plays the role of two experiments. Hence, it is generally sufficient to measure da/dft and P (although other parameters help in special situations); but both are essential.In ttN scattering up to 2 GeV/c we have high quality Tr±p elastic and charge exchange cross sections and polarisations. The quality of the data is illustrated by Cutkosky et al.7 In K^N, the cross-section data are a75factor 3-10 worse and except for K^p elastic scattering the polari­sation data are largely missing. It therefore comes as no surprise tha_t the uncertainties in KN phase shifts are vastly greater than in ttN. This is illustrated in Figs. 3 and 4. In the former, analyses of ttN data by Cutkosky «rt al. and by Hohler jjt a l . ,8 which both make large explicit use of dispersion relations, are in remarkably good agreement, even for S^  i , which is a difficult wave to fix. In Fig. 4, different analyses of KN elastic data show substantial disagree­ments. One jjhould remark that KN phase- shift analyses have not Fig. 3. Comparison of the Hohler ej: ad., (x) and Cutkosky et^  al. (o) Sji partial waves.generally made explicit use of dispersion relations. In­stead, resonances are fitted by Breit-Wigner amplitudes and backgrounds by amplitudes varying slowly (e.g. linearly) with momentum; the Breit- Wigner amplitude is a specific analytic function. This is therefore "poor man's" implic­it use of analyticity; there is scope for improved analysis.The second important con­sequence of dispersion theory is that below the inelasticFig. 4. Argand diagrams for KN S- and P-wave amplitudes. Centre-of-mass energies are marked by bars in GeV at0.1 GeV steps. LBL-MtH-C is from Ref. 9, RL-IC from Ref. 10, UCL from Ref. 11 and RL from Ref. 3.76threshold amplitudes are dictated largely by the pole terms from t and u channels and dispersion integrals over the s channel where Re f(s) and Im f(s) are directly related by unitarity. The pioneering work of Hamilton and collaborators (see, for example, Ref. 12) showed that one can understand quantitatively which waves are attractive and which repulsive in terms of exchange of p , a , N and A . This goes beyond quark models in fitting non-resonant amplitudes quantitatively. Likewise, the work of Hedegaard-Jensen, Nielsen and Oades13 gives a qualitative account of all K+N amplitudes and the more elastic KN amplitudes.IMPORTANT ttN AND KN EXPERIMENTSBefore coming to kaon physics, it helps to review briefly the extent of ttN data. There are extensive data onttN -> ttN (o ,P)-*■ ttttN ( a  only)-> A°K° (a,P,R)-*■ E K (a ,P)-»■ nN (a ,P)-> yN (a,P and data with polarised beam and target) .Although AK cross sections are small, the data have been valuable (a) for locating low spin resonances close to threshold, (b) in fixing mixing between multiplets.It is conspicuous that the missing data are P (irN^ imrN) , which would pin down the dominant inelastic decay modes Air ,  pN and aN. An important issue it would help to resolve is the existence of the Nj'7(1970) and A35(1915). This experiment could be done today at an accelerator likeSATURNE. Suppose, for example, one wished to bin data at one beam momentum into 20 mass bins and 20 angles with statistics of ±5% per bin; allowing a target polarisation of 70% and a factor 2 for back­ground, one needs 6><105 triggers/momentum at say 50 momenta. Although a large experiment, it is within the realms of present data processing. One envisages an omega- type detector, sketched in Fig. 5, to catch all final state particles inandIT — Ptt" pI T - p i T 0ir~mr+Fig. 5. Outline of a general purpose omega-type Assuming a detection detector capable of detecting y and n, hence mea- efficiency of 0.25 for suring ttN  and KN inelastic reactions. neutrals and a77conservative geometrical acceptance of 0.25, a 10 cm target and a total inelastic cross section of 10 mb, one gets the required statistics in 8 h/momentum with a beam of 4x105/sec and an event rate of 20 events/sec.(The feasibility of this class of experiment is being demonstrated at TRIUMF by an experiment on pp-*pnTr+ using a conventional polarised target and consequently reduced geometrical acceptance.)Turning now to KN physics, it is clear that there is a role for such an "electronic polarised bubble chamber" to improve current data onK~p -> A°tt° (1=1)* ?_*+ \ (Mixed 1=1 and 1=0)-*■ 1 T\ J-> K”pTr°-* K”mr+■+ K0pTt“-»■ Att+it- (e.g. E*(1385)tt) .Present bubble chamber data, after 15 years of effort, amount to typically1000 events/mb/25 MeV/c. One needs ~100 times these statistics (cf. ttN elastic) to adequately tackle inelastic decay channels of Y*s. Decays of A0 and E+ analyse their polarisations:a 1  +  otPcos<j> ,where <f> is the angle between normals to production and decay planes, anda=23 for A°,_l for E+ , 0 for E“. There are presently no polarisation dataon E“ir+ and KNtt channels. Consequently there are ambiguities in separa­tion of Ett channels into 1=1 and 0; this is a serious difficulty in identi­fying E* and A* resonances at present.With such a device one could also make a serious attack on E* resonances in reactions likeK“p -*■ K+5*° .Since cross sections are small, higher rates will be required, and it is highly desirable to identify the K+ by a TPC-type of detector sampling its ionisation dE/dx.Both experiments demand K“ beam intensities somewhat higher than are currently available (2><101+-2xl05/sec maximum at present) and cleaner beams (typically K:ir=l:10 at present).In the elastic KN channels, there are quite good data on a(K“p>K_p), although not of the quality of irN. The Yale-BNL-Kyoto group11* has pro­duced good P(K_p->K"p) data from 650 to 1070 MeV/c, and the QMC-Rutherford group16 likewise from 955 to 1272 MeV/c. The LBL-Mount Holyoke group16 has made high quality measurements of a(K~p*K°n) from 515 to 956 MeV/c. At these low momenta, bubble chamber data on cr(K-n-*-K-n) are reasonable instatistics, although marginal in absolute normalisation, and there aresimilar counter data from 610 to 940 MeV/c by the Rutherford-Birmingham collaboration17; above 1 GeV/c, the CERN-Caen counter experiment18 at CERN has produced good quality cr(K"n*K_n) data. It is now clear that the crucial missing elements are:(i) P(K"p -> K°n) _ „P(K-n - K-n) at a11 no,nenta ’(ii) o(K”p -*■ K°n) above 1 GeV/c ,78(although when these are mea­sured, inadequacies in the quality of cross sections may become apparent). The impact which such polarisation data would have from 500 to 1000 MeV/c may be judged from the spread of phase-shift predic­tions illustrated in Fig. 6.The polarisation measurements are feasible using convention­al polarised targets. A use­ful comparison can be made with an experiment at the Rutherford Laboratory19*20 onP(K+n -v K°p)P(K+n -*■ K+n) .Experience there indicates that one should preferably identify K° as by their in­teractions in a neutral detec­tor of the "neutron counter" type. Scaling cross sections and detection efficiencies from that experiment, one concludes that to measure P to ±5% in each of say 20 angular bins in a reasonable time (3 days/momentum) requires a K" beam of (0.5-l)xl06/sec. This is roughly a factor 5-20 greater than is available presently, putting such an experi­ment in the province of a K factory.A channel of great interest isK£p -* K§p ,whose amplitude |f(K+ ,I=l) + f(K+ ,I=0) - 2f(K_,I=l)}. Because of the interference between S=±l amplitudes it contains delicate information on relative amplitudes and phases of KN and KN, particularly the elusive S=+1,I=0 and S=-1,1=1 amplitudes. Bubble chambers have been used21”23 to study cross sections over limited momentum ranges, but there is scope for vastly improved statistics, systematics and also polarisation data. In a counter experiment, good k£ time-of-flight information would be a vital asset. Another reaction valuable in finding 1=1 amplitudes isK^p -*■ £+tt° (pure 1=1) .K+NK+p elastic data of adequate quality exist. Inelastic reactions and o(K+it>K+n; K+ir+K°p) have been studied extensively in bubble chambers up to 1.5 GeV/c by Bland et^  al.29 and the Bologna-Glasgow-Rome-Trieste collabora­tion.25 The quality of recent QMC-RL data on P(K+ir*-K°p) and P(K+rt*K+n) is illustrated in Figs. 7 and 8. Both leave something to be desired in statistics, but are adequate to rule out the existence of a Z* resonance in Pq i. To give a feeling for the difficulty of the measurements, they were obtained using 1012 protons/sec, a 12 cm longx 3.5 cm diameter polar­ised target (polarisation c*32%) and about 2 weeks running/momentum. TheFig. 6. Predictions of the LBL-Mount Holyoke phase-shift solution9 (full lines), the RL-IC solution10 (dashed) and the UCL solution11 (dotted).791976 phase-shift solutions of B. Martin26 are shown in Fig. 9; these solu­tions (either by luck or good judgement) are an excellent fit to the new polarisation data, with the result that the most recent phase shifts are very little different, except for some changes in small P and D waves. It is interesting that the P0i am­plitude stays almost completely elastic, climbs to a maximum of ~60° in phase and then falls again. The work of Hedegaard- Jensen et al.13 identifies this KN partial wave as the one where the long-range forces produce most attraction at low momenta. The dispersion inte­grals favour the amplitude resonating. The fact that it does not indicates strong short-range repulsion in K+N.Arndt et al.27 claim that the Pi 3 amplitude resonates atFig. 9. Argand diagrams for B. Martin's 1976 KN amplitudes.801780 MeV/c2. However, as in NN, it is difficult to distinguish whether or not a resonance is superimposed on the strong inelastic threshold. If there were a resonance, one would expect to see a rapid phase variation in the dominant inelastic channel K+p-»-KA. Analysis of a(K+p->KA) by Giacomelli et al.25 yields three solutions, but none displays a large rapid phase variation in the relevant amplitude, PP3. It therefore seems unlikely that there is a resonance. However, to clinch the issue, one needs data on P(K+p->-KA), which is sensitive to phases; this would be a straightforward experiment in the "electronic polarised bubble chamber" which I have advo­cated for K_p inelastic studies.Below the inelastic threshold (700 MeV/c), K+N amplitudes are of interest (a) as a probe of nuclear structure (in view of the ready pene­tration of K+ into nuclei), (b) for quantitative information on long-range forces. What is required are accurate data on a and P in K+p->-K+p, K+nr*K+n and K+ir*K°p from (say) 400 to 700 MeV/c. The K+p elastic channel is within reach of present K+ beams; the other two reactions require the flux of a K factory.BEAMSIt is not only extra beam intensity one requires, but beam quality.At present accelerators one has to compromise quality for intensities of lO^^xlO5 KVsec. At a K factory, one will require beams up to 2 GeV/c with an intensity 105-106/sec (or higher for studying E*s) and ir:K<l:l.It is general experience that separated beams of reasonable quality can cover only a factor 2 in momentum range, so one should foresee at least 3 ranges of K momentum, e.g. 400-800, 700-1400, 1200-2400 MeV/c.For experiments, good time-of-flight information (<0.5 nsec) would be a tremendous asset. I believe it would be of interest to investigate the possibility of making RF separated beams using the good bunch-length potentially available at a K factory.SUMMARYA short-list of attractive experiments which would advance hadron spectroscopy by a large qualitative and quantitative step is as follows:1) a ,P(K^N-^inelastic channels) using an "electronic bubble chamber", with beam quality K:ir<l:l characteristic of a K factory; beam intensities (l-4)*105/sec• With the same device, one could profitably measure P(-rrN->-mrN)_at present accelerators.2) P(K“p->-K0n), P(K-nr>K-n) from 400 to 2000 MeV/c, and a(K“p-»-K0n) from 1000-2000 MeV/c. Beam intensities of (0.5-l)xl06/sec are required. With the same equipment, one could profitably redo K+N physics from 400-700 MeV/c with much greater precision.3) o,P(K2P^-K°p; K2p-*-£+TT°); good time of flight essential.4) K”p->-K+E*, identifying the K+ in the trigger; beam intensity >106/sec.In addition, it is of the greatest interest to devise specific experi­ments to test the model of Isgur and Karl. For example, their model pre­dicts the existence of [70,0]+, [70,2]+ and [20,l]+ multiplets with low branching ratios to elastic channels. One should seek members of these multiplets in cascades where they are predicted to be strongly coupled,81^ JLe.g. K“p prominent known A or Z+ir + predicted multiplet state Zir ,Air .REFERENCES1. N. Isgur and G. Karl, Phys. Rev. D 18, 4187 (1978); ibid. D 19, 2653(1979); ibid. D 20, 1191 (1979); ibid. D 21, 1868 (1980).2. P.N. Hansen et al., in Baryon '76 Conference (Oxford) Proceedings, p. 275.3. G.P. Gopal, Rutherford preprint RL-80-045.4. P.J. Litchfield, Phys. Lett. 51B, 509 (1974).5. W. Lockman et^  al^ . , Saclay preprint D.Ph.H.E. 78-01.6. R.E. Cutkosky et: al. , Phys. Rev. D 20_, 2839 (1979).7. R.E. Cutkosky jet al., Phys. Rev. D 2Q, 2804 (1979).8. G. Hohler ejt al., Handbook of Pion-Nucleon Scattering, Physik Daten Vol. 12-1.9. M. Alston-Garnjost et al., Phys. Rev. D 18, 182 (1978).10. G.P. Gopal et al., Nucl. Phys. B119, 362 (1977).11. B.R. Martin et^  al., Nucl. Phys. B126, 266 and 285 (1977); ibid. B127,349 (1977).12. A. Donnachie, J. Hamilton and A.T. Lea, Phys. Rev. 135, B515 (1964).13. N. Hedegaard-Jensen, H. Nielsen and G.C. Oades, Phys. Lett. 46B, 385(1973).14. R.D. Ehrlich jejt al. , Phys. Lett. 7IB, 455 (1977).15. H.C. Bryant et al., Nucl. Phys. B168, 207 (1980).16. M. Alston-Garnjost et^  al., Phys. Rev. D _17^  2226 (1978).17. U. Adams et al., Nucl. Phys. B87, 41 (1975).18. Y. Declais et al., CERN report 77-16 (1977).19. A.W. Robertson et al., Phys. Lett. 91B, 465 (1980).20. S.J. Watts et al., Phys. Lett. 95B, 323 (1980).21. W. Cameron et al♦, Nucl. Phys. B132, 197 (1978).22. A. Engler et al., Phys. Rev. D 1^ 8, 3061 (1978).23. M.J. Corden et^  al., Nucl. Phys. B155, 13 (1979).24. R.W. Bland jet al., Nucl. Phys. B18, 537 (1970).25. G. Giacomelli et al., Nucl. Phys. B38, 365 (1972).26. B.R. Martin, Nucl. Phys. B94, 413 (1975).27. R.A. Arndt, L.D. Roper and P.H. Steinberg, Phys. Rev. D 18^ , 3283 (1978).82SOFT QCD : LIGHT QUARK PHYSICS WITH CHROMODYNAMICSNathan Isgur Department of Physics, University of Toronto,Toronto, Canada M5S 1A7ABSTRACTThe addition of dynamical ingredients suggested by QCD dramatically improves the ability of quark models to describe soft hadronic phenomena. This approach is discussed in terms of a particularly simple non-relativi9- tic potential model which has been used to study the spectroscopy, decays, and static properties of baryons and mesons. The application of the model to such QCD exotica as multiquark states and glueballs is also mentioned.In addition, an attempt is made to at least partially rationalise the success of the model in terms of more fundamental physics. In the conclu­ding section some of the outstanding problems of soft hadron dynamics are listed, and the role that a high intensity accelerator operating in the resonance region could play in resolving them is briefly discussed.I. INTRODUCTION TO THE MODELA. Why potential models? _  _The successes of quarkonium models for the cc and bb systems, based on a non-relativistic potential model with flavour and spin-independent confinement and one-gluon exchange, at least raise the question of where, as a function of quark mass, such models become useless. The models I will discuss here are, in response to this question, based on an optimis­tic extension of the physics expected from QCD for heavy quark systems into the light quark domain. We shall see that the models not only pro­vide a useful framework within which to describe the physics of such sys­tems, but moreover that this extension has, at least at some level, been successful. The reasons for this success are only partly understood; a possible beginning for an interpretation is given below.While there are many possible variants, I will concentrate on the version of such models that I know best.1-3 It has three main ingredients: confinement, "point-like" constituent quarks, and one-gluon exchange.B . How do potentials confine colour?It is non-trivial to construct a potential which will, for example, confine qqq but not qq. One solution14 is to assume — based on a colour electric flux tube mechanism for confinement— a colour-dependent two-body potential between quarks i and j of the formVij(?ij) = -V(ri:j) ^  (1)with V(r-£j) a flavour and spin independent confining potential and with the prescription that antiquark potentials follow by the replacement t + t c = ( - t*). The resulting model allows only colour singlet hadrons to exist,1 but has the property that while the confinement of qq and qqq is automatic, the existence of more complicated colour singlet bound states (like qqqq) becomes a dynamical issue. The model is also very economical in that it relates the physics of baryons, mesons, and multiquark systems; this feature will be discussed below.83C . What are the constituent quarks?The quarks of the model are not the current quarks of the QCD Lagrangian, but rather a set of "dressed" constituent quarks appropriate to the distance scale of light hadrons. These quarks (which are assumed to be approximately point-like) have masses which are (in part by theirnature and in part because they are at this stage also probably reposi­tories of some of our ignorance about the potential, relativistic correc­tions, etc.) ill-known, but the valuesmu ~  ny ci 0.33 GeV (2)ny - mu ^  6 MeV (3)ms =* 0.55 GeV (4)mc ^  1. 75 GeV (5)etc. are typical. These masses play a crucial role in the model because their differences are the principal origin of flavour symmetry breaking. Note that if we assume that the quarks in a proton are in a Gaussian wave function with the proton's observed charge radius, then with these masses p2/2m 100 MeV so that these light quark models are probably not hope­lessly relativistic.D. Where are the gluons?The last principal ingredient of the model is one-gluon exchange.The most important effects of this type are due to colour hyperfine (magnetic dipole-magnetic dipole) interactions which in lowest order in as are given bywhere(6)(7)The first term of Hftyp, called the contact term, is, in electromagnetism, responsible for the 21 centimetre line of hydrogen; the second (tensor) term is the usual interaction of a magnetic dipole with a magnetic dipole field. The most important characteristics of Hftyp are: 1) it is short range in Sj[*Sj, 2) it gives a fixed relation (8ir/3) between the strengths of the contact and tensor terms, 3) it has a strength inversely proportion­al to the product of the quark masses, and 4) it violates SU(6) and in particular automatically gives mp>mir and m^m^.One-gluon exchange also gives rise to spin-orbit interactions from the interaction of a moving quark colour magnetic moment with colour elec­tric fields. As in the case of electromagnetism, this effect tends to be masked by Thomas precession (the relativistic precession of an accelerated spin), but in this case the suppression of spin-orbit effects is (in the case of q"q with mq>>mq) by a factor of (l-^-f) where the and the "f"come from Thomas precession in the Coulomb-like and confinement potentials, respectively. In the light quark hadrons, the quark wave function overlaps very strongly with the confinement region so that f is very large and spin-orbit effects are suppressed.584Finally, one-gluon exchange gives rise to a variety of spin-indepen­dent effects which can normally be absorbed into the unknown confinement potential. Most prominent among these is, of course, the Coulomb-like 1/r potential itself.A. Why baryons first?We begin our discussion of the model with the qqq baryon sector even though the qq meson sector is simpler to treat theoretically. There are several reasons for doing this; probably the most important of these is that the baryons are much better known experimentally than the correspond­ing mesons (a consequence of their accessibility as s-channel resonances). Not only are more resonances known, but their masses and widths are better known and there is a wealth of information on the (signed) decay ampli­tudes. Specifically, the P-wave mesons remain very poorly known (think of the Ai and the e), while all seven expected S=0 P-wave baryons are known and have reasonably well measured amplitudes for both electromagne­tic and strong channels (typically 5 to 10 amplitudes per resonance).Aside from their being more extensively known, baryons probably have other advantages in practice. For one thing, the quarks in a baryon appear to be somewhat more non-relativistic than those in a meson, making their treatment more reliable. It is also possible that three bodies are suffi­cient to make the effective potential seen by a quark in a baryon signifi­cantly "smoother" than in a meson, thereby making baryons less sensitive to precise knowledge of the potentials. Finally, baryons do not have the isoscalar mixing problem (to be described below) which, while interesting, renders 1=0 meson data unreliable for spectroscopic studies and leaves very few mesons indeed to compare with a potential model.B . What is the model for baryons and its solution?The application of the model to baryons is quite straightforward in its simplest form.6*7 Building on the pre-QCD analyses8-1® (which were on their own terms already very successful) we take the simple Hamiltonianand treating H^yp and the anharmonicity U as perturbations. Note that V here contains both the "true" confinement potential and pieces of the one- gluon exchange potential (so that U may contain 1/r terms, linear terms, etc.); also note that spin-orbit effects have been completely dropped.We have already mentioned that Thomas precession is expected to make spin- orbit effects smaller, but the adequacy of completely neglecting them in baryons is not well understood. Evidence from mesons, where the suppres­sion is more easily studied, does, however, tend to support this approach.JThe approximate solution of this model Hamiltonian is simple. In the harmonic limit with mi=m2=m and n^Hm' (the most general case required for u, d, and s quarks in the approximation mu=md),II. BARYONS FIRST3 2H ■ E  (mi + w > + E  ( v W + H & > )i=l i<i( 8)and solve it approximately by settingV1^ = j  k rfj + U(rij) (9)+ 1  k(P2+i2) (10)85-p-A mode structure SU(6) mode structureLP(m > m) S=-l(m '< m) S— 2(m'=m)S=0,-32+ ,0+  ------2+ ,l+ ,0+  ------2+ ,0+ ------PPpX-----  XXXXXpPP[20,1+][70,2+][56,2+][70,0+][56,0+]1"  ----------- P X [70,1-]1" ---- -------------  X P0+ ---- -----  1 1 [56,0+]Fig. 1. The unperturbed solutions to the harmonic confinement problem (with arbitrary scales set to give the same spacing in each sector).where ,-* 1 .P = /2 (rl'r2) » C11)t = (r1+r2-2r3) (12)andmp = m (13)3mm '=  2 ^ 7  ( 1 4 )so that the unperturbed spectra with up to two units of excitation are those of Fig. 1. One interesting— and important— feature is that the solutions of the confinement problem maximally violate SU(6) in excited baryons.5 For example, the p-A basis L,P=2+ eigenfunction p+ is a 45° mix­ture of the [56,2+ ] wave function 1^2(p++A+) and the [70,2+ ] wave function ]//2(p+-A+) of SU(6). Clearly, to the extent that this phenomenon is im­portant, an SU(6) [or even SU(3)] analysis of excited baryons will fail.We next take these states and per­turb them with the anharmonic term U.It turns out to be unnecessary to actu­ally specify U since one can show that in first order every U gives the same pattern,11 shown in Fig. 2. One can therefore take the parameters ft and A of this figure as describing the poten­tial; the phenomenologically requiredsign of A is, however, consistent with the expected existence of the -1/r an- harmonicity. To deal with the case m ^ m p , the U-perturbed A excitations are scaled by a factor (mp/mx)1^ 2 appropri­ate to the harmonic limit.The next step in the approximate solution of (8) is to turn on the hyper- fine perturbations. These interactions are of crucial importance: they create huge spectroscopic splittings and veryFig. 2. The positions of the SU(3)-symmetric super-multiplets under the influence of an arbi­trary anharmonic perturbation.86strong mixings that destroy almost all vestiges of SU(6) symmetry (except in the ground states).The final step in the solution is the simplest: one takes the sectors of the Hamiltonian of fixed flavour and and diagonalises the resulting matrices.Fig. 3. (a) Photon coupling in the single quark emission model, (b) Meson coupling in the single quark emis­sion model.C . How can the baryon model be compared to experiment?There are two crucial elements in the comparison of a model like this with experiment: one is to compare with spectroscopic evidence and the other is to check, via an analysis of decay amplitudes, the predicted in­ternal structure of the eigenstates. The former check is relatively sim­ple; the latter requires the construction of a decay model. We have usedfor this decay model12 a slightly generalised form of the single quark emission model13 that has much in common with more algebraic approaches.14 It is based on the "elementary" emission processes shown in Fig. 3.As one example of the ways in which a decay analysis can reveal the internal structure of a state, consider the coupling of a uds staj e^ with some excitation in the variable p to the KN channel. As shown in Fig. 4, since the (ud) spectator pair remains excited, it cannot overlap with a nucleonic (ud) pair; the amplitude for this process is therefore zero and the model pre­dicts that such states should not be seen in KN partial wave analyses.6The full comparison of the baryon model to experiment thus involves comparing not only to an observed spectrum, but also comparing against hundreds of measured decay amplitudes. The flavour of this comparison— but not its extent —  is reflected in Figs. 5(a) to 5(d) and in TableI. The figures show a comparison between observed baryons and those predicted to be observable in S=0 and -1 partial wave analyses. (The ground state baryons are not shown since their agree­ment is to within 10 MeV for all states.) The table gives the full comparison between predicted and measured decay amplitudes for just two of the observed states. The model is clearly crude and of limited numerical accuracy— for a few of these hundreds of amplitudes it seems to simply fail—  but it appears nevertheless to have captured the principal features of the physics of baryons.In particular, the ordering of the multi­plets appears to be dominated by a simple anhar­monic term, with the p -X  splitting effect playing a crucial role in S=-l and -2 (consider, e.g., the A5/2~ - E5/2~ splitting in the P-waves) . Within a given mode, the contact part of the hyperfine interaction produces spin splittings that arecomparable to orbital splittings; these forces in turn cause large mixingsu d d d sFig. 4. The decoupling of Y*'s with p excita­tion from the NK chan­nel.87Fig. b. (a; The pre­dicted S=0 negative parity baryons compared to experiment; the re­gions in which the masses of the reso­nances probably lie are denoted by shaded boxes.(b) The predicted S=0 positive parity baryons compared to experiment; states that are predic­ted to decouple from ttN are shown as stubs.(c) As in 5(a) for the S=-l negative parity baryons; states that are predicted_to de­couple from NK are shown as stubs.(d) As in 5(b) for S=-l positive parity baryons; states predicted to de­couple from NK are shown as stubs.88Table I. The decay amplitudes of Sll(1535) and Sll(1650).theorySll(1535)experiment theorySll(1650)experimentNrr 5 8±3 9 9+2Nn + 5 + 9±2 - 2 - 2±1IK no no - 2 ' 2±1AK no no - 3 - 4±1Air - 2 (-) 1±1 - 8 - 4±2YP +145 + 80±20 +90 +50±15Yn -120 -110±35 -35 -45±25between SU(6) multiplets like [56,2+ ] and [70,2+ ]. Finally, in certain key places the tensor force produces strong S=l/2 -«-»■ S=3/2 mixings: the amplitudes of Table I would, for example, be completely wrong were it not for tensor forces.The net effect of the model is to resolve many old problems with the quark model of baryons. Perhaps the most crucial of these is that the violent SU(6) breaking of the model has the effect, as seen from Figs. 5, of decoupling large numbers of predicted resonances from s-channel phase- shift analyses, thereby resolving the problem of the "missing baryon resonances".12D. What else can it do?This simple baryon model has also had success in other areas which we will briefly mention:Baryon isomultiplet splittings15: After the model succeeds in making the S=0 to S=-l transition (e.g., uuu+uus), it is natural to let it make the transitions through an isospin multiplet (e.g., uuu-*- uud->- ddu->- ddd) . With ny-mu ^ 6  MeV, but no other new parameters, the model gives the iso­multiplet splittings of Table II.Configuration mixing in the nucleon15*17: The hyperfine interaction also has the effect of distorting the nucleonic wave function: it pushes the two parallel spin quarks toward the periphery and pulls the anti­parallel spin quark into the centre of the nucleon (i.e., it mixes [70,0+] into the pure [56,0+ ] nucleon). This has many observable effects includ­ing: a) it gives the neutron a charge radius,15>17_ b) it leads to viola­tions of the Moorehouse selection rules17 A^/2(N*5/2 "+Ny )=a5/2 (N*5^  -+Ny)=0,Table II. Baryon isomultiplet splittings.difference theory(MeV) experiment(MeV)p-n -1.3 -1.3I+-I° -3.3 -3.1±0.1E"-I° +4.9 +4.910.1S--S0 +6.8 +6.4+0.6A++-A° -3.0 -2.610.4A++-A“ -6.9 -5.913.1£*+_£*" -5.8 -5.1+0.7I*+-I*° +3.7 +5.412.6„*o +3.&1+3.210.6and c) i_t leads to violations of the Faiman-Plane selection rule17 A(A5/2“->NK)=0. The predicted effects are in each case in agreement with experiment.Baryon magnetic moments: The constituent quark masses of Sec. I lead, via their assumed Dirac magnetic moments [compare to Eq. (6) and (7)], to values for the baryon magnetic moments in good (though not per­fect) agreement with the observed values.18Charmed baryons: The model may easily be extended to the charmed18 and charmed-strange baryons.20 The predicted C=l, S=0 ground states seem to be in accord with experiment; there is as yet no information on other sectors. One interesting prediction of the model, however, is that the p-A and ZCV2+ ~^cV2+ splittings will have become sufficiently large to make the lowest-lying orbital excitation Aj.^ stable (or nearly stable) against strong decay.III. MESONS, TOOA. What's new in mesons?The mesons have several new features beyond the change from qqq to qq constituents. One is that all colour factors in the Hamiltonian change from 2/3 to 4/3.21 There are many consequences of this stronger colour coupling: for example, the p-ir splitting is predicted (and observed) to be about twice the A-N splitting. A low pion mass is thus natural in this model and the naive relation m(meson)^2/3 m(baryon) is satisfied by the hyperfine-unperturbed masses: (lMmff+lMmp) ^  2/3(l/2mN+l/2m^) . Mesons can, in addition to checking meson-baryon connections, play a role all on their own in checking various assumptions of the model. Since the two- body problem is easily solved numerically, mesons can provide explicit information on the potential V(r) as well as checks on phenomena like the (near) cancellation of spin-orbit effects via Thomas precession.5 There is already evidence from the cc system for the efficacy of Thomas preces­sion in reducing the strength of the spin-orbit interaction to give the observed x(2++)-x(l++)-x(0++) spacings;5 we shall see below that there may be additional evidence for this mechanism in light mesons.B. What is the model for mesons and its solution?For mesons we take the same Hamiltonian as for baryons, except that spin-orbit terms are shown explicitly, colour factors are changed, and qq annihilation may now occur, so that22H - S 7  +  S 7 + V l 2  +  H £ y p  +  H -  +  H A  < 1 5 >where the potentials are all twice as large as in baryons, where the spin-orbit interaction Hg£ is given byHso = Hs o (CM) + Hs o (TP) • (16)(CM stands for "colour magnetic" and TP for "Thomas precession") where(17)90Hso(TP) "J_ dV12 2r dr (18)and where is the annihilation interaction of Fig. 6 which must be tacked on to any model of in principle calculable, but in practice it requires the introduction of a new parameter A(nJP<") for each meson multiplet. This amplitude causes mixing between the uu, dd, and s¥ sectors so that after H-H^is used to calculate the masses of the excitations with PP Aquantum numbers nJ in these sectors, H creates a mix­ing matrix of the form (we neglect SU(3) breaking and radial excitations here for simplicity)M(nJPCn ._Am(dd)+AA(19) Fig. 6. The ori­gin of the anni­hilation term via gluon inter­mediate states.On diagonalisation this matrix gives one eigenvalue (assuming also mu=md for simplicity) mx=j ,l3=o=muu1= md"d=mud=ind"u anc* two 1=0 eigenvectors and eigenvaluesthat depend on A. Phenomenologically, A(nJ *0. is normally small (corre­sponding to nearly "ideal" mixing to ]^2(uu+dd) and ss, and leading to a nonet with one isoscalar mass just above (below) mj=j if 0(nJ^>(-') is just below (above) Qideal —  35°), though in the pseudoscalar nonet A is very large and leads to nearly "perfect" mixing23 to the statesn(n') = j ?/2 1/2(uu+dd)+ ss ]• ( 20)Fig. 7. A fit to the 1=1 meson spec­trum (preliminary).and to 0p ^ 35°-45° —  -10° . While this understanding of 1=0 mesons is at least partially satisfactory, it makes 1=0 mesons much less use­ful for spectroscopic analyses and makes it clear that it is necessary to focus on the limited number of established 1=1 and 1/2 states.The exact solutions of the meson problem (for 1^0) are most readily obtained by numerical in­tegration in a given (J,L,S) sec­tor of the Hamiltonian; tensor mix-O Oing (e.g., between Dj and Si) and spin-orbit mixing for mi^m2 can then be treated perturbatively in a (rapidly converging) nearby neighbour mixing expansion. A candidate fit to the 1=1 spectrum is shown in Fig. 7; work is inr \ rprogress on this problem and our final solution (which may look very different from this early one!) will be reported once91we have completed a decay analysis of mesons along the lines of the bary­on analysis reported on the previous page.C . What else can it do?As with the baryon model, the meson model has had success in other areas:Transition magnetic moments: The constituent masses and model wavefunctions lead (with a simple ansatz for dealing with relativistic ambi­guities) to meson magnetic dipole decay rates in quite good (though not perfect) agreement with experiment.26Annihilation decays: Decays like Tr->yv, p+e+e-, and Tr0-vyY proceed through qq annihilation and so are sensitive to ^(0), the qq wave func­tion at zero relative coordinate. These processes (once again with a simple ansatz for dealing with relativistic ambiguities) are in reason­able accord with experiment.Charmed mesons: The dominant physical effects in light mesons remain apparent in charmed mesons. For example, the splittings p-ir, K*-K, and D -D are in roughly the ratios l:m<j/ms :m(j/mc as expected from (7).Isospin violation: As with the baryons, the model can be applied to the breaking of isospin symmetry.15 In addition to ordering the observed isomultiplet mass differences, the model predicts dramatic violations of isospin symmetry in certain hadronic decays.27IV. COMMENTS ON QCD EXOTICAA. Do multiquark states exist?It is absolutely certain that multiquark states exist: consider the deuteron, or to be more extreme, a uranium nucleus. This comment is not made flippantly: in potential models there is an analogy between possible "novel" multiquark states and nuclei.In the bag model the existence of multiquark states28 is in somesense automatic: the static bag model has stationary states corresponding to any colour singlet combination of quarks and antiquarks. In this approach the "existence" of multiquark states is certain but their widths (and hence observabilities) are determined by the (presently uncalculable) rate at whi£h the bag undergoes fission into a "fall apart mode" (e.g., qqqq -»■ qq + qq) . Since the bag model was designed to confine, and in view of this problem, it would be prudent (perhaps I should say it would have been prudent) to be wary of drawing the conclusion from the bag model that novel multiquark states (baryonia, five quark baryons, etc.) exist,29 at least without support from other models.In the potential models the existence of multiquark states is an in­trinsically dynamical question.30 To examine the question one must, to take the simplest example of qqqq, set up a Schrodinger equation for the four-body problem and seek states which exhibit binding in all three relative coordinates. Such states, if they exist, will necessarily be below threshold for falling apart into two qq^  mesons (just as the deuter­on is below NN threshold) . It is actually straightforward to show thatthe possible colour and spin recouplings of two pseudoscalar mesons do lead to an attractive potential in certain channels (the cryptoexotic28 channels); calculations we have just completed31 in fact have now proved that this effect can lead to a fully bound qqqq system under certain con­ditions. This may well be the reason why the S*(980) and 6(980)-^two prime candidates28 for ssdd cryptoexotics — are found just below KK92threshold.32 It is also clear that, as with the deuteron, the binding may be SU(3) asymmetric so that there needn't be a full nonet of such crypto­exotic bound states. We hope to report more fully on these investigations shortly, including a report on the quark mass dependence of the effect important for the question of the possible existence of stable charm- strange exotics just below DK threshold.30*32These questions are, as already stressed, closely related to the prob­lem of the nucleon-nucleon force and preliminary results of an investiga­tion of this old problem along rather new lines look promising.33B . Do glueballs exist?As with multiquark states, the existence of glueballs is automatic in the bag,3i+ and so might be regarded once again with caution. On the other hand, the constituent quark model offers little guidance in this case (apart from suggesting the idea of a massive constituent gluon model35 with the corresponding sorts of colour dependent potentials) and I can only offer some comments here on possible alternatives.One alternative to the (basically reasonable!) bag model picture is that glueballs exist but with widths that are very large so that the entire glueball spectrum is smeared into a continuum. A less drastic (but re­lated) possibility is that the low-lying glueballs (assuming that they have non-exotic quantum numbers) have mixed with ordinary qq mesons and thereby become "diluted" in the spectrum. We certainly believe (see Sec. Ill B and Fig. 6) that ordinary qq- states with 1=0 do have a glue compo­nent and it is possible that at least the low-lying glueballs can only be disentangled from qq" spectroscopy once this experimentally difficult sub­ject is itself more clearly resolved.36V. CONCLUSIONSA. Why does it work at all?37Despite the optimism of Sec. I A, it is. surprising that the non- relativistic potential models work so well. Their phenomenological suc­cesses certainly lead one to try to understand the relation of such models to the quark model in its other guises: relativistic quark models like the bag, the quark-parton model, and current quarks.We have recently examined— in a very rudimentary exercise which we believe is still revealing—  the question of "relativisation" of the non- relativistic quark model.38 We took the similarity of the bag model ground state phenomenology with that of the potential models as a clue that relativistic effects are, for the most part at least, absorbed into the parameters of non-relativistic descriptions, and that as relativistic effects are added to the model, they can mostly be eliminated by a pro­cess of "renormalisation" of masses, couplings, etc. (e.g., in the bag the non-relativistic result yp=e/2m becomes yp~e/2E). To test this idea we took some typical momentum space wave functions for mesons and baryons (which are, as previously mentioned, actually rather relativistic) and calculated various properties (static and transition magnetic moments, GA /GV , annihilation amplitudes like f^, fp , fAl, etc.) using full Dirac matrix elements instead of the usual static (i.e., non-relativistic) approximations. We found, as hoped, that most of the results of the non- relativistic quark model are practically unchanged with a modest renormal­isation of its parameters. The few significant changes that did occur were, in fact, welcome: e.g., GA/Gy moved from its naive value of 5/3 to93nearly its observed value of 1.25, and (the amplitude for the transi­tion Ay+-*W± via the axial current operative in, e.g., t->AiVt) changed from its naive value of zero to near the current algebra prediction.The consistency between the constituent quark model and current alge­bra, exemplified by the cases of G^/Gy and f^j just mentioned, leads one to suspect that the massive constituent quark model may be a basis, appro­priate for discussing soft phenomena, which is actually equivalent to the current quark picture. The mechanism of this equivalence might be thata) confinement occurs at r ~ A -1 (where A is the QCD scale parameter),b) as at this scale is (by definition) very large, as ~l,c) meff~A at this scale (via confinement and/or the dressing of the quarks37), andd) residual interactions of strength as/r~A occur.;The net effect is to "conspire " to make m^~0, etc., so that the picture is physically equivalent to the current algebra approach. Of course one picture or the other may certainly be more convenient for discussing par­ticular phenomena: e.g., one would use constituent quarks to discuss bary­ons, and current quarks for discussing the effects of chiral symmetry.Such speculations aside, I believe it is now abundantly clear that one reason that the non-relativistic models work is that they provide a simple, calculable framework on which it is possible to hang the dominant physics of the quark model. Most all of the successes of the picture correspond to using this framework to describe simple physical effects like the repulsion of parallel spins, the smaller chromomagnetic interac­tions of heavier quarks, and the slower frequencies of heavy quark excita­tions .B. What have we learned and what are some outstanding problems?As just stated, it seems clear that the models, while crude, reflect the dominant physics of the qqq and qq states. In particular, we have learned from studying these systems that a) quark colour hyperfine inter­actions with the expected properties probably exist, b) the confinement potential indeed seems to be flavour independent, c) flavour symmetries are broken (apart from small electroweak contributions) by quark masses, and d) colour factors relate mesons and baryons.There are, of course, many outstanding questions. The multiquark and glueball sectors remain largely unresolved (including the nucleon- nucleon problem). The many "missing" baryon and meson resonances need to be found by looking at processes where they do not decouple. Finally, but by no means exhaustively, much theoretical work needs to be done on the foundations of the models, and especially on the elucidation of the rela­tions between partons, current quarks, and constituent quarks.In spite of these outstanding problems, I would conclude that QCD ingredients have dramatically improved the ability of quark models to describe soft phenomena.C. What can we learn with a high intensity accelerator?Despite the efforts of the first generation of accelerators operating in the region of 20 GeV, our experimental understanding of hadron reso­nance physics remains, if not rudimentary, at least somewhat unsatisfac­tory. For example, in the baryon sector over half of the expected low- lying resonances remain unseen (10 out of 30 in S=0, 29 out of 57 in S=-l, 25 out of 30 in S=-2, and 10 out 11 in S=-3) and many of the observed resonances have poorly known couplings. Meson resonances are in a similar state.94While the status of this system is adequate to demonstrate the basic validity of the quark model, there are several reasons for pursuing this subject further:1) One of the most astounding ideas of modern physics is the notion of confinement. As we learn to deal theoretically with this regime of QCD (assuming it to be correct!), rigorous predictions for the resonance re­gion should become available; at the very least we can expect some inter­play between models based on this regime and fundamental theory to occur in order to demonstrate at some level that we understand the confinement mechanism.2) Glueballs seem inevitable in QCD and present-day theory seems to be on the verge of being able to predict their spectrum and properties. This qualitatively new form of hadronic matter appears to be elusive, how­ever, perhaps for the reasons mentioned above, and it now appears likely that understanding them will require not only better data on isoscalar channels, but also a much better understanding of the entire qq^  spectrum.3) Hadronic resonances are interesting systems in their own right and the very incomplete state of our knowledge of them is unsatisfying. At the same time, models like the one described here are probably capable of guiding experimental work in this area in, for example, the search for missing resonances. The models can also usefully serve as a framework against which novel phenomena (like glueballs, non-qqq baryons, gluonic excitations, time-like resonances, etc.) can be seen.With these objectives in mind, it is easy to imagine a fruitful pro­gramme for a high intensity machine capable of operating in the resonance region. First of all, new high statistics partial wave analyses of reac­tions likettN -»- ttN, ttA, r|N, pN, KA, ... (21)andKN -*■ KN, KA, irE, ttA, pE, pE*, ••• (22)can uncover a large number of the missing baryon resonances. Perhaps more significant, however, is the fact that high intensity will allow isobar analyses of production experiments likettN -> irN*, nN*, ... with N* -* ttA, pN, KA, ... (23)and _KN -* ttY*, pY*, ... with Y* -> KA, ttE, ttA, ... (24)to uncover states that are very strongly decoupled from the elastic chan­nels. One can even hope to find decay chains likettN -* N* -> ttN* (25)where N* is a known strongly coupled resonance and N* a missing resonance.One could similarly look for S--2 resonances in, for example,KN -*■ KS*, K*S*, ... with S* -> Sit, AK, ... (26)with sufficient events for an isobar analysis of quantum numbers and coup­lings which has been lacking to date. Meson isobar analyses of reactions like95ttN  - *  M^s N with M^s -*■ t t t t ,  irq, irp, KK, ... (27)andKN -> M^ N with M^ + Kir, Kn, Kp, ... (28)would, one would guess, provide a new level of precision to the data thatcould lead to the disentangling of the qq and glueball resonances. Com­parison with the predicted glueball spectrum could then provide one of the earliest and most interesting tests possible of the non-perturbative regime of QCD.Though this list of topics is not at all exhaustive, perhaps it still serves to illustrate the value of a high intensity accelerator for further elucidating the properties of the confinement regime.ACKNOWLEDGEMENTSThe work reported here was almost all done in collaboration with others, especially Gabriel Karl, and including Kuang-Ta Chao, Les Copley, Stephen Godfrey, Cameron Hayne, Roman Koniuk, H.J. Lipkin, Kim Maltman, Hector Rubinstein, D.W.L. Sprung, Adam Schwimmer, and John Weinstein.REFERENCES1. For a review, see my lectures at Erice in 1978, in "The New Aspectsof Subnuclear Physics", ed. A. Zichichi, Proc. XVI Int. School of Sub- nuclear Physics, Erice, 1978 (Plenum, New York, 1980), p. 107. See also Refs. 2. This general approach to soft hadron physics flowed from the seminal papers of Refs. 3.2. G. Karl, in Proc. XIX Int. Conf. on High Energy Physics, Tokyo, 1978, eds. S. Homma, M. Kawaguchi, and H. Miyazawa (Phys. Soc. of Japan, Tokyo, 1979), p. 135;O.W. Greenberg, Ann. Rev. of Nucl. and Part. Phys. _28^, 327 (1978); A.J.G. Hey, in Proc. 1979 EPS Conf. on High Energy Physics, Geneva, and in Proc. of Baryon 1980, Toronto, 1980, ed. N. Isgur (Univ. of Toronto, 1981), p. 223;J. Rosner, in Proc. of the Advanced Studies Institute on Techniques and Concepts of High Energy Physics, Virgin Islands, July, 1980;N. Isgur, in Proc. XX Int. Conf. on High Energy Physics, Madison,1980, eds. L. Durand and L. Pondrom (AIP, New York, 1981), p. 30.3. A. de Rujula, H. Georgi and S.L. Glashow, Phys. Rev. D 12, 147 (1975); T. deGrand, R.L. Jaffe, K. Johnson and J. Kiskis, Phys. Rev. D 12,2060 (1975).4. This solution is very similar to some pre-confinement models considered by Y. Nambu in "Preludes in Theoretical Physics", eds. A. de Shalit,H. Feshbach and L. van Hove (North Holland, Amsterdam, 1966) and H.J. Lipkin, Phys. Lett. 45B, 267 (1973). The dynamical basis for the re­striction to colour singlets is, however, very different: see Ref. 1.5. See the discussion of this point by H.J. Schnitzer in Proc. XVI Rencontre de Moriond, Les Arcs, France, 1981 and the references there­in. See also A.B. Henriques, B.H. Kellet and R.G. Moorhouse, Phys. Lett. 64B, 85 (1976);H.J. Schnitzer, Phys. Lett. 65B, 239 (1976); 69B, 477 (1977); Phys.Rev. D 18, 3483 (1978);96L.-H. Chan, Phys. Lett. 7IB, 422 (1977);L.J. Relnders, in Proc. of Baryon 1980, Toronto, 1980, ed. N. Isgur(Univ. of Toronto, 1981), p. 203;F.E. Close and R.H. Dalitz, in a paper presented to the Workshop on Low and Intermediate Energy Kaon-Nucleon Physics, Univ. of Rome, 1980.6. N. Isgur and G. Karl, Phys. Lett. 72B, 109 (1977); 74B, 353 (1978);Phys. Rev. D 18, 4187 (1978); D 19, 2653 (1979); D 23, 817 (E)(1981);D ^0, 1191 (1979). For related work on baryons, see as examples Refs. 7.7. D. Gromes and 1.0. Stamatescu, Nucl. Phys. B112, 213 (1976);W. Celmaster, Phys. Rev. D 15, 1391 (1977);D. Gromes, Nucl. Phys. B130, 18 (1977);L.J. Reinders, J. of Phys. G4, 1241 (1978).8. O.W. Greenberg, Phys. Rev. Lett. 13, 598 (1964);O.W. Greenberg and M. Resnikoff, Phys. Rev. 163, 1844 (1967);D.R. Divgi and O.W. Greenberg, Phys. Rev. 175, 2024 (1968);H. Resnikoff, Phys. Rev. Dj8, 199 (1971).9. R.H. Dalitz, in "High Energy Physics", eds. C. deWitt and M. Jacob (Gordon and Breach, New York, 1966);R.R. Horgan and R.H. Dalitz, Nucl. Phys. B66, 135 (1973);R.R. Horgan, Nucl. Phys. B71, 514 (1974).10. G. Morpurgo, Physics 95 (1965), reprinted in J.J.J. Kokkedee,"The Quark Model" (W.A. Benjamin, New York, 1969).11. A general derivation of this rule was given in Refs. 1 and 6, butits origin was not understood. Recently K.C. Bowler, P.J. Corri,A.J.G. Hey and P.D. Jarvis, Phys. Rev. Lett. 45, 97 (1980), have shown that the rule follows from the Sp(12,R) spectrum-generating algebra of the three-body oscillator problem and have extended its application to higher excitations.12. R. Koniuk and N. Isgur, Phys. Rev. Lett. 44, 845 (1980); Phys. Rev.D 21, 1868 (1980); D 23, 818 (E)(1981);R. Koniuk, in Proc. of Baryon 1980, Toronto, 1980, ed. N. Isgur (Univ. of Toronto, 1981), p. 217.13. C. Becchi and G. Morpurgo, Phys. Rev. 149, 1284 (1966); 140B, 687(1965); Phys. Lett. 17, 352 (1965);A.N. Mitra and M. Ross, Phys. Rev. 158, 1630 (1967);D. Faiman and A.W. Hendry, ibid. 173, 1720 (1968);H.J. Lipkin, Phys. Rep. 8C, 173 (1973);J.L. Rosner, ibid.llC, 189 (1974);R. Horgan, in Proc. of the Topical Conf. on Baryon Resonances, Oxford, 1976, eds. R.T. Ross and D.H. Saxon (Rutherford Lab., Chilton, 1976);A. Le Yaouanc et al., Phys. Rev. D J.1, 1272 (1975);L.A. Copley, G. Karl and E. Obryk, Nucl. Phys. B13, 303 (1969);D. Faiman and A.W. Hendry, Phys. Rev. 180, 1572 (1969);K. Ohta, Phys. Rev. Lett. ji3, 1201 (1979);R.G. Moorhouse, Phys. Rev. Lett. JL6, 771 (1966);R.P. Feynman, M. Kislinger and F. Ravndal, Phys. Rev. D \  2706 (1971);R.G. Moorhouse and N.H. Parsons, Nucl. Phys. B62, 109 (1973).14. H.J. Lipkin and S. Meshkov, Phys. Rev. Lett. L4, 670 (1965);D. Faiman and A.W. Hendry, Phys. Rev. 173, 1720 (1968); 180, 1609 (1969);E.W. Colglazier and J.L. Rosner, Nucl. Phys. B27, 349 (1971);W. Petersen and J. Rosner, Phys. Rev. D jj, 820 (1972);A.J.G. Hey, P.J. Litchfield and R.J. Cashmore, Nucl. Phys. B95, 516 (1975),F. Gilman and I. Karliner, Phys. Rev. D JJ), 2194 (1974);97J. Babcock and J. Rosner, Ann. Phys. (N.Y.) 9M5, 191 (1976);J. Babcock et al., Nucl. Phys. B126, 87 (1977);D. Faiman and D.E. Plane, Nucl. Phys. B50, 379 (1972).15. N. Isgur, Phys. Rev. D 21, 779 (1980); D _23, 817 (E)(1981).16. R. Carlitz, S.D. Ellis and R. Savit, Phys. Lett. 64B, 85 (1976);N. Isgur, Acta. Phys. Pol. B8, 1081 (1977);N. Isgur, G. Karl and D.W.L. Sprung, Phys. Rev. D _23, 163 (1981).17. N. Isgur, G. Karl and R. Koniuk, Phys. Rev. Lett. 41, 1269 (1978);45, 1738 (E)(1980).18. This issue dates back to M.A.B. Beg, B.W. Lee and A. Pais, Phys. Rev. Lett. 13, 514 (1964);0.W. Greenberg, Phys. Rev. Lett. 598 (1964);H.R. Rubinstein, F. Sheck and R.H. Socolow, Phys. Rev. 154, 1608 (1967); J. Franklin, ibid., 172, 1807 (1968). The more modern literature can be traced from N. Isgur and G. Karl, Phys. Rev. D _21, 3175 (1980).19. L.A. Copley, N. Isgur and G. Karl, Phys. Rev. D ^ 0, 768 (1979); D 23, 817 (E)(1981).20. K. Maltman and N. Isgur, Phys. Rev. D 22, 1701 (1980).21. The consequences of this effect have been widely discussed, but seein addition to Ref. 1 especially H.J. Lipkin, Phys. Lett. 74B, 399 (1978) and I. Cohen and H.J. Lipkin, Phys. Lett. 93B, 56 (1980).22. For related work on mesons see H.J. Schnitzer, Phys. Lett. 65B, 239(1976); 69B, 477 (1977); Phys. Rev. D 18, 3482 (1978); R.H. Grahamand P.J. O'Donnell, ibid., 19, 284 (1979);B.R. Martin and L.J. Reinders, Nucl. Phys. B143, 309 (1978); Phys.Lett. 78B, 144 (1978);A.B. Henriques, B. Kellet and R.G. Moorhouse, Phys. Lett. 64B, 85 (1976); L.-H. Chan, Phys. Lett. 71B, 422 (1977);R. Barbieri j* al., Nucl. Phys. B105, 125 (1976);E. Eichten ejt al., Phys. Rev. D 17^ , 3090 (1978);M. Krammer and M. Krasemann, DESY report no. 79/20, 1979;L.J. Reinders, University College London report, 1979;1. Cohen and H.J. Lipkin, Nucl. Phys. B112, 213 (1976);J. Arafune, M. Fukugita and Y. Oyanagi, Phys. Rev. D 16^ , 772 (1977);A. Bradley and F.D. Gault, Durham/Manchester report, 1978;A. Bradley and D. Robson, Manchester report 1979;D.P. Stanley and D. Robson, Phys. Rev. D _21, 3180 (1980).23. N. Isgur, Phys. Rev. D 12, 3770 (1975); D 13, 122 (1976).24. I. Cohen and H.J. Lipkin, Nucl. Phys. B151, 16 (1979) go beyondRef. 23 to consider radial mixing and SU(3) breaking. See also in this regard P.J. O'Donnell and R.H. Graham, Phys. Rev. D _19, 284 (1979).25. S. Godfrey and N. Isgur, work in progress.26. See the review by P.J. O'Donnell in Proc. XVI Rencontre de Moriond,Les Arcs, France, 1981. For a narrower (and more naive) view see N. Isgur, Phys. Rev. Lett. _36, 1262 (1976).27. N. Isgur, H.R. Rubinstein, A. Schwimmer and H.J. Lipkin, Phys. Lett.89B, 79 (1979).28. The bag model discussion of multiquark states, and in particular the discussion of the qqqq sector stems from the work of R.L. Jaffe,Phys. Rev. D 15, 267 (1977). It is Jaffe who pointed out that the colour hyperfine interactions favour certain qqqq systems which he dubbed cryptoexotic since they had normal qTj quantum numbers. See also the talk by J.M. Richard in Proc. XVI Rencontre de Moriond, Les Arcs, France, 1981.29. The nature of the qq^q bag states in view of their being unboundagainst bag fission has been considerably clarified recently by the introduction of a P-matrix analysis of the bag model predictions.See R.L. Jaffe and F.E. Low, Phys. Rev. D 19, 2105 (1979).30. For discussion of these dynamics see H.J. Lipkin, Phys. Lett. 74B,399 (1978) and H.J. Lipkin in "The Whys of Subnuclear Physics", ed.A. Zichichi, Proc. 1977 Int. School of Subnuclear Physics, Erice,1977 (Plenum, New York), p. 11.31. J. Weinstein and N. Isgur, in preparation.32. N. Isgur and H.J. Lipkin, Phys. Lett. 99B, 151 (1981).33. K. Maltman and N. Isgur, work in progress.34. R.L. Jaffe and K. Johnson, Phys. Lett. _34, 1645 (1976).35. See the talk by Ted Barnes in Proc. XVI Rencontre de Moriond, LesArcs, France, 1981, and also D. Robson, Nucl. Phys. B130, 328 (1977);J.J. Coyne, P.M. Fishbane and S. Meshkov, Phys. Lett. 91B, 259 (1980).36. For a recent look at such a possibility, see J.L. Rosner, "Tests forGluonium or Other Non-qq Admixtures in the f(1270)", Minnesota pre­print, February 1981.37. For a discussion of these issues see H.J. Lipkin's summary talk inthe Proc. of Baryon 1980, Toronto, 1980, ed. N. Isgur (Univ. ofToronto, 1981), p. 461;see also I. Cohen and H.J. Lipkin, Phys. Lett. 93B, 56 (1980), and references therein.38. C. Hayne and N. Isgur, "Beyond the Wave Function at the Origin: Some Momentum Dependent Effects in the Non-Relativistic Quark Model",Univ. of Toronto report, March 1981.9899SEARCH FOR DIBARYONIC STATES WITH STRANGENESS -2 AND -1 IN THE INTERACTIONS OF KAONS AND PIONS ON DEUTERIUMCERN-Rome-Saclay-Vanderbilt Collaboration Speaker: E. Pauli,* CERN, Geneva, SwitzerlandABSTRACTWe present the results of a missing-mass spectrometer experiment (PS 159) at the CERN Proton Synchrotron, which is looking for dibaryonic states.In the reactionsK"d -*■ K+X" (S = -2) , (1)K"d + tt+X- (S = -1) , (2)ir"d ■+ K+X" (S = -1) (3)at 1.4 GeV/c, no structures have been found in the X“ spectra which wouldhave indicated the production of strange dibaryonic states in those chan­nels.On the other hand, a narrow dibaryonic state with strangeness S = -1and charge Q = +1 at a mass M = 2.130 GeV is clearly seen in the missing-mass spectra of the reactionK“d -+ tt"X+ (4)at 1.4, 1.06, and 0.92 GeV/c, and also in the line-reversed reactionir+d -*• K+X+ (5)at 1.4, 1.2, and 1.06 GeV/c.These results confirm strongly previous similar observations in the reaction (4) and represent the first observation of the reaction (5).Possible evidence for heavier dibaryons will be discussed.1. THE EXPERIMENTAL SET-UP1The missing-mass experiment is installed in the East Hall of the CERN Proton Synchrotron (PS) where the k2i+ beam line [Fig. 1(a)] delivers pions and kaons on a 40 cm deuterium target. The experimental set-up is shown in Fig. 1(b). The beam spectrometer measures the incident particle momen­tum with a resolution of 0.2%; the outgoing particle is detected in a forward magnetic spectrometer (VENUS), where its momentum is measured with a resolution of about 0.5%. The nature of the incident and outgoing par­ticles is selected by aerogel and water Cerenkov counters and by TOF measurement. The missing-mass resolution is a = 3 to 7 MeV/c2 depending on the reaction. The acceptance for a dibaryon state assuming an isotrop­ic production in the centre of mass is 0.6% in a range of missing mass 200 MeV/c2 as shown in Fig. 1(d). A set of 12 scintillator counters surrounding the target allows selection of the multiplicity of the decay products of the missing-mass object.*Also CEN-Saclay, DPhPE, Gif-sur-Yvette, France.100q 9 b m 2 v m 2Fig. 1(a). The k2i+ beam line at the CERN PS.Production forgetQl - Qg QuadrupolesC^, C2 Acceptance slitsC3 Momentum slitC4 Mass slitBM1, BM2 Bending magnetsSEP1,SEP2 2 m electrostatic separatorSEP3 3 m electrostatic separatorVM1, VM2 Vertical bending magnetsK 24 be om lineExperimental targetCh",'* ,» V 4.'9 ; ,mm *P°c' n9 MWPCC hi , * , s , 4  :2m m spacing MWPCFig. 1(b). TheScintillotion CountersSi : PILOT-U Scintillator S, : PILOT-U Scintillator P : NE 110 Scintillator H j f j - I . ,9 ) :PILOT-U Scint. He : NE 110 Scintillator5*10 *03 cm1 5» IO« I cm* 4 *  3 *  03cm* 23*75* 25cm» 225*55* I cm’experimental set-up.derenkov Counters20 : Aerogel (n *1 0 5 ) i i  : Aerogel (n>1.094)2, • Water with wave-length shifterMulti Wire - Proportionol - ChambersFig. 1(c). Resolution of the E+ mass in the missing-mass distri­bution for the reaction ir+p K+X+ at 1.4 GeV/c.Fig. 1(d). The solid line shows the ac­ceptance e of the experimental apparatus for a dibaryon state, assuming an iso­tropic production in the centre of mass. The dashed line shows the acceptance ob­tainable without requiring the fierenkov C2 in the trigger.101Fig. 2(a). The missing-mass distri­bution for the reaction K“d -> K+X“ at 1.4 GeV/c.MISSING MASS ( G e V / c 2 )Fig. 2(b). Upper limit of the backward cross-section of H^ as a function of the mass of the di- baryon Hjj in the reaction K“d -> at 1 • 4 GeV/c. (The width of the dibaryon is assumed to be neg­ligible in respect to the experi­mental resolution.)2. SEARCH FOR THE Hj (Ref. 2)2.1 K~d -> K+X~ at 1.4 GeV/cThe missing-mass spectrum for this reaction is shown in Fig. 2(a).The sample of 7119 events corresponds to an effective incident flux of 4 x 10 K~, i.e. a total sensitivity of 80 events/nb. The solid line isthe Monte Carlo simulation of the reaction K“p(ns) -> K+S“(ns), where (ns) is a spectator neutron. The data are well explained by this process; the other possible channels K~d -*■ K+ + MM, where the missing-mass MM is (E“A), (AAir-) , (Z"Z°) , and (S-TT°ns), give a negligible contribution.2.2 Upper limit for the production of HpThe 95% C.L. upper-limit curve for the c.m.s. backward production of H2 in the reaction K”d K+H2 at 1.4 GeV/c as a function of missing-massis shown in Fig. 2(b). At E~n threshold this limit is ~  10 nb/sr.3. SEARCH FOR THE Hi (Ref. 3)3.1 Tr~d -* K+X~ at 1.4 GeV/cThe missing-mass spectrum for this reaction is shown in Fig. 3(a).The sample of 25,802 events corresponds to an effective incident flux of2.9 x  1010 i t " ,  i.e. a total sensitivity of 52.8 events/nb. The dashed line is the Monte Carlo simulation of the reaction Tr“p(ns) -*■ K+E”(ns), where (ns) is a spectator neutron. The solid line includes the process ^"pCns) ->• K+ATr”(ns). The data are well explained by these two channels, and there is no evidence for structure either below or above the (Z“n) threshold.3.2 K~d ■» 7T+X" at 1.4 GeV/cThe missing-mass spectrum for this reaction is shown in Fig. 3(c).The effective incident flux is 6.8 x 109 K”, corresponding to a sensitivi­ty of 13.3 events/nb. The events below threshold are explained by the reaction K~p(ns) -*■ K9n(ns) . The dashed line is the contribution of102MISSING MASS (GeV/c’l MISSING MASS (GeVxlFig. 3. (a) The missing-mass distribution for the reaction ir_d -*■ K+X“ at1.4 GeV/c; (b) Upper limit of the backward cross-section of Hi as a func­tion of the mass of the dibaryon Hj in the reaction ir“d->K+Hi at 1.4 GeV/c;*(c) The missing-mass distribution for the reaction K“d -*■ tt+X" at 1.4 GeV/c;(d) Upper limit of the backward cross-section of Hi as a function of the mass of the dibaryon Hi in the reaction K“d -*■ ir+X” at 1.4 GeV/c.*K"p(ns) -»■ ir+E-(ns). The solid line includes K"p(ns) -*■ ir+ATT-(ns) , and the sum of all these channels adequately explains the data.3.3 Upper limit for the production of HjThe upper limits for the c.m.s. backward production of Hi at E"n threshold in the reactions ir-d -»■ K+X" and K”d ->• tt-X" at 1.4 GeV/c are, respectively, 23 nb/sr and 1.7 yb/sr. A rough model1* indicates that the upper limit of 1.7 yb/sr is physically more restrictive. The 95% C.L. upper-limit curves for do/dft at 0° (c.m.s.) as a function of missing mass are shown in Figs. 3(b) and (d).4. SEARCH FOR THE Hi AT 1.4 GeV/c4.1 K"d -*■ tt"X+In bubble-chamber experiments5 a signal has been observed in the back­ward (Ap) system in the reaction K"d -»■ ir“(Ap) between 0 and 1.65 GeV/c.This signal, called Hf, with a mass of 2.13 GeV/c2 and a total width of about 10 MeV/c2 suggests the existence of a dibaryon state with quantum numbers B = +2, Q = +1, S = -1, I = %.*The width of the dibaryon is assumed to be negligible compared with the experimental resolution.103This experiment confirms the signal at 1.4 GeV/c. The missing-mass distribution for the reaction K“d is shown in Fig. 4(a). The inci­dent flux of 5 x 109 K" corresponds to a total sensitivity of 9 events/nb. The A and E "backgrounds", with a nucleon spectator, are suppressed by asking for three particles in the counters surrounding the target together with a forward tt” in the spectrometer. We observe a clear peak around 2.13 GeV/c2 . A careful study of other physical contributions is under way to account for the asymmetry observed in this peak.A crude estimate of the cross-section lies between 200 and 400 pb/sr.4.2 TT+d K+X+The missing-mass distribution is shown in Fig. 4(b). The incident flux of 7 x 1010 tt+ corresponds to a total sensitivity of 135 events/nb.The data required three particles in the target scintillators in addition to a forward K+ measured by the spectrometer. For the first time in this reaction the Hi”(2.13) is clearly seen with an estimated cross-section of 4 ± 2 pb/sr. As a result of this low cross-section, the triggering condi­tions cannot totally suppress the physical "backgrounds", i.e. tr+n(ps) -*■ K+A(ps) and ir+n(ps) -*■ K E°(ps). The excess of events at higher mass has still to be analysed.5. SEARCH FOR THE H{ AT LOWER INCIDENT MOMENTAData have also been taken at lower incident momenta, i.e. 1.06 GeV/c and 0.92 GeV/c for the reaction K d -> it X+ , and 1.2 GeV/c and 1.06 GeV/c for the reaction iT+d ->■ K+X+ . The incident flux and corresponding total sensitivites are given in Table I. The missing-mass distributions are shown in Figs. 5(a) and (b) for the reaction K“d -*■ ir”X+ at 1.06 GeV/c and0.92 GeV/c. The triggering conditions are the same as previously at1.4 GeV/c. There is a clear signal of Hi"(2.13). The estimated cross- section at 1.06 GeV/c is about three times smaller than at 1.4 GeV/c, while at 0.92 GeV/c it is six times smaller than at 1.4 GeV/c. For the incident i t ' s  the H^(2.13) signal is contaminated by A and E "backgrounds" with a nucleon spectator. However, the cross-section of H*(2.13) at 1.2 and1.06 GeV/c can be estimated to be at least four times smaller than at1.4 GeV/c. For both reactions the analysis is still in progress.Table IIncident beam (GeV/c)K" K" TT+ TT+__________________1.06 0.92______ 1/2._____ 1.06Flux (109) 1.15 0.45 65 65Sensitivity 2.2 0.9 125 125(events/nb)K -  . D ------------ > P I -  . MISSING MASS exist/ G*^ /c. PI+ . D ------------ >  K+ , MISSING MASS AT 1.4 GEV/CFig. 4. The missing-mass distributions for the reactions (a) K“d -* tt“ X +  at1.4 GeV/c; (b) Tr+d K+X+ at 1.4 GeV/c.EVEKTS/3 MEV/O-2K -  . D ---------- >  P I-  . MISSING MASS AT 1.06 GEV/C K -  . D ------------ >  P I -  . MISSING MASS AT 0.92 GEV/CFig. 5. The missing-mass distributions for the reactions (a) K“d -* tt“X+ at1.06 GeV/c; (b) K'd -*• tt"X+ at 0.92 GeV/c.106REFERENCES1. G. D'Agostini et al., A missing-mass spectrometer for momenta below1.5 GeV/c, to be published in Nucl. Instrum. Methods.2. Rome-Saclay-Vanderbilt Collaboration (in preparation), Search for di­baryon states with strangeness -2 in the reaction K“d -*■ K+X" at1.4 GeV/c.3. G. D'Agostini e^t al. , A study of the missing-mass spectra in the re­actions ir“d -*■ K+X" and K“d ■> tt+X“ at 1.4 GeV/c submitted to Phys.Letters.4. D.F. Kane, Phys. Rev. D 5, 1583 (1972).5. Tai Ho Tan, Phys. Rev. Lett. 2 3 , 395 (1969);D. Eastwood et al., Phys. Rev. D _3, 2603 (1971);0. Braun et al., Nucl. Phys. B124, 45 (1977).107KAON-INDUCED NUCLEAR REACTIONS C.B. DoverBrookhaven National Laboratory, Upton, New York 11973ABSTRACTSome reactions which could be studied at a future kaon factory are discussed. These include elastic and inelastic regeneration of neutral kaons on nuclei, production of high spin A and I hypernuclear states via the (tt± ,K+) reaction, and the (K”,K+) process as a means of exploring the spectroscopy of doubly strange hypernuclei.1. INTRODUCTIONThere exist a number of reviews of kaon-induced reactions and hyper­nuclear physics in the literature.1-9 In this talk, I would like to select several topics which are appropriate for a discussion of future ex­periments at a kaon factory, rather than attempting a comprehensive survey. In particular, kaon regeneration on nuclei, the formation of high spin A or E hypernuclear states via the (ir^  ,K+) reaction, and the physics of doubly strange hypernuclei will be taken as examples. Kaon elastic and inelastic scattering from nuclei will be discussed by R. Eisenstein at this meeting; theoretical aspects of A and E hypernuclear structure are to be reviewed by A. Gal.2. NEUTRAL KAON INTERACTIONS WITH NUCLEIA more complete discussion of neutral kaon interactions is found in the review of Dover and Walker,9 from which this section is excerpted.We first sketch the basic^ concepts. The eigenstates of strangeness S are denoted_by K°(S =+1) and K°(S = -1). They are related by the CP trans­formation |K°> = CP|K°>, where C and P are the charge conjugation and parity operators, respectively^ The corresponding eigenstates of CP are the linear combinations K^ = (K° + K°)//2~(CP = +1) and K2 = (K° - K0)/(CP =-1). However, weak interactions do not conserve S, so the physi­cally observable eigenstates Kl and Kg are linear combinations of K° and K°, which are mixed through intermediate states like T r y v ,  rev, 2ir, or 3ir via second-order weak interactions. We write|KL> = (P|K°> - q|K°>)/(|p|2 + |q|2)^|Kg> = (p|K°> + q|K°>)/(|p|2 + |q|2)^ . (1)If CP were conserved, we would have p = q = 1, so |Kl> = |K2> and |Kg> = |Ki>. However, as first shown in the beautiful experiment of Christenson, Cronin, Fitch, and Turlay,10 CP conservation is violated in neutral kaon decays. They observed the CP-forbidden process Kl -*■ tt+7t- . This implies that Kl and Kg are linear combinations of Kj and K2 :|kl> = (|K2> + e|Ki>)/(l + | e |2)^|Kg> = ( | Ki >  +  e | K 2 > ) / ( 1  +  | e | 2 ) ^  , ( 2)108where the parameter e = (p-q)/(p+q) ~  2.3 x 10-3 exp(iir/4) registers the magnitude of CP violation.A phenomenon of fundamental interest in neutral kaon physics is regeneration. As first predicted by Pais and Piccioni,11 short-lived Kg's are created when Kl 's pass through a material. This effect occurs because Kl and Kg are different linear combinations of the eigenstates of strange­ness (K°, K°)._ In matter, there are several reaction processes for a K° (for example, K°p -»■ Air or Eir) which are forbidden for a K°, due_to the conservation of strangeness in strong interactions. Thus otot(K°) > atot(K°) for the total cross sections on any nucleus, and via the optical _theorem we have |Im f(0)| > |Im f(0)|, where f(0) and f(0) are the forward KO and K° scattering amplitudes on the nucleus. If we now consider an incident Kl beam scattered through an angle 0, the final state wave function islt(e»  . m  t  m,Kl> + 1(» - K . )  | K s > . (3)since f ^ f, we see that a Kg component is regenerated from an incident Kl beam.There are three different classes of regeneration phenomena,12 depend­ing on the degree of coherence in the scattering. They are: 1) coherentregeneration, occurring in the extreme forward direction (0 < 10“7 rad), which involves addition of amplitudes from a macroscopic thickness of tar­get (of order cm); 2) elastic regeneration from a nucleus. Unlike 1), oneadds intensities from different nuclei incoherently, but preserves thecoherence within the nucleus; 3) inelastic regeneration, which involves appreciable momentum transfer to the nucleus, leaving it in an excited state. Coherent regeneration has provided a very powerful tool for the study of CP-violating effects. It was first observed by Good _al.13 ina cloud chamber experiment. Using the coherent mixtures of Kl and Kggenerated by a target, one can study the interference between the CP-con­serving Kg ->■ 2tt and the CP-violating Kl -*■ 2tt decays. The so-called "regeneration phase" between incident Kl's and outgoing Kg's can be measured via the time dependence of K -*■ irev decays. One can also obtain a determination of the lifetime of the Ks (about 0.9 x 10-10 sec compared to a Kl lifetime of 5 x 10-8 sec) and the Kl - Kg mass difference Ml - Mg «0.5 x 1010 sec-1 ~  1/3 x 10“5 eV. These fascinating topics are treated in detail in recent review articles,12 so we do not pursue them here. We focus our attention instead on elastic and inelastic regeneration processes [types 2) and 3) above] on composite nuclei.There exist some measurements of total Kl cross sections, amplitudes for forward angle Kl Kg regeneration as a function of momentum for C,Cu, and Pb targets, and angular distributions for elastic and inelastic Kl -*■ Kg regeneration on Cu and Pb targets, averaged over a range of momen­tum. The datall+ on the Kl total cross section ntot on Cu are fairly well explained in the optical model. This model predicts a peak in Otot near 1 GeV, reflecting resonance structure in the KlN amplitudes. More data are needed to confirm this; such data could be supplied by a neutral kaon beam at a_kaon factory. The magnitude of the amplitude f21(0) =- f(0)) for coherent Kl -►•Kg regeneration at 0 = 0° from a Cu tar­get has been measured by Birnbaum et al. and others.15 Their results for If21(0)| in the low momentum region are given in Fig. 1. The theoretical curves in Fig. 1 correspond to optical model calculations in the eikonal limit. Here the K°-nucleus scattering amplitude f(0) is obtained as an109impact parameter integral:wheref(0) = ik f  bdb J0 (kb sin0)o[f fp <0) +(4)X (b) =2irkNA « o  ,]r dz p(r)Here fp°n are tlle K°P ancl ^°n fQrwar<i amplitudes, and p(r) is the total nuclea.r density. A similar expression obtains for the K°-nucleus ampli­tude f(0). The K°N and K°N amplitudes are related to the measured cross sections for K+N and K"N via relations of the type atot(K0P) = atot(K+n), etc. The real parts of f^°^and f^°^are usually evaluated from forward dispersion relations. The differential cross section for elastic regene­rative (Kl -*■ Kg) scattering on nuclei is then§  (9) - i  |f(e) - f(e)|2 (5)shown inf21(0)| occurs at An attempt to includeThe low momentum optical model predictions for |f21(0)Fig. 1, display a marked energy dependence in the region of 1 GeV/c. Thisis due to a sharp drop in the elementary K“N cross sections after the£(1770) resonance at 950 MeV/c and the A(1815) at 1050 MeV/c. The inclu­sion of the real part of the KN amplitudes (dashed to solid line in Fig. 1), while raising the magnitude of f2i(0), does not appreciably alter this energy dependence. Experimentally, the drop in higher momentum than predicted by the optical model, the effects of Fermi motion15 was unsuc­cessful in resolving this discrepancy.Corrections to the optical potential were also studied. However, interactions in­volving transverse momentum transfer are suppressed due to the sharpness(0 < IO"7 rad) of the coherent forwardpeak. There may be more complicated ef­fects of the nuclear medium which smooth out or shift the degree of energy depen­dence, but no detailed calculations have been done. This remains an interesting problem.In general, the forward regeneration amplitude f2i(0) is rather insensitive to the detailed properties of the neutron density pn (r). The calculations shown in Fig. 1 use in fact the same radial shape for Pn (r) and pp(r). The angular distri­bution for Kl ■* Kg regeneration, on the other hand, is more sensitive to the neutron radius, and the presence of a "neutron skin". For small 0, the optical model yields a diffractive form(do\vdn/KL->KsC e-(p9/p0)2Fig. 1. Regeneration ampli- (6) tude |f21(0)| on copper, from D. Birnbaum et al.15110Fig. 2. Optical model predictions for Kl elastic scattering (o l l ) anc* Kl -*■ Kg (o l s ) cross sections, from Kleinknecht.16Fig. 3. Angular distributions for Kl -*■ Kg regenerative scattering from Cu and Pb, together with optical model fits from Foeth et al.17where p0 ss 68 MeV/c according to Bohm et al.15 This is some 12% smaller than the corresponding value of 77 MeV/c for non-regenerative Kl Kl scattering. The more rapid fall-off of the Kl -»■ Kg angular distribution can be understood if^  one observes that the difference between the nuclear transparencies for K° vs. K° is maximum at the edge of the nucleus. The "effective radius" for Kl -*■ Kg regeneration is correspondingly larger than for the Kl -► Kl process. This effect is shown clearly in Fig. 2, which shows optical model predictions for (da/dfi)KL-»-KL S ’ ^or KL *  KS » tlie dif­fraction minimum is pulled in to smaller momentum transfer.The angular distributions for Kl Kg regeneration on Cu and Pb have been measured by Foeth et al.17 The results are shown in Fig. 3. The same group has also measured the angular distribution of inelastic regene­ration processes associated with particle production.17 The incident kaon momentum varied from 2.5 to 6.5 GeV/c; Fig. 3 represents combined data from all momenta, since no significant variation in momentum transfer dependence was observed as a function of incident momentum.The data in Fig. 3 were subjected to an optical model analysis, assum­ing a neutron densityPn(r> = Po/f1 + exp(r - Rn)/an) . (7)The parameters of the proton distribution are taken from electron scatter­ing and muonic X-ray analyses. The neutrons are found to have a regenera­tion power which is a factor 5 larger than that of protons at 4 GeV/c. As a consequence of strong absorption, Kl -*■ Kg is suppressed for small impact parameters; regeneration is thus particularly sensitive to pn at the nuclear surface.IllThe uncertainties in the KN and KN input amplitudes are mainly re­flected in changes in the absolute size of the Kl Kg cross section, while the angular dependence depends mostly on the nuclear shape param­eters of Eq. (7). For both Cu and Pb, the diffraction peak in Fig. 3 is narrower than predicted by the optical model with equal proton and neutron densities (Rn=Rp , an=ap). By augmenting either Rn or an , one can fit both the angular dependence of the Kl -* Kg cross section and its absolute value at 0 = 0° from coherent (macroscopic) transmission regeneration. With an = ap» f°r instance, Foeth et al.17 obtain Rn-Rp ~  0.6-0.7 fm for Cu and Pb. These radius differences are somewhat larger than those obtained from most other probes, but one should emphasize that the analysis assumes that the optical model can correctly describe regeneration phenomena, which are here characterized by an amplitude difference f(0) - f(0) an order of magnitude smaller than f and f themselves. However, Kl -*■ Kl and Kl -► Kg processes on nuclei represent a very promising probe of nuclear densities, which is worthy of further exploration. Such studies could be conducted with some precision at a future kaon factory.3. HIGH SPIN HYPERNUCLEAR STATES AND THE ( t t1 ,K+) REACTIONThe spectroscopy of A and E hypemuclei has been explored thus far by means of the (K",tt1) reaction.18 Since the momentum transfer q for the processes K-n -*■ tt"A and K-N ■* ttE is rather small at 0 = 0° for low inci­dent momenta (<800 MeV/c), low spin states of the residual hypernucleus are emphasized. For a closed shell 0+ target, the (K”,tt) cross section at 0° is dominated by the 0+ states of the hypernucleus formed by the coher­ent replacement of the nucleon by a hyperon. Recently, the crossed reac­tion (tt1 ,K+) has been proposed19 as an alternative method for producing hypernuclei. Since q for the associated production reaction iT+ n  -* K+A is large (q varies from about 325 MeV/c at pT = 1 GeV/c to 275 MeV/c at1.4 GeV/c, i.e., in the region where the elementary cross section is large), the (tt,K) reaction will preferentially populate high spin states, nicely complementing the (K,tt) measurements. An attractive experimental feature of the (tr,K) process is the availability of large pion fluxes, typically 101* it's per K at the Brookhaven AGS, for instance. This permits the measurement of much smaller cross sections (1 yb/sr is already acces­sible) than for (K,ir) with current beam intensities. Intense pion beams in the 1-2 GeV/c range at a kaon factory could also be used for these studies.The configurations which are predicted19 to dominate the (tt,K) reac­tion are the natural parity "stretch states" obtained by coupling a particle-hole state An-1 to spin J = £p + If we consider nodeless os­cillator wave functions for which Rj£(r) ~  (r/b)11 exp(-r2/2b2), the form factor Fj(q) in plane wave approximation (PWA) becomesJ — zFj(q) = i(J+l)!!]2 ’ (8)where z = (bq)2/2. The cross section da/dft is proportional to Fj(q). Notethat Fj(q) vanishes at q = 0 for J ^  0 and assumes its peak value forJ = (bq)2/2 . (9)The condition (9) represents the optimum matching of momentum transfer q and total spin J for the oscillator model. Note that ©l = 0° for (tt,K+)11250 150q (M eV /c ) 250 350 450corresponds to a large value q = q0 ; values of q < q0 are not accessible to experiment. The value q0 usually exceeds the optimum value (2j)1/2/b of Eq. (9), so that one is already past the peak of Fj(q) for ©l = 0° , and the (ir+ ,K+) cross section is a de­creasing function of 0E j as shown in Fig. 4 for the (ap3/2 ® np3/2)2+ con_ figuration in ^C. In PWA, the same Fj(q) describes the (K” ,Tr“) process, except that 0 = 0 °  now corresponds to small q, and the cross section for a J 4- 0 state peaks at a finite angle.Distortion effects suppress the magni­tude of the cross section [differently for (K~,tt”) and (tt+ ,K+)], but have only a minor influence on the angular shape.The question now arises: What is the highest spin An-1 state that one can manufacture in a given hypernuc­leus? For systems with A > 40 or so, calculations with a A-nucleus poten­tial, whose depth V0 «  30 MeV is ad­justed to reproduce ground state binding energies of light systems, yield the conclusion19 that the A orbit corresponding to the last bound nucleon orbit is a single-particle resonance in the continuum. For typical sys­tems like t+8Ca, 90Zr, 188Ba and 208Pb, which have closed j = I  + 1/2 neutron shells with H = 3,4,5 and 6, respectively, the corresponding A orbits lie at roughly 5-6 MeV in the continuum. The elastic width of these A states becomes narrower as A increases (rEL «  2.4 MeV for the If in ^Ca, rEL «  0.3 MeV for the li in 20^Pb) , so they could be observable as relatively narrow An-1 states, even though they are unbound. The high-bqFig. 4. Form factor F(q) for the (K“ ,ir_) and (tt+ ,K+) reactions, leading to the (ap3/2 ® np3/2)2+ state of ^C, assuming b= 1.64 fm, P£- = 800 MeV/c and p7r+ =1.04 GeV/c.est spin An states that we anticipate are then obtained by coupling13Fthese single-particle resonances to n-1 states: 2®Si, ^Ca, 9{{Zr, 1C!^ Ba, and 20^Pb are good candidates, since n_1 also has high spin. We can also couple the A in the next lowest orbit to n-1 unit of J. We findgiving states with one lessand so forth. In Fig. 5, we show these high spin states on a J vs. A plot, along with continuous curves corresponding to the optimum matching condi­tion (9). The A dependence of the optimum J arises from the oscillator radius parameter b, which we have taken as proportional to A1^ 8. Note that q decreases with increasing p^, so that by varying p^ we sweep out a band of optimum J values. The elementary ir+n -* K+A cross section peaks(10)113Fig. 5. Optimum J of Eq. (9) for (tt+ ,K+) as a function of target mass number A for several incident pion momenta. The dots indicate the available natural parity stretch con­figurations for various A hypernuclei.Fig. 6. Differential cross sec­tions for the (tt+ ,K+) excitationof high spin states in 9^Ca. The solid curves correspond to using Woods-Saxon wave functions for n-1 and A, while the dashed curves use oscillators.near p-^ = 1.04 GeV/c, but remains sizable up to about 1.5 GeV/c. From Fig. 5, we see that for light systems such as 2^Si or 9j(Ca, the highest spin state is very well matched at1.04 GeV/c, so the largest (tt+ ,K+) cross sections are to be expected for these states. For heavier hypernuclei,we are no longer well matched at 1.04 GeV/c, so smaller cross sections will result. In Ref. 19, estimates of (ir+ ,K+) cross sections are given for a range of targets and incident momenta, using PWA, DWIA and eikonal approx­imations. A typical DWIA theoretical prediction19 is shown in Fig. 6 for 1+0Ca(ir+ ,K+)1+^ Ca* at 1.04 GeV/c. The cross sections for stretch states decrease when J is decreased, but by less than a factor of two per unit of J. Hence several states should have measurable cross sections. The results shown in Fig. 6 are reduced by only about a factor of 5-10 with respect to PWA estimates, since the K+ is weakly absorbed in the exit channel. The corresponding 0° excitation functions are shown in Fig. 7.The dominance of the high spin states is clear. The (asi/2 ® n^i/2)ground state configuration is only weakly excited, for instance. Since q is large, the quasifree spectrum is rather flat [unlike that for (K-,Tr-)],but extends over a wide range of excitation energy 10. In Fig. 8, we dis­play the predicted19 (tr+ ,K+) excitation function at 0l = 0° for an 160 target, including both the A and E regions. For the excitation of E states, the use of the (7r- ,K+) double charge exchange reaction is more ap­propriate than (ir+ ,K+), since it filters out the isospin 1 = 1/2 states in |c, and also suppresses the A quasifree background, which is seen to belarge in Fi|. 8, even in the E region.The (ir-,K+) reactions could open up a new domain of hypernuclear structure physics. The high spin "stretch" states discussed here are of a particularly simple structure, since only one An-1 configuration of the114Fig. 7. Predicted excitation spec­trum at 0° for tf0Ca(Tr+ ,K+)ltj|Ca at 1.097 GeV/c. Summed cross sections for various An-1 configurations are indicated.Fig. 8 .  Spectrum for the 1 6 0 ( tt+ , K + )  process at 0°, including both A and Z hypernuclear states, as a function of excitation energy co.maximum J exists. In heavy systems, the "spreading width" of very high spin states will be less than that for lower spins, since there is a lower density of compound states (2p 2h, etc.) of the same spin. Thus narrow excitations may exist, even quite high in the continuum. There is as yet no experimental data on the (ir+ ,K+) reactions, but an experiment is planned20 for the Brookhaven AGS. Experiments at TRIUMF, SIN and LAMPF are not feasible at present, because the available pion momentum is insuf­ficient. However, a kaon factory producing K- and K+ beams should also be designed to yield intense t t ±  beams in the 1-2 GeV/c regime.4. DOUBLY STRANGE HYPERNUCLEIThe (K“,K+) reaction has been suggested21 as a means for exploring the spectroscopy of hypernuclei with S = -2. A E“ hypernucleus can be produced in the one-step process K“p ->■ K+E“. The E- state subsequently decays via the strong conversion S“p -*■ AA. Alternatively, a AA hypernuc­leus may be formed by the second-order process K"p -* tt°A followed by TT°p K+A. The cross sections are very small for the production of double hypernuclei, as we see below, so current K- beam intensities are probably not adequate to obtain definitive results. An intense K- beam (momentum range 1.1-1.4 GeV/c) from a "kaon factory" would be required in order to realize the full potential of the (K”,K+) reaction. Such studies would be of fundamental interest from several points of view: a) to explore a newtype of hypernuclear spectroscopy; b) to shed some light on the nature of SN and AA interactions,thereby extending our knowledge of the SU(3) structure of baryon-baryon forces; c) to exploit the possibility of ob­serving narrow E states in nuclei; and d) to provide a possible test for bag model predictions22 of a strangeness -2 dibaryon, the H.Two events corresponding to double hypernucleus production are known from emulsion work23 (y^He and j^Be). These are identified by tracks corresponding to two successive weak decays A -»• pir“. In the case of AAHe> the first step is a K +p K +n reaction, followed by the slowing down of the S“ in the emulsion, and finally the capture process E“+12C -*■ Li+^He.121P,ob(MeV/c)Fig. 5The mean free path in nuclear matter as a function of lab momentum for various projectiles. Taken from ref. [ 2].By approximating the above expression with a factorized form one obtains the simple "tp" optical potential, the most com­mon variation of which is the Kisslinger form:V(£,t') <V ACbQ+bj ic-t’jpCq). (2)Here p(q) is the Fourier transform of the ground state nuclear density and t ^  is the on-shell two-body t-matrix. This potential suffers from several difficulties which arose originally because of the desire to use these potentials in coordinate space. The principal problems are the zero range of the interaction, its off-shell 8oobehavior, and the omission of d-wave and higher £-value ampli- . tudes in the two-body t-matrix. Nonetheless, coordinate space codes using the Kisslinger potential for analysis of elastic tt and K data26*27 are in wide­spread use.Many of the shortcomings mentioned above for the "tp" potential can be cured by working in momentum space. This was first elucidated by Landau, Phatak and Tabakin,21 who wrote a more general form for the two-body t-matrix:go WgpfK')—  ----- P^cose). (3)In this form t^ represents the on-shell two-body information and g£ the off-shell form factors. The resulting optical potential can then be inserted into a relativistic Lippmann-Schwinger momentum space calcu­lation (PIPIT, ref. 28) to generate elastic cross sections. Some results will be shown below.As an indication of the influence of nuclear effects on the basic two body physics, Rosenthal and Tabakin5 examined the role of Fermi motion in determining the propagation of K”N resonances in nuclei. To do this they averaged the two-body t-matrix over the nucleon momentum distribution in the nucleus, which was constructed from momentum space harmonic oscillator wavefunctions. The results are shown in fig. 6, where Kisslinger parameters bg and bj with and without Fermi averaging are plotted. It is disappointing that the presence of the two body resonances is so greatly muted by the averaging procedure. It appears that it will be difficult to learn about some aspects of resonance propagation due to momentum smearing.= IIJJAhhFig. 6The effect of Fermi averaging (dashed curves) on the Kisslinger parameters bo and bj. The solid curves are the unaveraged values. See ref. [5].Fig. 7(Upper) Pie diagram showing the divi­sion of TT-nucleus Hilbert space into entrance states (P), doorway states (D) and reaction states (0). (Lower) Dia­gram showing formation of tne A-hole state and its dependence on g^N^, the A propagator and the nuclear medium (hole state).Let us now turn our attention to another way of describing meson- nuclear interactions, one which focusses directly on the formation of resonant structures as the principal feature of the interaction.29-35 This model stipulates that the incoming meson interacts with a single nucleon, forming a baryon-hole state which acts as the "doorway" to all other states. The baryon thus formed, and which propagates through the nuclear medium, may have properties which are quite different from those in free space because of its interaction with the medium.These ideas find an extremely natural expression in the projection operator formalism of Feshbach.29 "Doorway" ideas were first applied to pion scattering by Kisslinger and Wang30 and extensively studied by groups at MIT and SIN,31*32 Erlangen,33 and Regensburg.3  ^ They have also recently been applied to kaon scattering by Kisslinger.6 In all models of this type, the meson-nuclear Hilbert space is broken up into three segments (see fig. 7). These correspond to (1) the entrance channel and any other states which are to be treated explicitly, labelled P; (2) the possible doorway states, labelled D; and (3) the remaining states, labelled Q, which account for reaction processes. In the usual formulation all states Q must be reached by passing through D; D may also decay back to P thus allowing for elastic scattering. However, in cases where true absorption may take place, some direct coupling between P and Q should be allowed.30 Fig. 7 also shows schematically the formation of the A-h state in pion scattering and indicates the dependence of the process on the irNA coupling constant123and the A propagator G^h- Thus, the theory allows very naturally for the formation, propagation and decay of the resonance and the influence of the nuclear medium. It also allows one to include nucleon recoil and non-localities in the interaction, which are known to be present.As one might expect, such a theory works best in the cases when strong resonances are present. If the absorption takes place in the surface region of the nucleus rather than the entire nuclear volume, rather few baryon-hole states will be available. The resulting matrix can be diagonalized to provide wavefunctions for the system, as is the case for nuclear shell model calculations. Even so, such calculations can be very cumbersome and have been limited to light nuclei.31-34 However, the Green function techniques now in use by the Seattle group35 promise to make possible calculations in much heavier systems.SOME K1 SCATTERING DATAAnalysis of BNL experiment 692 has recently been completed.36 The experiment involved elastic and inelastic scattering from 12C and 40Ca at 800 MeV/c. It is of interest to compare these data with some of the theoretical calculations outlined above. An interesting side aspect of the experiment was the simultaneous accumulation of rather high quality tt~  elastic data in an energy region where no previous data exist. Some of these latter data will be discussed below.All data were accumulated at the Moby Dick spectrometer installation at BNL. A schematic diagram of the apparatus is shown in fig. 8. The device is in reality two spectrometers symmetrically placed about the target location. Each arm is about 8 m long, and together with the LESB I channel (see figure 16), make up a flight path of roughly 24 m. At the momentum of our experiment only 10% of the kaons survive to form good event triggers. The tt/K ratio at the entrance to the spectrometer was about 12/1, so that pion counting statistics were quite high. The kaon rates at the target for 4 x IO12 protons on the production target were 20,000 and 60,000 for K" and K+ respectively.The larger elementary cross sections for K"N over K+N nearly equalized the number of scattered particles for each sign of kaon. Kaons were well identified using a combination of time-of-flight measurement and Fitch Cerenkov counter techniques. Pions were not so well identified and that part of the experiment suffers uncertainties due to muon con­tamination. A typical spectrum for kaons is shown in fig. 9; the resolution is about 2 MeV.All of the data were normalized by measuring the scattering from hydrogen in a CH2 target. This was done at several angles for all pro­jectiles; the results are shown in figure 10 for kaons. Running on the CH2 target allowed a direct normalization of carbon scattering to hydrogen scattering. For the kaons, an additional check was possible by observing "straight-through" decays K->yv. Results of this check com­pared well to our Monte Carlo simulation of the spectrometer acceptance.Let us now turn to an examination of the data. Figure 11 shows all of the elastic K1 data on 12C and 40Ca. The data extend roughly over the angular range from 3 to 38 degrees. (We were limited at the upper124^ S2*  oA p2i '  P19} '/ *  1CK Kaon' SI spectrometerFig. 8. Schematic diagram of Moby Dick.E x c i t a t i o n  E n e r g y  ( M e V  )Fig. 9. A typical K~-12C spectrum. Fig. 10. Comparison of K“-p data from this experiment to other data (see refs. 43,44).125c.m. Angle c.m . AngleFig. 11.Comparison of measured 56 differential cross sections for K“ elastic scattering on 12C and 1,0Ca to coordinate space optical potential calculations.The upper curves use electron scattering nuclear densities corrected for the finite nucleon size; the lower curves are uncorrected.end of the range by physical constraints of the spectrometer and also by counting rate.) The data for both nuclei fall rather sharply with angle and display minima which are characteristic of the nuclear sizes in­volved. However, they are not sharply diffractive because the basic KN amplitudes are not resonance-dominated or particularly absorptive. If one is so inclined, one might conclude that the K” minima are sharper than those for K+ , For both nuclei, the K+ minima are further out in angle (typically a- 3°) than for K~^ indicating, if the language of dif­fraction theory is correct, that K sees a smaller nucleus than K".Shown also in fig. 11 are calculations using the coordinate space optical potential program NPIRK.26 The predictions shown were generated5 using the Kisslinger form of the optical potential, eq. 2. The complex parameters bp and b^ were generated using the best available phase shift information, and correspond in the theory to KN s- and p-waves respectively. For K+ , our data show a clear preference for the results obtained by B. R. Martin10 over the earlier work of the BGRT collabor­ation.57 The parameters5 used for the K+ calculations are given in126Table I. In calculating the coefficients bg and bj, K+ partial waves s through f were used. Since there are ambiguities associated with the generation of optical potential terms in coordinate space corresponding to KN partial waves higher than the p-wave, all such higher waves were lumped together with the s-wave to yield an effective b0. In fact the bi term includes only the contribution from P0i, since it is the largest contributing amplitude.For the K~ calculations the amplitudes of Alston-Garnjost et al.8 and also of Gopal et al.9 were used, but there was no discernible dif­ference between them in predicting K~-nucleus scattering. In these calculations, all elementary partial waves were lumped together to give only an effective bo (see table I). No separate term in bj was included since the p-waves were all of equal size, or smaller, than the higher partial waves.Several effects (described above) which could conceivably be impor­tant have been left out of these coordinate space calculations. The Kisslinger potential has several known deficiencies, including a zero- range fundamental KN amplitude with unphysical off-shell behavior. In addition, the nucleon finite size, which must be removed because it is already included in the elementary t-matrix, must be extracted simply by alteration of the parameters in the ground state nuclear density.For all of these effects, there are considerably more precise models available in momentum space; these are described below. The so-called ’’angle transformation" was omitted from consideration in the coordinate space calculations because there exists no accurate way to admix properly the d, f, g waves with the s and p waves. Therefore, this effect was also left to the momentum space treatment.The curves shown for each case in fig. 11 correspond to different choices of the ground state density. The lower curves are obtained using unmodified electron scattering densities, while the upper ones are den­sities modified for finite size. For reasons not well understood, the K+ data prefer the modified densities while the K” prefer unmodifiedTable 1: Table of the optical model parameters calculated byRosenthal and Tabakin.5 The elementary kaon nucleon amplitudes have been taken from the analyses of Gopal et al.,9 Martin,10 and the BGRT group.37 Note that for the K", all of the kaon nucleon partial waves have been combined into a single complex parameter, bQ.Re(bQ) Im(bQ) Refbj) Imfbj)K"Gopal 0.61 0.84 - -12C Best Fitv +0.32 0.88 “KMartin -0.335 0.241 0.084 0.161BGRT D(i) -0.142 0.209 0.101 0.19812C Best Fit -0.445 0.010 0.035 0.082Cross Section (mb/sr)12710000tooIS. 0.010  12 2 4  3 6  4 8Fig. 12. Momentum space calcul- c.m. Angieations using PIPIT28.densities. However, the modified densities correspond to a smaller geometrical size and thus may correspond to deeper penetration by the K+ . The proper way of calculation using this particular coordinate space formulation is unclear, because while it is certainly true that the finite nucleon size is already included in the t-matrix and there­fore should not be "double-counted" in the nuclear density, using an uncorrected density is a conceivable way of mocking up range effects not otherwise included in the model. In any case the calculations, which are unadjusted, reproduce the essential features of the data. If the parameters bg and bj are allowed to vary, excellent agreement can be achieved (see Table I). This was done to describe the entrance channel as accurately as possible for the inelastic measurements des­cribed below. The phenomenological result is less absorptive than in the free K+N case.More accurate momentum space calculations also were done for these nuclei. The results for K* scattering from 12C are shown in fig. 12.In these calculations, the questions raised above regarding KN range, nucleon size, and inclusion of higher partial waves in the elementary t-matrix are correctly resolved in the context of a first-order optical potential. Good agreement is obtained for K~ scattering when the nuclear finite size correction is included; however, the difficulty in describing the K+-12C data still persists. The calculation is not very sensitive to changes in the off-shell form factor, and, as one would expect, the full distorted K+ result is hardly different from the Born approximation.Calculations of K“ scattering from 12C and lt0Ca using a coordinate space rendition of "doorway" theory have been made. This theory, which has been formulated for kaons by Kisslinger,6 seeks to describe the K“-nuclear interaction via the formation and decay of A and E resonances as the K" propagates through the nucleus. Kisslinger's paper provides a scheme for expressing these ideas in coordinate space using an optical potential of the form2EV(r) = A[- bQk2p + b^-pV + b2V2p + b3V4p] , (4)c.m. Cross Section (mb/sr)128Fig. 13. The 12C (4.44 MeV) data compared to DWBA calculations.Fig. 14. The quantity 4irr2p(r) for three different nuclear models.129where the coefficients bp through b3 are generated from the elementary phase shift information.8 The mediocre agreement of the theory with the data probably points more to the deficiencies of the coordinate space optical potential form given above than to problems with the basic doorway model. It is clear, however, that more work in this area remains to be done.The last results to be discussed are the inelastic scattering data obtained for the 2+ and 3" states in 12C at 4.4 MeV and9.6 MeV, respectively. The 2+ results are shown in figure 13 compared to calculations using the coordinate space distorted wave program NDWPI.38 As mentioned above, the elastic channel is described using a best- fit optical potential to the elastic data from NPIRK. The inelastic transitions are described using transition densities which are taken from electron scattering, as pre­sented by Gustaffson and Lambert.39 These are of the formr i L, , 2 4. -dr^PtrO) = r (a + b r + c r )e , (5)with the parameters a, b, c, d depending on the nuclear transition involved. Other values of these parameters can be found from a standard rotational model or from the particle-hole calculations of Gillet and Vinh Mau.90 The three densities so obtained are very different from each other, as shown in figure 14 and yield different predictions for the angular distributions. Comparing the electron form factor to the collective model shows that the former is much larger in the nuclear interior. For the K“, this does not matter so much. On the other hand, the K+ data obviously prefer the electron form factor. Since the transition density for a given state is the same for K” or K+ , theFig. 15. Schematic diagram of possible kaon beam line.Fig. 16. Present kaon beam line at BNL.130observed differences must be due to the distortions in the elastic channel. These clearly have a large effect on the inelastic scattering. This lends qualitative support to the statement that the K+ meson is a strongly interacting but highly penetrating "electron-like" nuclear probe. It is both interesting and satisfying that each of these tran­sitions can be so well described for different projectiles by a common transition density.During 1979 the Kaon Beam Line Working Group was formed. It con­sists of representatives from Camegie-Mellon University, University of Houston, Massachusetts Institute of Technology, Brookhaven National Laboratory, Los Alamos Scientific Laboratory and Argonne National Labor­atory. The purpose of this group was to evaluate the possibility of building a new kaon beam line in the United States and to recommend a course of action.With guidance from the Kaon Beam Line Working Group, H. Enge developed a beam line, some of whose properties are listed below:A schematic drawing of the beam line is shown in figure 15. The proposed design will allow for the possibility of extending the channel momentum to above 1.2 GeV/c by decreasing the bend angles of the dipoles. The decrease in bend angles is accomplished by physically moving D1 and D4 with respect to the rest of the channel. D1 through D4 are supercon­ducting 5 tesla dipoles. The new beam line will provide about 100 times more kaons per second than are now available at the present target location and a reduction of about a factor of 10 in the number of un­wanted particles in the kaon beam. The reduction in the number of unwanted particles will be achieved by a reimaging of the production target at the velocity slit before Q1 in figure 15.However, in view of the fact that a new kaon beam line may not be a reality until several years into the future, modifications to the present LESB-I beam line are anticipated to take place during the current year. The present LESB-I beam line and hypernuclear spectrometer are shown in figures 8 and 16. The kaon flux at the target location between wire chambers P4 and P5 is about 5 x 103 K“/1012 protons and the flux between Q6 of LESB-I and Q1 of the kaon spectrometer is about 4 x IO*4 K”/1012 protons. The proposed design change will consist of moving the experimenter’s target location to about the P2 location and either move the rotatable pion spectrometer forward to replace the kaon spectrometer or fix the kaon spectrometer at a small angle and eliminate the pion spectrometer. The kaon momentum will be measured by tracing the kaons through the Q5, D3 and Q6 elements of LESB-I. The principal difficulty with such a move involves making a scintillation counter,A POSSIBLE NEW FACILITY AT BNLmomentumAnAp/pir/K ratio K”/1012 protons energy resolution750 MeV/c 6 msr ±5%13 x 105 500 KeV131x (cm)9 (mr )A  P/P (%)y (cm)<p Imr)- -  Actual data —  TURTLE predictionFig. 17. Comparison of beam study to TURTLE output.Q D 00</> (m r) g (m r)L E S B - I  Second Order 8eom Envelope Phase Space at Production Torqet x = ± 0 .6  cm 9 = ± 60 mr y = ±  0.06 cm = ± 8 mr g p /p  = + 2%Fig. 19. Resulting output of the beam line in figure 18.Proposed  Modification To L E S B - Iy focus x focus y focus8 0 2 4 8012 8 0 2 41 m e t e rFig. 18.132Cerenkov counter, and a wire chamber work efficiently in the high back­ground environment encountered between the mass slit and Q5 in LESB-I.We at Camegie-Mellon have studied the properties of the kaon beam at the proposed new target location. The study has been carried out using the program TRANSPORT41 and TURTLE.42 TRANSPORT was used to determine the field strengths of the beam line elements after the LESB-I mass slit and TURTLE was used to simulate a beam of kaons origi­nating from the production target. The following constraints were placed on the study:1) The beam line elements and tune upstream of the mass slit remain unchanged;2) The distance from the last element in the beam line to the target shall be no less than is now available at our present target location (0.88 meters);3) The kaon flux shall not be reduced by any changes made to the beam line.The TURTLE simulator assumes a kaon production target that is6.4 cm x sin 10.5 deg wide and a proton beam 1.2 mm high. The transport coordinates theta (6) , phi (<|>) and momentum range (6) were chosen large enough to cover completely the entrance phase space of the LESB-I beam line. TURTLE then transports these particles through the beam line, taking into account the aperature constraints presented by the various elements. Figure 17 shows a comparison of the turtle simulator output with actual data at approximately the new target location. The TURTLE results shown in the figure are gated by those events that make it through the kaon spectrometer (as are the real beam events). The dif­ference between the <f> measured and predicted distributions is principally due to the 5 mr angular resolution in the actual measurement.Figure 18 shows a schematic of a configuration that meets the criteria specified previously and allows one to adjust the x and y widths on the target to suit the experiment. The only change incorporated in figure 18 is the insertion of Q7 between Q6 and the target. The dis­tance between Q6 and the entrance quadrupole Q1 (see figure 16) has remained unchanged. Without Q7 a small y dimension is not possible at the new target location. In fact, the phase space shown in figure 17 is a result of a Q5 D3 Q6 tune which minimizes the y dimension at the target consistent with an x waist at the target. The target can be moved closer to Q6 with a reduction in the y dimension, however the x magnification becomes so large (3 to 5 from the target area to PI) that the momentum resolution is seriously degraded. Even with a target closer to Q6 the y dimension is still over 3 cm. The phase space for a tune of the QDQQ configuration which minimizes the y extent of the beam while maintaining a 6 cm wide waist in the x coordinate is shown in figure 19.All other combinations of three quadrupoles and one dipole were tried (i.e. QQDQ, DQQQ, etc.) and were found unacceptable because of low dispersion (about 0.5 cm/% from P3 to PI). The QQD and DQQ combinations proved undesirable because of grossly unequal x and y magnifications.133The momentum resolution obtainable with the QDQ or QDQQ combinations should be comparable. The tune giving the phase space shown in figure 17 gives a first order transport between P3 and PI ofX - -2.26 XQ + 1.74 «Pwhile the QDQQ tune giving the phase space shown in figure 19 gives (this time between P2 and PI).X = -1.91 XQ - .007 eQ + 1.63 6Pwhere X, 0, and <5P have respective units cm, mr and %. With 1 mm chamber resolution and 8 mr (0.5 deg) 0q resolution the first order momentum resolution will be about 1.5 x 10"3 in either case (1.1 MeV/c at 800 MeV/c). Equations (1) and (2) should be compared with similar transport equations for the present kaon spectrometer, for example, between P3 and PI in figure 16 we haveX = -1.82 XQ + .024 0Q + 3.51 6Pwhich gives a momentum resolution of about 8 x 10-lt (or 640 KeV at 800 MeV/c). The intrinsic resolution of the QDQQ spectrometer is there­fore about a factor of two worse than the kaon spectrometer resolution.The design presented in this section is one solution which looks attractive since it will give the experimenter flexibility in choosing the beam size at the target and does not require major modifications to be made to the beam line. However, the design study is not complete and more work remains to be done.CONCLUSIONSKaon scattering calculations at 800 MeV/c, using first order optical potentials in co-ordinate and momentum space, are in qualitative agree­ment with data obtained by the CMU-Houston-BNL collaboration. These data include elastic K* angular distributions from 12C and lt0Ca, and inelastic scattering angular distributions for the 2+ (4.44 MeV) and 3" (9.6 MeV) states in *2C. All the data are consistent with the idea that the K+ projectile penetrates more deeply into the nucleus than does the K”. Partial indication is that the elastic calculations are not able to predict simultaneously the K+ and K_ results with a common nuclear geometry. To obtain good agreement with all data the K cal­culations must incorporate smaller nuclear sizes.The inelastic data afford similar conclusions. The 2+ and 3“ dis­tributions have been calculated in DWBA using distortions generated by best fit optical potentials that describe the elastic channel data.When this is done, it is found that a standard rotational model form factor will describe the K" data fairly well while failing for the K+ .In fact, only the phenomenological electron scattering form factor can describe simultaneously the K and K" data. This distribution is peaked at a smaller radius than is the rotational model. In the surface region, where the K“ interacts, the two models are not very different. Further inside, where the K+ interacts, the differences are larger.134From the above, we conclude that the claim for the K+ , that it isthe "electron of strong interaction physics" has some validity. Itwould be quite interesting to explore systematically other nuclei to see if this claim is borne out, and perhaps to learn more about nuclear matter distributions away from the nuclear surface. For a program such as this, we need a more robust kaon facility.A partial step in this direction has been outlined in the latter part of the talk. There a new design for an interim improvement of the BNL kaon channel and spectrometer has been outlined. Such a facility would do much to help improve the quality and quantity of kaon data,and thus help make the case for a true kaon factory.ACKNOWLEDGEMENTSI would like to thank Peter Barnes, Phil Pile, Bill Wharton and Frank Tabakin for many useful discussions and much valuable information on the subject of kaon physics and beam design.REFERENCES* Work supported in part by USDOE grant DE-AC02-76ERO 3244.A006.1. J. M. Eisenberg and D. S. Koltun, T h e o ry  o f  M eson  I n t e r a c t i o n s  w i t h  N u c le i 3 John Wiley (1980); P r o c e e d in g s  o f  t h e  1979  I n t e r n a t i o n a l  C o n fe r e n c e  on H y p e r n u c le a r  a n d  Low E n e rg y  K aon P h y s i c s 3 Nukleonika25 (1980); P r o c e e d in g s  o f  t h e  Kaon F a c t o r y  W o rk sh o p , TRIUMF TRI-79-1; P r o c e e d in g s  o f  t h e  W orkshop on N u c le a r  a n d  P a r t i c l e  P h y s i c s  a t  E n e r g i e s  u p  to  31  GeV; Los Alamos Scientific Labs Report LA-8775-C.2. C. B. Dbver and G. E. Walker, Phys. Rev. C19 (1979) 1393.3. C. B. Dover and P. J. Moffa, Phys. Rev. C16 (1977) 1087.4. S. R. Cotanch, P r o c e e d in g s  o f  t h e  K aon F a c t o r y  W o rk sh o p , Voucouver, 1979 (TRIUMF Pub. 79-1).5. A. S. Rosenthal and F. Tabakin, Phys. Rev. C12 (1980) 711.6. L. S. Kisslinger, Phys. Rev. 22^ (1980) 1202.7. Y. Sakamoto, Y. Hatsuda and F. M. Toyama, Kyoto Preprint.8. Mi Alston-Garnjost, R. Kenney, D. Pollard, R. Ross, R. Tripp andH. Nicholson, Phys. Rev. D17 (1978) 2226.9. G. Gopal, R. Ross, A. Van Horn, A. McPherson, E. Clayton, T. Bacon and I. Butterworth, Nuc. Phys. B119 (1977) 362.10. B. R. Martin, Nuc. Phys. B94 (1975) 413.11. M. Betz and T.-S. H. Lee, Phys. Rev. C23 (1981) 375.12. L. Heller, in M e s o n -N u c le a r  P h y s i c s - 1 9 7 6 , AIP Conference ProceedingsNo. 33, American Institute of Physics.13. M. K. Banerjee and J. B. Cammarata, Phys. Rev. D19 (1979) 145.14. G. A. Miller, in M e s o n -N u c le a r  P h y s i c s - 1 9 7 9 , AIP ConferenceProceedings No. 54, American Institute of Physics.15. J. V. Noble, Nuc. Phys. A329 (1979) 354.16. C. B. Dover and R. H. Lemmer, Phys. Rev. C7 (1973) 2312.17. L. Foldy and J. Walecka, Ann. Phys. 5£ (1969) 447.18. W. R. Gibbs, A. T. Hess and W. Kaufman, Phys. Rev. £13 (1976) 1982.19. L. S. Kisslinger, Phys. Rev. 98 (1955) 761.20. M. M. Stemheim and E. H. Auerbach, Phys. Rev. Lett. 25_ (1970) 1500.21. R. Landau, S. Phatak, and F. Tabakin, Ann. Phys. 7£ (1973) 299.13522. K. Strieker, H. McManus, J. A. Carr, Phys. Rev. C19 (i979) 929.23. L. C. Liu and C. M. Shakin, Phys. Rev. C16 (1977)~T963.24. R. H. Landau and A. W. Thomas, Nuc. Phys. A302 (1978) 461.25. N. DiGiacomo, A. Rosenthal, E. Rost and D. Sparrow, Phys. Letts. 66B(1977) 421.26. R. A. Eisenstein and G. A. Miller, Comp. Phys. Commun. 8 (1974) 130.27. M. D. Cooper and R. A. Eisenstein, "FITPI", Los Alamos ReportLA-5929-MS (unpublished).28. R. A. Eisenstein and F. Tabakin, Comp. Phys. Commun. \2_ (1976) 237; and work in progress.29. H. Feshbach, A. Kerman, and R. Lemmer, Ann. Phys. 41_ (1967) 230.30. L. S. Kisslinger and W. L. Wang, Ann. Phys. 9£ (1976) 374.31. M. Hirata, J. H. Koch, F. Lenz and E. J. Moniz, Ann. Phys. 120 (1979)205.32. Y. Horikawa, M. Thies and F. Lenz, MIT Preprint CTP #844.33. K. Klingenbeck, M. Dillig and M. Huber, Phys. Rev. Lett. 41_ (1978)387.34. E. Oset and W. Weise, Nuc. Phys. A329 (1979) 365.35. R. A. Freedman, G. A. Miller and E. Henley, Univ. of WashingtonPreprint RLO-1388-842.36. D. Marlow, P. Barnes, N. Colella, S. Dytman, R. Eisenstein,F. Takeutchi, W. Wharton, S. Bart, R. Hackenberg, D. Hancock,E. Hungerford, B. Mayes, L. Pinsky, T. Williams, R. Chrien,H. Palevsky, R. Sutter, in progress.37. G. Giacomelli, P. Lugaresi-Serra, G. Mandrioli, A. Minguzzi-Ranzi,A. M. Rossi, F. Griffiths, A. A. Hirata, I. S. Hughes, R. Jennings,B. C. Wilson, G. Ciapetti, G. Mastrantonio, A. Nappi, D. Zanello,G. Alberi, E. Castelli, P. Poropat, M. Sessi, Nuc. Phys. B71 (1974) 138.38. R. A. Eisenstein and G. A. Miller, Comp. Phys. Commun. 11_ (1976) 95.39. C. Gustaffson and E. Lambert, Ann. Phys. Ill (1978) 304.40. V. Gillet and N. Vinh Mau, Nuc. Phys. 54 (1964) 321.41. K. L. Brown, D. C. Carey, Ch. Iselin, and F. Rothacker, CERN 73-16 (1973).42. K. L. Brown and Ch. Iselin, CERN 74-2 (1974).43. C. J. Adams et al., Nuc. Phys. B66 (1973) 36; and S. Focardi et al.,Phys. Lett. 24B (1967) 314.136EXOTIC ATOMSJ.D. Davies University cf Birmingham, Birmingham, UKABSTRACTExperimental data on and theories concerned with hadronic atoms are surveyed. Success and failures in the fields of chemistry, particle properties, hadron-nucleon scattering lengths and nuclear structure are examined to provide a program for a kaon factory. Some pion data are included to show what can be done with good quality beams.There have been few hadronic atom experiments in the last few years save at the pion factories. This is principally due to the poor quality of suitable K" and f> beams (E~ are made from K“ captured in the experi­mental target); in comparison with pion beams, they are a) reduced in in­tensity by 102-103 b) few in number— the Bevatron and Nimrod have been terminated while beam time is very rare at the Brookhaven AGS or CERN PS c) have large emittance, momentum spread and contamination e.g. ir/K~10-60.In other than matter of lowest density, a it", K‘, p  or I (labelled as h”) slows, is captured into an atom— replacing an electron— and then cascades down to the one or two levels within the outer range of the nuclear matter distribution that are detectable, all in~10~12 sec. For a point charge nucleus, QED giveswhere y = reduced hadron mass, k = £ for it- or K~, k = j for p or E“ . Capture occurs when the velocities of valence electrons and h” match, for which n ~ 30-40, with a statistical, 2 £+1 angular momentum distribution as good as any. The initial cascade is via Auger transitions down to n~10 where radiative dipole emission becomes important; for both,A£ = 1 (An = any allowed energetically) transitions dominate. Thus circular, £ = n-1, orbits are formed. NB an £ = 0 state is a straight line through the nucleus from whence it is removed from the game.The game is to obtain X-ray line spectra to study three ranges of interest around the nucleus:A) r(h“) ~ r  (valence electrons) —  the domain of chemistry and solid state physics which have large effects on the yields of inner transitions.B) r(e“ min.) > r(h") > r (nuclear matter, max.). Here QED calculations of transitional energies, fine splitting and hyperfine splitting give m^-, Up- and y£- (magnetic moments) and Q (spectral quadrupole moment) of de­formed nuclei respectively. This region is inside the orbiting electrons and outside the range of the nuclear force.C) r(h”) ~  that of the outer nuclear force/matter distribution which affects the QED predictions.INTRODUCTIONaverage h” radius, r = (1)( 2)137For regions B) and C), the QED energy levels are those of a one orbiting particle system with small, calculable corrections. The X-ray energies are in the range few (keV-MeV). Typical detectors are:SiLi for <50 keV, e.g. 300 mm2 , 250 eV at 5.9 keV FWHM resolu- solid tionstate GeLi for >50 keV, e.g. 4 cm3 planar, 600 eV at 122 keV FWHMresolution; 70 cm3 coax., ~1.7 keV at 1.33 MeV FWHM resolution gas proportional for large areas and low energies, e.g. -2.0 kV at5.9 keV FWHM resolutioncrystal spectrometer for 10-70 keV, having eV resolution and 10-6 acceptancePion contamination of K", p beams provides a little known rate limi­tation of solid state detectors that already has been reached with SiLi detectors of optimum resolution. These have slow optical feedback to com­pensate the large amounts of energy deposited by charged particles which, to first order, are proportional to the pion interactions in the degrader.Most factual data up to 1980 can be found in the good, large, compre­hensive review by Batty1 which also includes technique, analysis and theory.REGION AFor a given, inner transition there are changes in yield up to a factor four between a) neighbouring elements in the periodic system2 and b) elemental form and chemical compound, e.g. the yield of the n = 4 ->- 3 line in 12C changes from 0.36 X-rays/atom in graphite to 0.08 in PVT.3 In a gas mixture, exotic atoms are formed in the ratio ni(Zi)X/n2(Z2) where X > 1, Z^ > Z2, n2 >> n^ and n is the atom density; however there is a large reduction in the ratio no. inner transitions/no. outer transitions for the higher Z element between pure gas and mixture.1*Thus small changes in the outer electron structure provide large changes in the number of h~ reaching the lower energy levels, presumably by increasing the fraction of high n, low i  states. The rapid removal of low Si states magnifies the effect for hadronic atoms although most work has been done with muons. It is possible that the effect increases with i%_. Hadronic, exotic atoms could provide a powerful tool in chemistry and solid state physics. Presently there is little phenomenological law and theoretical content.REGION BParticle propertiesMeasures of 1%  and yp, gp, y^- are given in Table I. The errors in the corrections to Eq. 2— finite nuclear size, electron vacuum polariza­tion (ctm (Za) 2n+l) , electron screening, nuclear polarization— are compar­able to the uncertainties in the reference source energies, viz. a few eV. These are the principal contributions to the errors in 1%- thus illustra­ting the sophistication of the line shape fitting which allows for detec­tor response function, competing X- and y-ray lines and a continuum back­ground. K“, “p and E" mass measurements are limited by statistics as are those of y^ and y^-.138Table I. Hadronic masses and magnetic or yk MeV or nucleon magneton Method" 139.5686 + 0.0020 GeLi 5tt" 139.5667 + 0.0024 Crystal spectrometer 6tt+ 139.5652 + 0.0019 y momentum from ir-*-yv 7K" 493.691 + 0.040 GeLi 8 ) No otherK" 493.657 + 0.020 GeLi 9a accuratemethod+ 938.2796 + 0.0027P +2.793-  938.179 P -2.791+.+0.0580.021GeLi 10a-  938.130 P -2.817++0.1300.048 GeLi llb1197.24 Z -1.40++0.150.410.28GeLi transitions in Pb 12a£”1197 .43 + 0.08 Recoil momenta from K“p+ 13E" -1.48 + 0.37 GeLi 14ba same group; b same groupThe fine structure splitting is given bya _  , o \  ( a Z )_ 4 yn » £ ( 8 o  +  2 g l )  2 n 3 £ ( « , + ! ) (3)where magnetic moment, y^- = (g0 + gl)VH> go is the Dirac factor (equal to particle charge), gi is the Pauli or anomalous term and all quantities are expressed in units of the appropriate hadron magnetonehyH - 2mh-c •To keep a consistent notation, y is the reduced hadron mass. Even for those orbits of high Z atoms closest to the nuclear surface, splittings are only comparable to the GeLi resolution. The two measurements of yj;- are not independent since they use the same technique, accelerator, ... Theoretical predictions, normalized to yp and yyv, are usually significant­ly smaller than -1.48 n.m., thus Brown with the cloudy bag model obtains -0.58 n.m.15 However, Thomas e£ al. with a fuller calculation in the cloudy bag model claim -1.08 n.m."1"^Deformed nucleiThe spectral quadrupole moments, Q, of high Z nuclei with I £ 1 can be determined to a few % from the hyperfine splitting of exotic atoms.The method is the most accurate since the anomalies in the calculation of multi-electron systems and in the electric field inhomogeneity at the nucleus do not exist. Figure 1 shows the splitting of the 7 -> 6 line in kaonic holmium,17 the other background lines, the large continuum and the lack of statistics; Fig. 2 has the X-ray spectrum of tt- on natural rhenium.18 Table II gives various measures of Q for 181Ta.E N E R G Y  K E VFig. 1. Kaonic holmium 7 -*■ 6 transition. The fitted com­ponents of the peak are shown: (1) 7 -* 6, (2) Ilk -* 8j ,(3) llj -> 8i and (4) 8+ •> 6+ y-ray transition in 156Dy.17Fig. 2. The prompt y-ray spectrum from pions stopped in a natural Re target as measured with a large volume Ge(Li) detector.18140Table II. Spectroscopic quadrupole moments in 181Ta.Q(barns) Method Ref.3.30 ± 0.12 K“ atom, 7i level 173.28 ± 0.06 V- atom, 4F level 183.35 ± 0.02 ir" atom, 4F level 173.30 ± 0.12 Coulomb excitation (0-KL) 19Compared with using pionic atoms to determine Q, the use of muons is more model dependent and has a greater contamination from background lines. For the mesic atoms kaonic X-rays show a wider spread17 and hence greater sensitivity but presently suffer from a lack of statistics.The spectral quadrupole moment determined from higher transitions is then used with inner lines to determine strong interaction effects. With increased accuracy, it may be possible to determine mass quadrupole den­sities .REGION CFor several reasons Z = 1 atoms are peculiar and will be considered together at the end of this section.Here the outer nuclear force affects the energy levels: scattering shifts the levels which are broadened by absorption (reduced life-time). The largest effects are for the last observed circular orbit which varies between n = 1 for %  to n = 7 for 238U. One measures the shift e from, and the broadening T of, the QED predictions.Absorption from the next highest level has an e,F not directly measurable. However, the width of the upper level can be determined from the yield, Y, of the U -*■ L transition compared with all channels feeding the upper level;rUru+ rL 'The various theoretical models fall between two extremes— the purely microscopic calculation restricted to the lightest nuclei and the pheno­menological optical potential whose parameters are adjusted to fit the data when inserted into the Klein-Gordon equation. These parameters can then be expressed in terms of the basic hadron-nucleon interactions. We will summarize the data in terms of phenomenological potentials and dis­cuss the deviations from such.Pionic atomsWith S and P waves dominant the potential is written asU = Us  + Up .US, Up are then expressed in terms of nucleon densities - Pn(r) and Pp(r)- the coefficients b0, bj, c0, c^ which can be represented by the pion- nucleon scattering lengths, ap and an , and the complex B0 and C0 which scale the pion absorption and which must be determined experimentally.Up provides a non-local potential and a non-linear term scaled by the factor E, coming from nucleon-nucleon correlation effects (called the Lorentz-Lorenz effect).1419  0The latest fits to the data give values for b0 ••• ci approaching those calculated from ap, an . Experimental data presently do not dis­tinguish between further extensions to the potential such as a different form for the Lorentz-Lorenz effect or adding terms for spin dependence in the n-N p wave.20 The same conclusion applies to the semi-microscopic calculations such as Alexander et al.'s allowing for the finite range of the tt-N p wave interaction.21For the lightest nuclei, microscopic calculations provide reasonable agreement with experiment and thus confirmation of existing concepts in the structure of light nuclei.16Consider the successes and failures of the optical potential model into which a considerable amount of effort has gone.i) A wide range of data has been well described with a few parameters. Further experiments have removed some of the low Z anomalies— e and F for the 2p-ls transitions in 3He;22>23 6T for 180-160 (Ref. 23)— but not all.24 Very broad states of high Z atoms depart from the predictions of the potential, e.g. the 3d states in 181Ta and 209Bi have e and F smaller by a factor of two or more.25 However, Ericson and Tauscher26 have proffered an explanation through the energy dependence of the local part of the ir-nucleus potential coming from the strong Coulomb potential.ii) Parameters are introduced and tested complementary in ir-nucleus scat­tering and exotic atoms. At TRIUMF27 an optical potential has been de­rived for ir-12C, ir“ 1 3C from low energy scattering and from atomic X-rays but further work is needed to check that there is one set of parameters.iii) The model does not yet have predictive power. With parameters fitted from one set of atom data, then the potential is used, through its ex­plicit dependence on Pn(r)-Pp(r), to determine the neutron density of a specific isotope. Most work has been with isotope pairs, e.g. 44Ca and 40Ca have been used to give a difference between the rms radii of the neutron and proton distributions of 44Ca of A(44) = rn (44) - rp(44) =-0.05 ± 0.05 fm,28 0.128 ± 0.065 fm,29 -0.01 to 0.07 fm20 for the real part.K~ and p atomsHere the long-held aim was, and is for the few, the determination of the outer nucleon (neutron in particular) distribution where the K” and pannihilate, being so strongly interacting.Reasonable data sets of e, Tl and are available but of smaller dimensions and poorer statistical accuracy than that for pions, p having the inferior. An optical potential of the formV = - —  ( l  + — ) a x p(r) , (4)W \ mN /when X = K" or "p, "a is an average, complex, effective, X-N scattering length and p(r) is the nucleon density distribution; distinguishing be­tween neutron and proton distributions is not justified by the present data. Batty1 lists and fits the data to obtainaK - (effective) = (0.35 ± 0.03) + i(0.82 ± 0.03)fm e and FL only;l ip  (effective) = (1.53 ± 0.27) + i(2.50 ± 0.25)fm.Other fits to more limited data sets and with different p(r) change a^ by±o and aR by ±(2-3)a but always having the above sign. Including142worsens the fit for kaonic atoms, presumably through our poor knowledge of the overlap of the kaon wave functions and the very outer nuclear matter distribution.Again the optical potential has not yet predictive power— shifts of -230 ± 72 eV and -330 ± 60 eV have been measured in the last observed transition, 3d-2p, in "p 6Li and p 7Li.30 The group then hoped to get apn (free) using the optical potential; however, this predicts small and smoothly varying shifts.E atomsK- and E“ atom data are recorded simultaneously. A K"-nucleus inter­action can give a low momentum E“ having a reasonable chance of escaping from the nucleus; theory31 and experiment both indicateNo. Z~ atoms ^No. K~ atomsA few yields were obtained at the Bevatron32 and the CERN PS.33 Shifts and widths for 5 light elements measured with very poor statistics at NIMROD gave31*aE (effective) = (0.33 ± 0.05) + i(0.14 ± 0.006)fm e and Tr onlywhen fitted to an optical potential of the form of Eq. (4). K-matrix analysis of E* p scattering by Alexander jit al. 35 provided a£jj(free) having aR in the range -0.1 to +0.1 fm and aj ~  0.5 fm.Now E_ hypernuclei have been observed in several light nuclei such as 6He with widths of 8-10 MeV.36 The free aj suggest widths too broad to be observable— strong coupling between the EN and AN channels— while aj (eff.) would have widths ~ 20 MeV. Mechanisms by several authors to generate narrow width are listed by Barnes.37 Stopien-Ruddha and Wycech38 have developed an optical potential that is consistent with E data from production with stopping K~, atoms and hypernuclei; this has an S~wave, separable, multi-channel E-N potential of finite range with an exclusion principle suppression of EN AN that increases with depth below the nuclear surface.Exotic hydrogen atomsBesides the creation of new forms of hydrogen, the great interest in exotic, hadronic hydrogen is the direct connection between the strong interaction shift and broadening of the IS level and the complex, S-wave h“-p scattering length ace + i T/2 = 4 E0 ac/a0 (5)where a0 is the Bohr radius and E0 the Bohr energy. The formula is valid if ac for the interaction radius is small compared with a0;39 originally there was a perturbation derivation.1+0There are many experimental problems:1) There is considerable Stark mixing; the small, energetic (h"p) atoms with no screening electrons have many close collisions with hydrogen mole­cules where the intense Coulomb field of the protons transfers many h“ to the S-state; yields are approximately proportional to collision rates and thus density. The cascade calculations of Borie and Leon1*1 agree with the poor data— 0.1% 2p-ls yield for K“p in liquid and 6% L X-rays in 4 atm, room temperature gas.1*3143Table III. QED X-ray energies.Atom X-ray energyTT"pkeVK-pkeVP P keVZ-pkeV2 + 1  (Kc) 2.43 6.46 9.37 10.503 + 1  (Kg) 2.88 7.66 11.10 12.453 + 2  (La) 0.45 1.20 1.74 1.952) Table III QED X-ray energies (very low and easily absorbed in windows)3) There are many contaminant lines, particularly from X-ray windows and from container walls struck by beam4) A large continuum background5) Stopping per centimetre of hydrogen which is poor and approximately proportional to density6) Large 2p absorptionThere are two types of apparatus: a) gas targets -> poor yield and bad stopping + large dimensions proportional counters of poor energy resolution; b) SiLi detectors with good resolution and very small area + liquid hydrogen target with bad yield and poor stopping.Those experiments having positive results are (plus one other):Tr“p —  2p-ls seen with proportional counter in gasir“D —  a 2p-ls shift of -4.8^2 ]o measured with absorption edgesand proportional counter in gas; the small value is due to the cancellation between ap and an p" p, pD —  L X-rays seen in gas with proportional chambers1*3 K“p in gas with proportional counters —  kaon decay dominate1*5 Two experiments have claimed results for K“p in liquid hydrogen.Izycki et al.1*6 used a conventional system having flask and X-ray windows of mylar and SiLi detectors outside the target vacuum, with crystals unshielded from mixed metal, vacuum vessels. Consequently their reported spectrum contains very many lines, with some unlabelled, amongst which is claimed a Ka-Kg-Ky pattern with the QED separations of Table III; cascade calculations1* 1 indicate comparable intensities for these lines. This would give for the Is level e = 270 ± 8 0  eV, T = 560 ± 260 eV or ac = (0.66 ± 0.19) + i(0.68 ± 0.32)fm.The Nimrod experiment1*2 had a SiLi detector which penetrated the target vacuum and was collimated to see Be windows and Al not in beam and hydrogen high purity metals being used. Their reported spectrum has two lines, both clearly seen. If the lower one is identified as 2p-ls trans­itions, giving e = 40 ± 60 eV, T = 0.00 1 q !oo keV or ac = (0-10 ± 0.15) + i(0.00 ^Q’Qg)fm, then the upper line could be Cu fluorescence and it Be X-rays obscuring the K”p Kg line.From an analysis of low energy KN scattering with dispersion rela­tion constraints, Martin1*7 obtained as = -0.66 ± i 0.71 fm. Now the low energy K“p and K“ nucleus systems are dominated by the A(1405), below mK + mP = 1432 MeV, and the K"N potential is attractive and strongly absorptive. This leads to an apparent anomaly; if the interaction were weak with perturbation calculations applicable, then a repulsive poten­tial would be indicated by a negative real part of as; however, this sign, of the real part, is determined by the absorption when strong.The discrepancy between as and ac is a mystery— if either experiment is correct. as refers to the neutral kaon-nucleon system and ac to the144K“p+ combination which has threshold and Coulomb corrections; however, the latter would have to be very extreme to attempt reconcilation. It should be remembered that 1) QCD cannot explain the A(1405)-A(1520) mass difference, 2) A(1405) could be a bound state or a resonance, and 3) the atomic line shape must depart from the Breit-Wigner form to conserve uni- tarity; for the K“p system direct photon emission to the bound state can be comparable to the more usual atomic transitions.1+8As a final note of warning, K"D X-ray intensities will be reduced by at least a factor of 10 compared with K_p because of the smaller atomic radius around a large nucleus.Rationale between ~a (free) and a (effective)The Martin analysis47 gives "a^ - (free) = -0.16 + i 0.69 fm to be com­pared with a£- (eff.) = (0.35 ± 0.03) + i(0.82 ± 0.03)fm from kaonic atoms. Almost certainly a major part of the discrepancy comes from the effective mass of the K 'p' system in the nuclear potential being closer to 1405 than 1432 MeV. There are many theories— see Ref. 1— with differ­ent emphases giving reasonable but not good agreement with experiment.As one example, for kaonic 12C and 32S, Brockmann et al.49 included many- body correlations and a non-locality due to propagation of the A(1405) which itself was shifted in position and width.The K"He system is most illustrative. The above a^ (eff.) would give e = 0.1 eV, T = 2.0 eV for the 2p level. In a preliminary experi­ment to Ref. 42, e = -35 ± 12 eV and T = 30 ± 30 eV were obtained. 0Presumably the very strong binding of the protons in the a-particle gives a K ’p' effective mass very close to 1405 MeV. Both hydrogen and helium experiments have been repeated at CERN; confirmation of the large shift and width of the 2P K"He level, with better statistics, has been given.51There are no low energy scattering experiments giving a (free) for the "pp system. There is strong absorption and models usually give nega­tive a^, e.g., the static potential of Bryan and Phillips52 gives a (free) = -0.92 + i 0.70 fm. The discrepancy with the sign of 1 r (eff.) is no problem with our present lack of knowledge. Although there are no knownbound states below threshold, there is a wealth of baryonia and the "ppsystem is coupled to the many resonances of the tht system.PRESENT AND PLANNED EXPERIMENTSiTp and irD atoms are being re-examined in gas with 1) a crystal spec­trometer at LAMPF using graphite to reduce absorption (signal to noise of 1:20 still) — a preliminary report53 gives a 'irD' 2p-ls shift comparable to that of Ref. 44B; and 2) a SiLi detector and absorption edges at TRIUMF.The authors of Ref. 14 are reconvening to remeasure y£- with improved GeLi, electronics and software and a series of thin, heavy metal plates in liquid hydrogen in which 46% of the K” interact via K“p -* I_ir+ . About half of the E~ escape decay to stop in the heavy metal and the tt+ provides an excellent handle.The Low Energy Anti-proton Ring (LEAR) at CERN should provide 106 p/sec with dp/p ~  10-3 and no contamination, at 600, 300 and possibly 100 MeV/c. Approved p atom experiments include three using hydrogen and deuterium gas. Their apparatus are 1) the target of Ref. 42 rebuilt with Compton suppression and 4ir scintillator to distinguish singlet and trip­let states, 2) low pressure gas and a reverse cyclotron to slow the "p and 3) an extended version of the target and proportional counters of145Ref. 43; however, its purpose is to use the type of X-ray — K or L—  to measure the angular momentum of the pp (pD) system. A high statistic measure of p atoms having Z >1 is also approved; initially it is hoped to use isotope pairs to get a^n (free); it is also considered that signifi­cant information on the very outer nucleon density can be obtained.39It should be noted that a crystal spectrometer has not been used with K“, p or E” atoms; for the Dirac particles there is a wealth of spin information.A HADRONIC ATOM PROGRAM FOR A KAON FACTORY1) Theoretical development to parallel the experiments.2) Apparatus development: a) crystal spectrometer; b) suppression of the continuum background which almost entirely comes from Compton scattering of higher energy y-rays. Bismuth germanate (BGO) with its smaller radia­tion length (25%) and greater mechanical strength— but less light (10%) —  may be preferable to Nal (Tl); c) large area detector of reasonable resolution. Probably there will only be small increases in area/unit cost for Si(Li) and Ge(Li) detectors. For the lower energies, a scintil­lation proportional counter may be the answer— this has a noble gas with an accelerating voltage just below that to give electron gain. There is an initial, fast light pulse and then secondary, proportional light of good resolution— 8% FWHM at 5.9 keV. Use for large areas has come from space research511 with focussing rings and photo-multipliers, and from CERN55 with a MWPC that also provides spatial information.3) (Light) E atom data to complement the E hypernuclei industry— there is an optical potential to be tested at the nuclear surface with atoms and with hypernuclei in the interior of the nucleus. A crystal spectrometer would be very rewarding.4) m^, m£- and y£- with crystal spectrometer.5) Search for Ka-Kg-Ky pattern with SiLi detectors in gaseous hydrogen and deuterium; deducing ^ p  will give information on p-wave annihilation about which little is known. For E- atoms it will be necessary to distin­guish singlet and triplet states.6) Having understood the Z=1 system to steadily increase the magnitude of Z. One may be able to use X-rays to give the angular momentum at capture, emitted pions to distinguish E(1385) and T(1405), nuclear y-rays to give the identity of the residual nuclei and how they were formed. This should give information on a) the outer nuclear surface through its strong effect on e, TL and Fu (Ref. 56) even if present theory and experi­ment does not allow much exploitation, b) the propagation of E(1385) and A(1405) in nuclear matter. There is considerable interest in baryon ex­citations in nuclei but energy resolution confines such to the well sep­arated, lower members, presently N* and A. Several authors have suggested 'other quark' excitations, e.g. Moniz for the Y 's.577) Exotic atoms may provide some of the more sensitive tests for a) kaon- nucleus bound states, b) a long range component of the strong interaction, e.g. glueball exchange; so far this has been tested from pion data and rather old p and K~ data.58ACKNOWLEDGEMENTSThese are gratefully made for the pleasure of and the benefits from discussions with C.J. Batty, L. Tauscher and the private communications below and to Mrs. P.M. Richens.146REFERENCES1. C.J. Batty, Rutherford RL-80-094.2. R.M. Pearce et al., Can. J. Phys. 2084 (1979).3. G.L. Godfrey and C.E. Wiegand, Phys. Lett. 56B, 255 (1975).4. H. Daniel ^  al., Z. Phys. A275, 369 (1975).5. A.L. Carter jit al., Phys. Rev. Lett. J7, 1380 (1976).6. V.N. Marushenko jet al., JETP Lett. 23, 72 (1976).7. M. Daum et al., Phys. Lett. 74B, 126 (1978).8. G. Backenstoss et al., Phys. Lett. 43B, 431 (1973).9. S.C. Cheng etj al., Nucl. Phys. A254, 381 (1975).10. E. Hu et^  a]L. , Nucl. Phys. A254, 403 (1975).11. B.L. Roberts, Phys. Rev. D 17, 358 (1978).12. G. Dugan et al., Nucl. Phys. A254, 396 (1975).13. P. Schmidt, Phys. Rev. 140, B1328 (1965).14. B.L. Roberts et al., Phys. Rev. D L2, 1232 (1975).15. G.E. Brown, Invited talk, 9 ICOHEPANS, Versailles, 1981, to bepublished.16. S. Theberge and A.W. Thomas, Phys. Rev. D Z5, 284 (1982) and private communications.17. C.J. Batty et al., Nucl. Phys. A355, 383 (1981).18. J. Konijn et al., Nucl. Phys. A360, 187 (1981).19. B. Elbek, University of Copenhagen thesis (1963).20. E. Friedman and A. Gal, Nucl. Phys. A345, 457 (1980).21. Y. Alexander jit a]L, Nucl. Phys. A356, 307 (1981).22. G.R. Mason t^_ al., Nucl. Phys. A340, 240 (1980).23. I. Schwanner et^  al., Phys. Lett. 96B, 268 (1980).24. A. Olin et^  al., Nucl. Phys. A312, 361 (1978).25. J. Konijn et al., Nucl. Phys. A326, 401 (1979).26. T.E.O. Ericson and L. Tauscher, Contribution 19 of 9 ICOHEPANS, Versailles, 1981.27. C.A. 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J. Bailey e^ t al., Phys. Lett. 33B, 369 (1970);44B. J. Bailey et al., Phys. Lett. 50B, 403 (1974).14745. J.D. Davies, private communication.46. M. Izycki et al., Z. Phys. A297, 11 (1980).47. A.D. Martin, Phys. Lett. 65B, 346 (1976).48. T.E.O. Ericson and L. Hambro, Ann. Phys. 107, 44 (1977).49. R. Brockmann et al., Nucl. Phys. A308, 365 (1978).50. C.J. Batty et al., Nucl. Phys. A326, 455 (1979).51. P.M. Bird al^ . , Contribution 133 of 9 ICOHEPANS, Versailles, 1981.52. R.A. Bryan and R.J.N. Phillips, Nucl. Phys. K5, 201 (1968).53. E. Bovet et al., Contribution 16 of 9 ICOHEPANS, Versailles, 1981.54. G. Manzo et^  al., Nucl. Instrum. Methods 177, 595 (1980).55. M.A. Feio et al., Nucl. Instrum. Methods 176, 473 (1980).56. R.C. Barrett and M. Krell, private communications.57. E.J. Moniz, Invited talk, 9 ICOHEPANS, Versailles, 1981, to be published.58. G. Feinberg and J. Sucher, Phys. Rev. D 2C), 1717 (1979).148PROGRESS REPORT IN HYPERNUCLEAR PHYSICS A. Gal*TRIUMF, Vancouver, B.C., Canada V6T 2A3 ABSTRACTNew developments in A-hypernuclear structure are reported in light of recent studies of the ( K " , T r - )  reaction at BNL, particularly on 13C. The smallness of the A-nucleus spin-orbit potential and the appreciable degree of coherence involved in the forward ^Z(K“ ,ir“)^Z reaction are discussed, suggesting a generalization in the former case and a breakdown in the latter case for E hypernuclei. Specifically, it is argued that the coher­ence generally expected in low momentum transfer production of E hyper­nuclei may substantially deteriorate, because a strong spin and isospin dependence of the EN interaction is likely to lead to a considerable energy spread of the ( K - , tt“ )  strength with occasionally large energy shifts for some states. Finally, several observations are made on widths of E-hyper- nuclear states, both from a theoretical point of view as well as in con­nection with the relatively narrow levels discovered first in CERN for ^Be and recently at BNL for |h. Further implications of the selectivity to the spin-isospin level structure argued for E-hypernuclear widths are suggested in 3He and 4He.INTRODUCTIONThe (K“,ir) nuclear reactions have for the last few years been the primary source of spectroscopic information on A hypernuclei, and quite recently also on E hypernuclei. This information is rather impressive, particularly in view of the insufficient quality of the available kaon beams relative to beams of other projectiles probing at present nuclear targets. With the advent of kaon factories one expects a reaffirmation of the dominant role played by (K“,tt) reactions in the study of hypernuclei, with two clearly defined goals in mind: (i) to unravel the structure of these new kinds of nuclei, and (ii) to study the YN interactions in order to reach a unified description of the baryon-baryon strong interactions.For these reasons, past and future, I have chosen to highlight in this report the progress achieved since the First TRIUMF Kaon Factory Workshop in 1979 through the use of (K“,tt) reactions.THE SPECTROSCOPY OF 13CThe ( K " , tt_ )  reaction at 800 MeV/c on 12C, 13C, 11+N  and 180 has been studied1’2 at the Brookhaven AGS for pion spectrometer settings between 0° and 25° (Fig. 3 of the preceding talk by Bassalleck). Angular distribu­tions have been published for 12C (Ref. 1) and 13C (Ref. 2). The spectrum of 13C displays a richness of peaks, providing grounds for a fully consis­tent spectroscopic analysis. Here I shall describe in some detail the recent analysis by Auerbach £t al.3 of the reaction and structure effects associated with the 13C(K“ , tt“ )  1][c reaction. I shall also comment on the necessary generalizations of the earlier 1^C analysis by Dover et al.4 The*0n leave from the Racah Institute of Physics, The Hebrew University of Jerusalem, Israel 91904.149discussion is geared to focus on the determination of the A-nucleus spin-orbit potential, the smallness of which has al­ready been deduced by Bouyssy and Hiifner5 by analyzing theCERN PS 0° data, in particular■ 1 6,the 1G0(K“ ,tt") i^0 reaction^ at 715 MeV/c.spectra taken2 at 800 MeV/c (K- ,ir-) are shown in Fig. 1 for 6l=4° (correspond­ing to a spectrometer setting of 0°) and 15°. With energy resolution of 2.5 MeV, each peak may represent a number of unresolved hypernuclear levels.In a weak-coupling limit the five peaks observed at 4° are assigned to transitions lpn-Kn£)A according to the classification given in Table I . The lp^ excitation in this mass range is between 10 and 11 MeV. It can be shown3 that, for each multi­polarity (A£) of transitions to unresolved hypernuclear levels built on the same nuc­lear core state, the (K-,tt-) cross section is proportional to the corresponding neutron pickup spectroscopic factor in C. The spectroscopic factors C2^ (pj) quoted7 in the table (for A£=0) for five 12C core states saturate 4 out of 5 (p neutrons in 13C) of the re­action strength. The strength missing in the table for A&=1 is due mainly to transitions to peak 4, centered at 16.4 MeV, associated with excitation of the listed T=1 core states, but the corresponding A£.=l (K_ ,Tr“ ) strength is small at 4° relative to that of A£=0. Since the experimental energy resolu­tion cannot decide between various models for the ls^ configuration, the latter was taken from the work of Gal, Soper and Dalitz8 and the appropriate components were sub­tracted from the peaks under consideration. For this reason I deal here only with peaks 3, 4 and 5, at 10.4, 16.4 and 25.7 MeV, respectively, which for 4° are dominantly populated by A£=0 transitions to 1/2150Table I. Structure of peaks at 4° in the weak coupling limit.peaknumberE*( ^ C )(MeV)dominantA£ ( n l ) A12CjJ,Tcore specifications Ec (MeV) C2tf (lPj)a1 0 1 Is 0+ ,0 0 0.613 (p1/2)2 4.4 1 Is 2+ ,0 4.44 1.122 (p3/2)3 10.4 0 IP 0+ ,0 0 0.613 (Pl/2)4 16.4 0 lp 2+ ,0 4.44 1.122 (P3/2)5 25.7 0 IP i+ .o 12.71 0.661 (p3/2)5 25.7 0 IP 1+ ,1 15.11 0.599 (p3/2)5 25.7 0 lp 2 \ 1 16.11 1.012 (p3/2)^ h e s e  spectroscopic factors for p., neutron pickup on 13C are taken from the intermediate coupling calculation of Cohen and Kurath.7substitutional states of the lp^ configuration. Of these peaks, the upper peak at 25.7 MeV broadens appreciably in going from 4° to 15°, and the calculation3 shows indeed a considerable spreading and fragmentation that makes it premature to reach specific conclusions from the angular distri­bution of this peak. However, as it will become clear below, the 9.3 ±0.5 MeV spacing between peaks 4 and 5 at 4° provides a useful check on the strength of the AN residual interaction. The calculated3 angular distri­butions for peaks 3,4,5 are compared with the data2 in Fig. 2. The data points and curves represent cross sections summed over the same region of excitation energy. The separation between the "16" and "25" MeV peaks is changed from 20 to 18 MeV for angles greater than 10° in accordance with the data. An additional error of ±20% in overall normalization assigned in Ref. 2 is not shown, and theoretical uncertain­ties are of this order. The cross-sec­tion shapes for Pn^PA A£=0 or 2 and Pn">sA A£=l are shown in the breakdown of the cross section for the 16 MeV peak.The 15° spectrum is seen to offer a use­ful method of studying A£^0 transitions.For the 25 MeV peak the incremental con­tributions from Pn+PA (A£=0+2) , pn->-(sd)^(A£=l+3) and sn->s^  (A£=0) transitions are given. In the A£=0 contribution to the "10" MeV peak there is destructive inter­ference between the jn=jyy=l/2 and jn^jA =3/2 amplitudes. The cross section is thus small and sensitive to the model chosen for the core wave functions; cross sections are given for two interactions which fit well the available data on p- shell nuclei, one due to Cohen and Kurath7 (POT) and one due to Millener (MP4). In distinction with the weak coupling limit, sufficient core statesFig. 2. Measured2 and calculated31 3C(K” ,ir") ^ C *  angular distributionsat 800 MeV/c. LABORATORY ANGLE ( dag)151are employed in the calculation to guarantee convergence, accounting for all pick-up strength and all states of high spatial symmetry. The AN in­teraction parameters used in the cross-section calculation are discussed below. Details of the DWBA reaction calculation are given in Ref. 3.The interesting features of peaks 3 and 4, "10" and "16" MeV respec­tively, are summarized as follows:(i) The cross-section ratio of the two peaks at 4 ° ,  p = a (^>)/ a (h < ) — 5 , deviates strongly from the pick-up ratio, whether taken from experiment,9 p ^ = 1 . 4 5 ,  or from intermediate coupling calculations,7 pCK=1.83 (or from the unrealistic jj limit for the 0+ and 2+ 12C core states, p j j = 5 / 4 ) .  This difficulty cannot be removed, within the weak coupling limit, by in­voking a nonzero value of ep=e(pi/2)-e(P3/2) since in this limit each of the states is of a pure jA nature, | h~<y= 112C(0+)xpi/2y  and\h~>>= 112C(2+)xp3/2>.(ii) The 6.0±0.4 MeV spacing between the two peaks at 4° clearly deviates from the 4.4 MeV spacing between the corresponding 12C core states. Ignor­ing the AN residual interaction results in a negative A-nucleus spin-orbit splitting, ep=-1.6±0.4 MeV.(iii) Peak 4 undergoes a downward shift of 1.7±0.4 MeV in going from 4° to 15°. After subtraction, at 15°, of the A£=l Pn^s^ transitions (a procedure which affects little this shift) , the remaining M = 2 pn-*PA transitions within this peak are dominated (90%) by 5/2" states of the |12C(2+)xp> configuration. Ignoring the AN residual interaction results, again, in a negative value of ep , -2.210.5 MeV in the limit of a weak A-nucleus spin- orbit potential (hence, a posteriori, an inappropriate limit) and -3.2 ±0.8 MeV in the limit of a strong spin-orbit potential.(iv) Peak 3 undergoes only a small (almost consistent with zero) downward energy shift of AE=0.36i0.3 MeV in going from 4° to 15°, corresponding in the weak coupling limit to I 12 C ( 0 + ) x p 1 / 2)> -*■ | 3/2<)>= 11 2 C ( 0 + ) x p 3 / 2 )> and thus resulting in a positively small A-nucleus spin-orbit splitting, ep= 0.3610.3 MeV. This feature apparently contradicts the previous two fea­tures when analyzed in the weak coupling limit, which therefore is inap­propriate: a nonvanishing AN residual interaction is imposed by the 1 ?C data.Since the 0+ and 2+ 12C core states are well approximated by Pauli spin singlet wave functions, only the central, spin-independent component of the AN interaction is effective in the hypernuclear diagonalization for the 1 V2", 3/2~ and 5/2_ states mentioned above. For a spin-independentWigner residual interaction between lp baryons, all splittings and relative shifts are given in terms of the Slater integral F^2  ^ which determines the strength of a quadrupole-quadrupole effective interaction:Veff(AN) = F(2>QA-QN , QB = (4tt/5) 112Y2 (rB) . (1)First consider the effect of the effective interaction (1) on the 1'jc . sp c^tjjrum for ep=0 so that the A-nuclear interaction is independent of sA - «C=Jc+£a is a good quantum number and doublet degeneracies corresponding to ^f=»C+sA arise, independent of F^2  ^ and of the size of the nuclear core basis. The 12C(0+ ,2+)xPA spectrum for F^2^=-3 MeV is shown in Fig. 3. The dominant spatial symmetry, [f^] and [f] for each nuclear and hypernuclear state respectively, is also given. These symmetry symbols distinguish here between the two<£=l doublets. States in the 10 and 16 MeV peaks with appreciable (K”,tt“) production at 4° (V*f) and 15° (^2 , 5/£ ) are marked with asterisks. For example, the. A&=2 production rate for states based on the 2+ is given in DWIA by an appropriately Fermi-averaged K"n->ir"A lab152cross section times an effective neutron number given bywith cf2 + (p3/2) denoting the spectroscopic factor for 13C(g.s.) pickup into 12C(2+) and M^2) standing for the A£=2 amplitude which in PWIA and for harmonic oscillator wave functions reduces toM^2) (b2q2/6) exp(-b2q2/4) , (3)r  “Sfq being the momentum transfer. According to (2), the production of v2 saturates 84% of the sum 2 1M^2 ^ |2ef2+ (P3/2) over Jf and <Cf, so that the downward shift observed in peak 4 [feature (iii) above] is naturally accom­modated in this scheme, with no recourse to the A spin-orbit splitting, as due to the dominance of the<£=3 5/2 state at 15°. Features (i) and (ii) above, relating to the two V2 states, are also explained by_invoking F^2  ^of the magnitude indicated above; in fact, both p and AE(V2 - V2 ) which strongly depend on F^2  ^ become somewhat larger than the values required by experiment, a situation corrected by the introduction of a small spin- orbit splitting. Ref. 3 demonstrates that all measured energy separations, including the 9.3±0.5 MeV between peaks 4 and 5 at 4°, can be accounted for with -3.4<f(2)<-3.0 as well as ep=0.5 MeV.The AN residual interaction, as given by F^2  ^, is "weak" relative to that appropriate to the nuclear lp shell, F^ -10 MeV. Its effects, nevertheless, are far-reaching, particularly on the two V2 states. This is not just a matter of the magnitude of F^2  ^ with respect to the 4.4 MeV core separation; for instance, a repulsive AN interaction, say F^2^=3 MeV, would lead to a complete reversal of the 4° strengths between peaks 3 and 4. For a weakly spin-dependent attractive AN interaction a tendencyappears to reach a good spatial symmetry [f] such that the upper V2” state has a large ampli­tude for the symmetry [441] which dominates 13C(g.s.), thereby giving rise to a coherence in the small momentum transfer (K-,T7-) reaction. The lower V2” state, which for F ^ = - 3 . 0  MeV and £p=0.5 MeV has the form♦ 0 0  = 0. 959 112C(0+) x Pl/2>- 0.283|12C(2+)x P3/2> , (4)has amplitude of 0.878 of the supersymmetric10 [54] while, among the remaining components, only -0.15 for the substituted 13C(g.s.). Since the [5,4] cannot be reached with A£=0 from any of the spatial symmetries contained in 13C(g.s.), the strong departure of p from the pickup value follows immediately. Incidentally, a substan­tial exchange mixture e of the AN interaction, moving away from a Wigner force (e=0) to aFig. 3. The calculated structure of (-)ve parity levels in the "10" and "16" MeV peaks for spin-independent AN interaction specified by f (2)=_3 MeV. The assignment of symmetry types [ffl] and [f] is approximate.153Serber one (e=1/2) , would increase p unacceptably beyond the experimental value. If the AN residual interaction were "strong", close to the nuclear one (but short of the spin-orbit strength) with parameters e=V2, F^°^=-5.6, F (2)=-10.1 MeV, the two main peaks 4 and 5,which for the physical situation carry most of the Prf^ PA coherence of the (K”,ii”) strength at 4°, through their dominant [441J symmetry, would coalesce into approximately one peak (spread only to about 2 MeV between T=0 and T=l) , the pn->-p/\ analog state. Similar considerations, for the analogous case of the 0° 3Be spectrum, have recently been detailed by Dalitz and Gal.11With the A spin-orbit splitting the only spin-dependent term which is not a priori suppressed by the singlet nature of the 12C lowest core states, any doublet splitting in Fig. 3 is directly related to the strength of the A spin-orbit potential. In practice, only the lowest doublet is fully observable, with the 1/2< state dominating over the 3/2< at 4° and the reverse at 15°. Thus, one is led to a rather precise determination of the small A spin-orbit splitting Ep in terms of AE(1/2<-3/2<) • To further pin down £p one would like to observe the y de-excitation (in correlation with the production pion) of the particle-stable 10.4 MeV peak by means of El transitions to the 1 ground state: V\/Z*s \/1 (isotropic) at 0^=4° and P3/2"*s 1/2 at 0^=15° with angular distribution12 1-0.6 cos2©^. For a small value of Ep, in fact up to about 3 MeV, deducing it from this doublet splitting has the virtue of independence to first order of F^2  ^, even though a nonzero value of the latter implies that neither the Vjj” state is of a pure pi/2 (A) nature nor the 3/2 is of a pure P3/2(A) nature. For the range of interest one finds Ep = aAE(1/2<-3/2<) , with a=1.15±0.03. Thus,E p  = 0.4±0.3 MeV. (5)Previous determinations of Ep, in which F ^  entered in first order, assumed specific models for F^2  ^ and other residual interaction parameters. Bouyssy,5 starting from a fairly simple central AN interaction, effective­ly chose a value for F ^  in ^ 0  rather close to the range of values allowed by the data and so, a posteriori, came to the right conclusion concerning the smallness of the A spin-orbit splitting; a different choice for F ^  , e.g. F 2^^ - 6  MeV, as appropriate to a scaling of the 50 MeV nuc­lear well-depth to the 30 MeV A well-depth, was shown13 to lead to a com­pletely different conclusion, namely that the A spin-orbit potential is stronger than that of a nucleon! To conclude this discussion with an ex­ample of negative finding I argue that the measured spectrum1 is in­sensitive to Ep, at least in the range 0<Ep<2 MeV. In the jj coupling limit for 12C one anticipates that the A£=0, P3/2 (n)-*-p3/2 (A) , strongly ex­cited 0+ state at 0° is replaced in going from 4° to about 15° by two 2+ states, excited through A£=2, P3/2(n)-»-pj (A) with j = 1/2j3/2- While this ex­pectation is borne out by the angular distribution1* of the singly observed peak in the appropriate excitation domain, no energy shift has been seen as function of 0^, thus yielding an upper limit of 0.4 MeV for the separa­tion between the 0+ state (at 4°) and a preferentially excited 2+ state (at 15°). On a more realistic basis7 for the J1C core one evaluates3 two near­by 0+ states and three 2+ states within a range of 2.7 MeV, consistent with the reported 2.5 MeV resolution. The separation between these 0+ and 2+ groups, averaged over the appropriate (K~,tt“) formation rates, is calcu­lated then, for F ^ = - 3 . 7  MeV, as follows:Ep(MeV): 0 1 2E(0+)-E(2+): 0.39 0.12 -0.09 MeV . (6)This establishes the insensitivity claimed above.154COHERENCE IN (K",tt) REACTIONSI wish to discuss the issue of coherence in (K- ,ir“) A-hypernuclear formation within the example of 1 because of the prominence of a single, and narrow, pn^PA peak observed6 at 0° for this fairly simple system. Just one 0+ state, P3^2P3/2» is expected in the jj limit. However, the Cohen- Kurath calculation7 gives only 71% for the spectroscopic factor of 12C(g.s.) to i:LC(g.s.); where in the ( K “ , tt“ )  spectrum is the remaining 29%? To answer this question, the J1C basis is enlarged3 to include the \i~  level at 2.0 MeV and the 3/2~ level at 4.8 MeV which together with the ^2” g.s. saturate the 12C pickup strength. The 3^3 0+ ^Cxp^ matrix is diago- nalized for a central residual interaction specified by f(°)=-1, f(2)=-3 MeV and variable a, where the spin-independent AN central interaction defined by these values of F ^  is modified by the spin-dependent factor (l+aOA*ON)• Results of this calculation are shown in Fig. 4 for a in the range [-1,2]. This involves a large variation of the interaction, as for a=-l the singlet interaction becomes four times stronger than for a=0 while the triplet interaction vanishes; for a=l, both triplet and singlet inter­actions become doubly stronger, with the latter also changing sign into repulsion. The excitation energy Ex is given, for each a, relative to the lowest 0+ state while the absolute A interaction energy (MeV) within the p-shell is shown in brackets.under this lowest level. The fractions marked on the right upper corner of the levels stand for the relative pro­duction rates; their sum for a given a is one. The first observation is that the 0+ formation strength goes higher in energy with a, about 6 MeV per unit of a. It is encouraging to note an increase from 71% to 90% in the coherence of the lowest 0 state for a=0, a situation close to the physical case (a=-0.1 according to Refs. 3,5,11). This arises- from the considerable coherent mixing in­duced by the spin-independent AN attraction between the lowest two X1C core states:|0+> a 0.857|11c(3/2"<)xp3/2>+ 0.515| 11c(1/2")xp1/2> ,(7)while the next 110(^2) state strongly mixes with 11C(V’2” ) in the construction of the two higher 0+ states. Two limiting cases are offered by Fig. 4 for a strong spin- dependence of the AN residualinteraction: (i) if a is large nega­tive, a limit satisfied already for a=-l, the coherence of the lowest1^C(0+) state improves to betterthan 98.5% by admixing in between5% to 10% of the 11C(^2>)xP3/2 com­ponent, whereas (ii) if a is largepositive the coherence graduallymoves to the highest 0+ state, thedepletion of the lowest 0+ statebeing complete already for a=l.However, for a=l one notes aFig. 4. The calculated *?C 0+ spectrum as function of the AN spm-dependence parameter a.155considerable spreading of the reaction strength between two 0+ states separated by 4.5 MeV from each other.The above observation serves as a reminder that coherence in low momentum transfer (K",tt) reactions should not be taken for granted. Coherence is found to be well satisfied in A-hypernuclear production, but for E-hypernuclear pro­duction things may differ^-depending (among other properties) on the spin dependence of the EN interaction. The OBE models14’15 of the Nijmegen group for this spin-dependence suggest16 that it is strong, with triplet and singlet interactions differing in sign from each other within each isospin channel. This is shown in Fig. 5, for Model F,15 where the 3S potentials are shown in continu­ous lines and the potentials by dash lines. For the attractive I=V2 3S chan­nel, the effects of tensor forces are included, as discussed in Ref. 16, with a considerable attraction thus added.The 1=^2 1S channel, on the other hand, is repulsive; hence a (I=1/2)> V3 , and any E hypernuclear configuration, the EN interaction within which is dominated by the I - / 2  EN interaction, could exhibitFig. 5. EN S wave hard core (rad­ius rc) potentials from the OBE model15 of de Swart and collabora­tors as reproduced in Ref. 16 with tensor closure energies as speci­fied in the figure. Note the two separate scales in the ordinate.spreading. For £C, for instance, this requirement singles out the 1=^2 states and, consequently, the predicted narrowness17 of the 0+ state in the jj limit could be effectively destroyed by spreading the (K“,ir) strength over a group of 0+ states, the width of some of which is not suppressed by the mechanism that leads to narrowing for the 0+ state of interest.SPIN-ORBIT POTENTIALSThe smallness of the A-nuclear spin-orbit coupling, as deduced5 from x^0 and more recently3 from l ^ C , received appreciable theoretical attention in the last few years. Several authors18-20 have used the relativistic mean field theory (MFT) in which the smallness of the A spin-orbit potential relative to that of the nucleon arises from (i) the assumption that the AAa and AArn vector coupling constants (g) are considerably smaller than the NNo and NNw coupling constants, respectively, a and w representing phenom­enological exchanges of scalar-isoscalar and vector-isoscalar (boson) fields, fitted to reproduce the central baryon-nucleus binding, and from(ii) a partial cancellation between the contributions of the vector term (related to the Thomas term of the baryon magnetic moment) and the tensor term (related19 to the anomalous magnetic moment and represented by a coupling constant f) in the AArn coupling. It is interesting to note that these two features arise in a natural way from the quark structure of the ^2+baryons, although the argument cannot be made strict at present: (i) the strange quark within the A does not participate in the exchange of the156nonstrange a,u>, which leads to g^A a/8NNa=§AAio/8NNa)=2/3, and (ii) the mag­netic coupling %Aoj-(g+f) AAu vanishes21 if ideal rn-tj) mixing within the vector meson nonet is assumed and the F/D ratio for the BBV SU(3)-invari­ant magnetic couplings is taken from SU(6), following the underlying quark structure of the 56 multiplet. In fact, carrying the analogy between the magnetic coupling of the w and the induced B-nuclear spin-orbit coupling to its extreme quark model limit (ignoring along the scalar-isoscalar ex­change that is not related in any naive way to the vector gluon exchange), one obtains for the spin-orbit strengths16v£S : VLS : VLS : V£S = 0 : 4/3 : -1/3 : 1 » (8)identical to the results obtained for A and I by Pirner.22 Within the MFT approach, though, the current estimates23"25 call for a E spin-orbit poten­tial which is not as strong as implied by (8), but still substantially larger than that of the A. For example, the Dirac-Hartree calculation by Bouyssy23 givesVLS : v£S : v£S : Vls = 0.23 : 0.54 : 0.04 : 1 . (9)There are several serious drawbacks to the MFT approach, the main one being the omission of short-range repulsive correlations. The a and w contributions to the central potential are individually very large, theirsum forced to reproduce the phenomenologically required well-depths. Fornucleons, the substantial repulsive (Fock exchange) contributions of it and p to the well-depth are ignored. No link exists in the MFT approach between the boson exchange contributions to the BB interactions and their contri­butions to the nuclear potentials. In addition, most of these MFT evalu-Vations overestimate the ratios v£g/v£g by ignoring the sizable coherent Fock exchange contributions for (adding 50% to the a and io contribu­tions, and a p-exchange contribution which is not of order A-1). These arise by making the natural assumption that the nuclear spin-orbit poten­tial is due to the nuclear folding of the two-body spin-orbit interaction which is significant only for the 3P (necessarily T=l) channel.These shortcomings may be improved upon by starting from YN OBE models11*’15 which fit the available YN scattering and reaction data, and folding the two-body potentials with the nuclear density accounting proper­ly for repulsive short-range correlations (dominated by hard cores in the two-body potentials). This project has recently been undertaken by Dover and Gal who use the Moszkowski-Scott separation method26 to derive an effective nucleon-nucleon or hyperon-nucleon central interaction G from the free-space OBE potentials. In this method a part of the short- and intermediate-range attraction (up to r0 c*l fm) is used to cancel the repulsive phase shift produced by the hard core. The resulting interac­tion G corresponds essentially to the tail (r>r0) of the free-space poten­tial, having an order of magnitude smaller volume integral than the cor­responding interaction used in MFT. The various individual terms which contribute to the single-particle potentials are each smaller with the in­clusion of short-range correlations and the results of the calculations become more stable against moderate changes of the parameters. For spin- orbit nuclear potentials, derived from two-body P-wave interactions, the separation method is replaced by using a hard core correlation function.The results16 of this calculation are given in Table II for Model D of de Swart and collaborators,11* along with a breakdown into the largest specific contributions; for comparison, the results for Model F15are also given with no breakdown, The strength V^g (in MeV) is defined by the convention157V-BLSfti%cd(p/p0)    5,-ctbdr (10)with the nuclear density p(r), such that p(r=o)=p0 . The value Vls — 9.5 MeV is required to fit the nucleon Pi/2“P3/2 spin- orbit splitting in 160 (for a two-parameter Fermi shape for p(r) with c=2.71 fm, a=0.65 fm), but generally values of v|Jg between 5 and 10 MeV are accept­able. The a and w contributions to V^s already include the fac­tor 3/2 from antisymmetrization mentioned above which does not appear, of course, for hyperons. The antisymmetric two-body YN spin-orbit potentials lead tosome cancellations for V-LS1 theTable IX. Meson exchange contributions3 to V?c (MeV) in Model D.1* LSB - N A Z =°S 1.35 0.63 0.59 0.53°A — -0.11 -0.14 -0.18i*>S 4.30 1.09 2.01 0.61“A — -0.51 0.35 -0.51P 1.35 — — —K§ — 0.74 -0.03 —K* — -0.13 -0.01 —Ka — -0.35 0.00 —Total 7.3 1.9 2.9 1.1Total (F)15 8.8 1.7 2.4 -0.7most significant of which occurs for to exchange and is related to the cancellation between f andCalculated in Ref. 16. The subscripts S and A denote contributions from symmetric and antisymmetric twg- body spin-orbit interactions of the form (sgisfi)*^BN’ The dots stand for smaller, insignificant contribu­tions. The S results depend on assumptions made for the appropriate hard core radius which has not been constrained by data.g couplings noted in the beginning of this section.m i -wv 1— /— wt /v a /t m wt 4 It . , 4- 4 /t tt /t T 7 “1 r-\ /tin n T 1 T— /t /t /t « ■ /t /.The overall *strangemeson exchange contribution to VLS is small because the K and K* terms tend to cancel. v£g is almost entirely due to co and cr exchange, with the symmetric and antisymmetric co contributions in phase. For a exchange, which in Model D is treated as an SU(3) singlet, the symmetric contribu­tions to V^g are very close to each other while the antisymmetric contri­bution is always negative, but small. To sum up, the smallness of the A spin-orbit potential emerges in a natural way from these OBE calculations. The E spin-orbit potential is predicted to be about 50% stronger than that for A, yet small with respect to that for a nucleon.E-HYPERNUCLEAR WIDTHS AND SHIFTSThe central issue in the study of E hypernuclei at present is the issue of their level widths. The optical potential analysis of E” atom data by Batty et al.27 in terms of an effective complex scattering length b, .2yV(r) = -4Tr(l+mz/mN)bp (r) , / p(r)d3r = A , (Ha)leads to the following determination:b = (0.35±0.04) + i(0.1910.03) fm , (lib)provided the nuclear charge density shape is adopted for p(r). For the parametrizationV(r) = - (U + iW)p (r) /p (0) , (12a)one finds then in nuclear matter the values:U = 2813 MeV , W = 1512 MeV . (12b)Hence, for deeply bound states in heavy nuclei the conversion width is about 2W(0) — 30 MeV. Gal and Dover,17 and recently Gal, Toker and Alexander,28 have shown that this estimate is compatible with the known low158energy E-p-*An cross sections. Several investigators29-32 pointed out that relatively large off-shell corrections, which generally decrease the values given by (12b) for both U and W, may apply to the physical situa­tion. Kisslinger29 emphasized the possible suppressive effect of EN short- range correlations on the optical model estimate, but his treatment of density dependence has been criticized by Dabrowski and Rozynek.30 The latter authors stress the role that dispersive corrections play in the Pauli suppression of the E”p->-An conversion. Others31’32 obtained a reduc­tion in W by invoking a fairly large EN interaction range which, when superposed on the range of p(r), allows for smaller values of Reb and Imb in the atomic fit. Furthermore, by decreasing thus also U, the computed single-particle E-hypernuclear states become narrower as their binding de­creases. However, OBE models do not support this assumption of long range since the chief meson exchange contributions in E-nuclear interactions are probably due to o and w. For example, it is found in Ref. 32 that Model D of de Swart and collaborators11* (but not F15), reproducing among other shifts and widths the most accurately measured E" atomic shift, that in 4f28Si, yields values for U and W in agreement with (12b). If E-hypernuc­lear widths were as small as argued in some of the above works, ground states of E hypernuclei should have been observed and will definitely be observed. There is no evidence at present for such ground states. The states observed to date lie all in the E continuum, corresponding to con­figurations higher than the ls£ ground state configuration.Of the several targets studied33 in the first run of (K“,ir) experi­ments in the CERN PS at 720 MeV/c, only the reaction 9Be(K-,ir-)|Be shows a clear signature of hypernuclear structure, with two peaks spaced 10 MeV from each other with widths of less than about 8 MeV. The lowest of these peaks, lying about 10 MeV in the E° continuum, is likely to be of a simplestructure, as related calculations11 on ^Be indicate; it is a E° lp state coupled to a fairly coherent combina­tion of the 8Be ground and first ex­cited states. The EN spin-isospin in­dependent residual interaction, which is the only component effective with­in these spin and isospin saturated core states (well approximated by 11S and ^D), is expected to shift this state upward by about 2 MeV. Thus, the position of the E° lp single­particle state is about 8 MeV in the continuum. Figure 6 shows the results28 of evaluating this state, as unstable bound state (UBS) of the Schrodinger equation for the opticalFig. 6. Calculated28 E° binding en­ergies and widths in 9Be for the Is and lp UBS (continuous lines) and the lp Gamow state (in dash lines). The density p(r) is harmonic oscillator density that fits 9Be charge distri­bution.159potential (11) with a normalizable wave function. The imaginary part of the optical potential is not sufficiently strong to form such a £=1 state with T>0 (the T<0 section accommodates S-matrix poles which do not admit physical interpretation), except with the upper error bar for both U and W. A narrow UBS develops then at 6.5 MeV in the continuum. By increasing W further by 25%, the UBS is brought to lie 8 MeV in the continuum and its width then is 3.3 MeV. On the other hand, the £=1 £ Gamow state (repre­sented in the usual analysis by a resonance pole the wave function of which is non-normalizable) appears with a slight positive binding, way off the energy region required by experiment. In addition, the Is UBS in the figure is calculated to be considerably wider, in fact over 20 MeV wide for the values U=28 MeV and W=20 MeV that fix the position (although non- uniquely) of the lp state.In Fig. 7 I show the results of a similar calculation for ^C.Again, the Is state is wide while the lp state, lying 4.4±2.3 MeV in the E° continuum, is not as wide:I’1p=10.1±4.3 MeV. Generally, the E single-particle states with the high­est £-value to appear as UBS in the E continuum could well have widths of somewhat less than 10 MeV. The interpretation of these UBS is dis-r ( M e V )Fig. 7. Calculated28 E° binding en­ergies and widths for the Is and lp UBS in 18C. The density p(r) is a standard three-parameter Fermi charge distribution.Fig. 8. Schematic representation28 of resonance A trapping in A-nuc­leus scattering with incoming ener­gy E(A) smaller (a) and larger (c) than the EA mass difference AM. The E-hypernuclear bound state in (b) [in (d)] evolves from (a) [from (c)], causing A-nucleus resonance phenomena below (above) the E-nuc­lear threshold. Unmarked circles stand for nucleons while empty ones denote nucleon holes.cussed in Ref. 28, emphasizing that, when occurring in the E continuum, no resonances should be expected in E- hypernuclear channels at the approp­riate energies. Rather, these UBS may give manifestation as A-nucleus resonances near the E-hypernuclear threshold, according to the schematic description of Fig. 8. The AN-EN coupling will provide access to in­termediate E-hypernuclear states as shown in (b) for the particular choice of E(A) < M^-M^ in (a) and as shown in (d) for the particular choice of E(A)> Mj-M^ in (c). The diagrams (b) or (d) provide nuclear trapping mechanism for the incident A as the formed E occupies a "bare" single-particle orbit while a nucleon is lifted up to a higher orbit in the nuclear well, due to the AN-EN coupling. These bare E levels show up as resonances in the A channels,160with energy that shifts upward and widens by amounts which depend on the coupling strength. If the bare binding is small, the resonance corre­sponds to a positive value of E(A)-AM, i.e. it appears in the £ continuum.The imaginary part W of the E optical potential (12a) reflects the strength of the AN-EN coupling within the nucleus and, thus, gives rise to a level width as well as an upward energy shift.An important feature of £N*AN conversion is its selectivity to spin and isospin, which modifies in light hypernuclei the results of applying the optical potential discussed above. It has been found14’15 that the low energy E"p->An cross sections are dominated, to about 90%, by the 3Si , I=V2, EN conversion. This feature will be shown below to arise most natu­rally for the OPE mechanism because the tensor component of this influen­tial exchange is kinematically favored in the 80 MeV EN>AN conversion. Furthermore, according to Fig. 5, the EN I=1/2 initial state interaction is attractive for 3S, enhancing EN conversion, and repulsive for 1S, suppress­ing conversion. Dramatic effects of selectivity in light E hypernuclei have been discussed by Gal and Dover17 allowing for some of the lp statesto become as narrow as 5 MeV. In the p-shell, these relatively narrowstates are almost exclusively of a coherent type (p^p^) with the highest possible value of isospin. Their observation would be enhanced by using the (K",tt+) reaction which selects the highest isospin values, rather than the (K~,ir-) expected to excite also the wider states. It is advisable to operate as low momentum K" beams as possible, close to the "magic" momen­tum of about 300 MeV/c, in order to separate the A£=0 transitions out of the A£^0 transitions to wider states. However, even if A£=0 dominance is kinematically achieved, it is possible that the conjectured strong spin and isospin dependence of the EN residual central interaction spreads this A£=0 strength among several levels, some of which are not likely to be par­ticularly narrow. This feature was discussed here in an earlier section; preliminary calculations34 show that this may indeed be the case in 12C(K",ir) reactions. For 160 target, on the other hand, significant spreading is less likely because of the minimal number of nuclear core states participating in the construction of the observed lp E-hypernuclear states. However, even for this fairly simple target, and ignoring the above spin-isospin dependence of the central interaction, variations in the calculated width of the produced states can arise17 upon changing the strength of the assumed E spin-orbit potential.Perhaps the most remarkable consequences of selectivity hold for very light targets35 as shown in Tables III and IV for forward (K",ir) reactions on 4He and 3He targets, respectively. The relative production cross sec­tions are given in terms of the Fermi-averaged forward K-N-mtE amplitudes.The quenching factors Q which multiply the optical potential width are given for s-shell targets by the general expression:NcQ = ^  (3 + Oj'OiXl - tz*Ti)/3Nc , (13)1 j ->■ .where Nc is the number of nucleons in the hypernucleus and |tj|=l. In particular, for E-hypernuclear states with isospin I and spin S produced on 4He:q = i - i[i(i+i) - x ]  + f[s(s+1> “ f ] + f[I<I+1> ~ t ][s(s+1) _ 1 }  (14a)while for 3He target:161Table III. Quenching factors Q for jHe and £n widths and relative forward production cross sections on ^He. I and S denote the isospin and spin of the hypernuclei.I S Q 0 ( K " , Op*=1UD1/2 0 2 2/31 fn-*-!0 + &  V l + !2 —3/2 0 0 */3| W >  - 1//2 f ^ H 2 2 | f p * H 21/2 1 14/9 0 —3/2 1 8/9 0 0Table IV. Same as in Table III, but for |He and |n produced on 3He. Ic is the isospin of the nuclear core.I(IC) S Q o (K',tt*)P1*D0(1) 1/2 3 — —1(0) 1/2 1/3 3/2|fp^r+|2 3/2|fp^z-|21(0) 3/2 4/3 0 01(1) 1/2 2 1 / 2 | V £o + 1/^2 V I + |2 1 M |  V z - | 22(1) 1/2 0 1 / 2 1 ^ 0  -1//2 f ^ + l 2 l A l V z - l 21 + j[s(S+l) - , Ic = 0 ,Q - . r (14b)c = 1where Ic is the isospin of the nuclear core. Consider, for example, the reactiontfHe(K",ir+)Jn (15)which in the forward direction conserves the Pauli spin, S=0. E“p conver­sion in the final state (E"p)s=o(nn)s=0 is forbidden inasmuch as the con­version is dominated by S=l. This I=3/2 state is therefore predicted to be narrow, Q=0 in Table III. On the other hand, the (K_,tt~) reaction produces also the I=1/2 S=0 wide (Q=2) state in ^He, in addition to the I=3/> S=0 ^He which is the isospin partner of ^n and hence narrow. The ad­vantage of (K“,ir+) in this case is clear. In the case of A=3, since 3He is a proton-rich target, (K”,tt+) is not more selective than (K-,ir-). The 1=2 state in Table IV is narrow since it is obtained by isospin rotation on E"nn, but its production is not favored on 3He. On the other hand, a relatively narrow state with S=V2 and 1=1 (Ic=0 for the nuclear core) is predicted to be preferentially excited in (K",ir+).It is important to recall that the observation of narrow ls^ states is not likely if the EN interactions place these too high in the E con­tinuum. Thus, for a model calculation28 of |He, Fig. 9 shows that for a given W the ls£ UBS is pushed intd the continuum, with decreasing U, up to a maximum energy connected with a minimal value Um;Ln . Choosing W=24 MeV (a value not particularly large in view of the high central density of162‘♦He) , for instance, yields Umin =*18 MeV for 1° with a maximal "unbinding" of about 8.5 MeV. For W decreased to 15 MeV, Umin — 22 MeV holds for 1° and the corresponding maximal shift into the continuum is only about 3.3 MeV.If W is significantly quenched, it may happen that the actual value U is not sufficiently large to allow a ls^ UBS embedded in the continuum to develop. For the narrow states singled out in Tables III and IV, the fol­lowing spin-isospin shifts occur:"iHe, ;nV . 1 1 C ,  y la = h  , S-0)I H e > I  ( 1=2)iH e ,n6V = U * o t l /2  " ^ 1 , 1 / 2  + ^ 0 , 3 / 2  6V = “^ 0 , 1 / 2  ~ " ^ 1  , 1 / 2  +  ^ 0 , 3 / 2= -2.1 V , (16a) (16b)3/2 = -1.5 V6V =  2 ^ 0 , 1 / 2  - 3 V 1 , 1 / 2 + 3 V o , 3 / 2 - 3 V 1 , 3 / 2 =  1.6 V (16c)(1=1,Ic=0,S=^)where V^j is the lsj-lsjj interaction matrix element for spin S and isospin I, and V is the spin-isospin independent combination:v  =  ^ 0 , 1 / 2  +  ^ 1 , 1 / 2  +  ^ 0 , 3 / 2  +  | v l , 3 / 2 (17)In estimating 6V/V, the G-matrix evaluation of Ref. 16 (based on s-wave IN interactions alone) was adopted, with well-depths given as follows:Do,1/2 = 31.5, D} t \/ 2 = -85.6, D0 }3/2 = -90.0, Di^/2 = 22.0 (MeV),(18)resulting in D = -22.8 MeV. The spin-isospin shifts of_Eqs. (16) are quite significant if one considers matrix elements for V typically of order -2 MeV. The states (16a,b) are pushed upwards, mainly due to the prominence of the 1=1, S=V2 IN attractive interaction which appears with anegative, and relatively large, coeffi­cient in these expressions. Since the width of these states is zero in the limit considered here, the theoretical conditions for their observation are, a priori, poor. For the state (16c), however, the width is predicted quenched (Table IV) but not to the extent of vanishing, so with an attrac­tive shift (due mainly to the 1=0,S=3'2 attractive interaction) chances are more favorable for its observation.Prior to a design of 1+He(K",TT+) ex­periment, a poor man's ^He target has already been used. The 4° 6Li(K" , tt+ ) | h  spectrum at 713 MeV/c is showninFig. 10 according to preliminary results36Fig. 9. Variation of calculated28 binding and width of the lsj UBS in |He as a function of U for two rep­resentative values of W. The density p(r) is a three-parameter Fermi Br(M«v) charge distribution.163from the BNL AGS. The clear and relatively narrow (T ~3  MeV) peak observed at -B£-=22 MeV is assigned35 to the coherent lsp-^ls^- transition (15)on the 4He cluster within 6Li. In heavier targets, particularly for A>9, no clear ls-*ls transitions are expected simply because of the large Is-1 proton width, of order 10 MeV and more. However, an appreciable fraction of the Is-1 proton strength in 6Li resides within the extremely narrow 5He (3^ ) state at Ex=16.76 MeV, r=0.10±0.05 MeV. This interpretation is supported by the observation37 of a similarly narrow peak in ^Li, the narrowness of which arises38 from being (slightly) bound with respect to its natural decay channel ^He+d. In the present case, the threshold for ijn+d with just unbound E in £n is at -B^-(|h)=16.70 MeV (related to the prominence of the 5He* state as due to a 3H+d cluster). Hence, if the observed narrow ^H excitation is visualized as a bound ^n+d cluster, the hypernucleus £n must have a narrow UBS at about 5 MeV in the E continuum. The spin-isospin upward shift of this cluster is of the form (16a), precisely as for jtn.For such a structure, the E—hypernuclear width arises only from E“ conver­sion on the proton within the deuteron and so does not amount to more than a few MeV. I conclude that the observation36 of a narrow £h excitationLihigh in the continuum lends support to the existence of a narrow £n UBS to be produced in the reaction (15).The considerably broader ^H peak of Fig. 10 at 7 MeV in the continuum contains the lpp-*-lp£- strength and possibly some part of the wider lpp-^lsj- AZ=1 transition to the ground state configuration. It is interesting to note that no lsj g.s. level has been identified in this experiment,3 al­though the momentum transfer is sufficiently large to allow35 its observa­tion. The lp-^ lp transition strength is calculated35 to be shared about 2:1 between the A£=0 and AZ=2 transitions. Working with a lower K“ momen­tum may therefore establish a structure narrower than that observed at present (T~12 MeV) in this excitation range, by suppressing the AZ=2 contribution. Similar remarks hold for 160: preliminary calculations34 employing a EN residual interaction with strong spin-isospin dependence as given in (18) indicate that the relatively wide AZ=2 (K~,ir+) transition strength is cen­tered in the neighborhood of the much narrower AZ=0 transition. The latter is dominated by a 0+ (1=^2) state that is shifted to order 10 MeV in the E continuum.To conclude the discussion of E-hypernuc- lear widths, I wish to comment on the micro­scopic mechanisms responsible for these widths and for associated effects of selectivity. The. r  100OPE contribution to the imaginary part or the £E optical potential is evaluated39 by assuming § closure on the A-hypernuclear intermediate states in Fig. 11 and neglecting the magnitudes p and p' with respect to q (q=280 MeV/c for50Fig. 10. Preliminary36 excitation spectrum of |H. Eexc denotes here the E" energy with respect to 5He ground state. The quasi-free assignment is suggestive with the continuousline representing the result of superposing °0 0 10 zotwo peaks. E . , c( M e v )164on-shell EN->-AN). Correcting for several misprints, the result is:W ( t t ) (r) - 8 tt f fNNir yAN q (q//mTr)1+( with pseudovector coupling constants40 cAEtt q2+m?)' (19a)P (r) ,f (fftNir=0.081 and faZit-  0.044) and a reduced AN mass Pa n - Expression (19a) ignores Fermi averaging,17’30 binding28’30 and Pauli blocking30 effects and short-range correlations,29,30 the sum of which may reduce32 it perhaps by as much as a factor of two.For q=280 MeV/c and a central nuclear density p(0)s:0.16 fm-3, this ex­pression reduces tow (fT)(r) = l64(MeV-fm3)p(r) => W (ir) e W7r(0) ^  28 MeV (19b)to be compared with the phenomenological determination (12). In view of the claim made by Kisslinger29 that short-range correlations alone reduce the optical potential estimates of type (19) by several orders of magni­tude, it is of interest to account for such correlations at least by ex­cluding the 6-function part of the OPE potentials in Fig. 11. A straight­forward algebra leads then to the modification of (19) by the multiplicative factor( 20 )V d )q ( A )so for (n%/q)=0.5 the quenching in the singlet channel is almost complete while, practically, no reduction arises in the triplet channel, the factor 8/9 in the limit m7r/q->0 arising from the fully included tensor component of the OPE mechanism.Dropping the spin term for nuclear matter, a quenching of (19) by about 0.7 results. Of course, further exclusions may be required beyond this minimal exclusion of the 6 part, but these will probably affect less the tensor component. Introduction of p meson exchange in Fig. 11 gives rise to new contributions to both spin channels, but the general pattern of triplet dominance remains, particularly when the EN initial and final state interactions are considered; actually, this is the spirit in which the calculations by de Swart and col­laborators1 4 ’15 have been done, yielding triplet spin selectivity for the low energy conversion cross section.It has been recently noted by Dillig et^  al.41 that the OPE mechanism gives rise to a relatively large spin-orbit term in w('IT)(r).Indeed, by retaining the p and p' dependence a step beyond the q4 factor in (19a), one ob­tains for the pion couplings in Fig. 11, after dropping terms that depend on cr^  and on q:p(X )Fig. 11. Meson exchange contributions to the ima­ginary part of the E-nuc- lear optical potential.-»■CTv ( q - p ) (q-p) V ( P ' - q)Or equivalently,in (19)(21a)(2 2 )(23a)165then W^17) is given to leading order by (19b) andA V  = * (23b)However, repeating this procedure for a combined irp exchange in Fig. 11 one obtains:oE*(q-p) 0N* (q-p) (p '-q)) • (oNx(p'-q)) (2lb)so to leading order in (p/q)2 no modification occurs in W^11) , while• f t>  -  ■*:> - 2 f  )  •where fp are the tensor coupling constants for the p meson. The cancella­tion in W^s induced by the exchange of p meson is substantial, as is evi­denced by the observation that apart from the factor 2 it coincides with that between the tt and p contributions to the AN-EN tensor potential Vip in momentum space; Ref. 16 demonstrates the latter cancellation in coordinate space for the OBE models of Refs. 14,15. Thus, a strong model dependence is expected for the evaluation of this reduced W^g.REFERENCES1. R.E. Chrien, M. May, H. Palevsky, M. Sutter, P. Barnes, S. Dytman,D. Marlow, F. Takeutchi, M. Deutsch, R. Cester, S. Bart, E. Hungerford, T.M. Williams, L.S. Pinsky, B.W. Mayes and R.L. Stearns, Phys. Lett.893, 31 (1979).2. M. May, H. Piekarz, R.E. Chrien, S. Chen, D. Maurizio, H. Palevsky,R. Sutter, Y. Xu, P. Barnes, B. Bassalleck, N.J. Colella, R. Eisenstein, R. Grace, P. Pile, F. Takeutchi, W. Wharton, M. Deutsch, J. Piekarz,S. Bart, R. Hackenburg, E.V. Hungerford, B. Mayes, L. Pinsky, R. Cester and R.L. Stearns, submitted to Phys. Rev. Lett.3. E.H. Auerbach, A.J. Baltz, C.B. Dover, A. Gal, S.H. Kahana, L. Ludeking and D.J. Millener, submitted to Phys. Rev. Lett., and in preparation.4. C.B. Dover, A. Gal, G.E. Walker and R.H. Dalitz, Phys. Lett. 89B, 26 (1979).5. A. Bouyssy and J. Hiifner, Phys. Lett. 64B, 276 (1976); A. Bouyssy,Phys. Lett. 84B, 41 (1979); ibid. 91B, 15 (1980).6. 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, Phys. Lett. 79B, 157 (1978).7. S. Cohen and D. Kurath, Nucl. Phys. 73, 1 (1965); ibid. A101, 1 (1967).8. A. Gal, J.M. Soper and R.H. Dalitz, Ann. Phys. (N.Y.) 113, 79 (1978).9. H. Taketani, J. Muto, H. Yamaguchi and J. Kokame, Phys. Lett. 27B, 625 (1968).10. R.H. Dalitz and A. Gal, Phys. Rev. Lett. 36^, 362 (1976).11. R.H. Dalitz and A. Gal, Ann. Phys. (N.Y.) 131, 314 (1981).12. R.H. Dalitz and A. Gal, Ann. Phys. (N.Y.) 116, 167 (1978).13. A. Gal, in "Common Problems in Low- and Medium-Energy Nuclear Physics",eds. B. Castel, B. Goulard and F.C. Khanna (Plenum, New York, 1979),p. 485.14. M.M. Nagels, T.A. Rijken and J.J. de Swart, Phys. Rev. D L2, 744 (1975); ibid. D 15, 2547 (1977).15. M.M. Nagels, T.A. Rijken and J.J. de Swart, Phys. Rev. D 20_, 1633 (1979).16. C.B. Dover and A. Gal, "Nucleon and Hyperon-Nucleus Potentials in a Meson Exchange Model", submitted for publication.17. A. Gal and C.B. Dover, Phys. Rev. Lett. 44_, 379 (1980); ibid. 962.18. R. Brockmann and W. Weise, Phys. Lett. 69B, 167 (1977); Nucl. Phys.A355, 365 (1981).19. J.V. Noble, Phys. Lett. 89B, 325 (1980).20. J. Boguta and S. Bohrmann, Phys. Lett. 102B, 93 (1981).21. A. Gal, J.M. Soper and R.H. Dalitz, Ann. Phys. (N.Y.) 63^ , 53 (1971).22. H.J. Pirner, Phys. Lett. 85B, 190 (1979).23. A. Bouyssy, Phys. Lett. 99B, 305 (1981); Dr. Bouyssy has informed meof a numerical error in the first line of his Table I, with the cor­rected values quoted here in (9).24. M. Dillig, V.E. Herscovitz and M.R. Teodoro, J. Phys. G7_, L39 (1981).25. R. Brockmann and W. Weise, contribution 131 to the Ninth International Conference on High Energy Physics and Nuclear Structure, Versailles, July 1981.26. S.A. Moszkowski and B.L. Scott, Ann. Phys. (N.Y.) JLL, 65 (1960).27. C.J. Batty, S.F. Biagi, M. Blecher, S.D. Hoath, R.A.J. Riddle, B.L. Roberts, J.D. Davies, G.J. Pyle, G.T.A. Squier and D.M. Asbury, Phys. Lett. 74B, 27 (1978); C.J. Batty, Phys. Lett. 87B, 324 (1979) and Nucl. Phys. (in press).28. A. Gal, G. Toker and Y. Alexander, Ann. Phys. (N.Y.) ,137, 341 (1981).29. L.S. Kisslinger, Phys. Rev. Lett. 968 (1980).30. J. Dabrowski and J. Rozynek, Phys. Rev. C 23, 1706 (1981).31. J.A. Johnstone and J. Law, Can. J. Phys. 5i8, 294 (1980).32. W. Stepien-Rudzka and S. Wycech, Nucl. Phys. A362, 349 (1981).33. R. Bertini, 0. Bing, P. Birien, W. Bruckner, H. Catz, A. Chaumeaux, J.M. Durand, M.A. Faessler, T.J. Ketel, K. Kilian, B. Mayer,J. Niewisch, B. Pietrzyk, B. Povh, H.G. Ritter and M. Uhrmacher, Phys. Lett. 90B, 375 (1980).34. C.B. Dover, A. Gal and D.J. Millener, in preparation.35. C.B. Dover and A. Gal, submitted to Phys. Lett.36. E.V. Hungerford et^  al. (private communication, BNL-Houston-MIT-CMU-Vassar collaboration).37. R. Bertini et al., CERN-EP/81-14, submitted to Nucl. Phys. A.38. L. Majling, M. Sotona, J. Zofka, V.N. Fetisov and R.A. Eramzhyan,Phys. Lett. 92B, 256 (1980).39. A. Gal, Nukleonika Z5, 447 (1980).40. M.M. Nagels, T.A. Rijken, J.J. de Swart, G.C. Oades, J.L. Petersen,A.C. Irving, C. Jarlskog, W. Pfeil, H. Pilkuhn and H.P. Jakob, Nucl.Phys. B147, 189 (1979).41. M. Dillig, V.E. Herscovitz and M.R. Teodoro, contribution 132 to the Ninth International Conference on High Energy Physics and Nuclear Structure, Versailles, July 1981.166<167EXPERIMENTAL HYPERNUCLEAR PHYSICSB. Bassalleck Carnegie-Mellon University, Pittsburgh, PA, 15213ABSTRACTRecent experimental results from the study of A- and E-hypernuclei through the (K",ir-) reaction are reviewed. New experiments which are just beginning or being actively prepared are also discussed. In addition, an outlook is given at possible first experiments that could utilize the much higher fluxes of a kaon factory.INTRODUCTIONAlthough the field of hypernuclear physics is an old one by now there has been a strong renewed interest and a lot of experimentalactivity in this area. This is demonstrated by many papers presentedat workshops and conferences over the past few years. 6The strangeness exchange reaction (K- ,TrT) on many different nucleihas played the dominant role in producing A- and E-hypemuclei and instudying their spectroscopy. Due to its kinematical properties it isvery well suited to replace a nucleon with a A-or E~hyperon in a small momentum transfer reaction. This is true for kaon momenta in the region of 400-800 MeV/e and pions detected under small angles with respect to the incident kaon direction. These are the conditions under which allrecent data, both at CERN and BNL, were taken. I will report on thesemost recent experiments on A- and E-hypernuclei and mention some of the experimental limitations. I will also discuss several new and more ambitious experiments which will be performed over the next 2-3 years.At the end an outlook will be attempted at the possible initial program in hypernuclear physics at a kaon factory.RECENT EXPERIMENTS ON A-HYPERNUCLEIAt CERN the systematic investigation of A-hypemuclei by the Heidelberg-Saclay-Strasbourg collaboration using the (K- ,ir_) reaction has been finished and the results published.7,8 Using kaon momenta between 640 MeV/c and 790 MeV/c the spectra were obtained in missing- mass technique. For each event the momentum of the incoming kaon and of the emitted pion are analyzed, as well as the angle between the trajectories of the two particles. With all the masses being known the mass of the hypemucleus or the hyperon binding energy can then be calculated. The kaon momentum analysis was done in the last stages of the beam line whereas the pions were analyzed in a special magnetic spectrometer SPES II from Saclay.9 This QDD spectrometer incorporates large angular (s 40 msr) and momentum acceptance (<±18% ^P) and a reso­lution of better than 0.5 MeV/c at 700 MeV/c.9 Fig. 1 shows the beam line and spectrometer set-up. The kaon flux on target was typically around 2 x 10^ per beam burst at 720 MeV/c with a ratio of about12. More details about the experimental set-up can be found in ref. 7.168Fig. 1, (K,ir) set-up at CERN. The particle trajectories are determined by the hodoscopes HI and H2 and the wire chambers W1-W8, Kaons and pions are identified by the liquid hydrogen Cerenkov counters Cl and C2 at the target position and by time-of-flight measurements between the scintillation counters PI, P2, and H2.KaonFig. 2, (K,?0 set-up at BNL, The particle trajectories aredetermined by the wire chambers P1-P8. Kaons are identified by the Cerenkov counters CK and CP and by time-of-flight measure­ments between the scintillators SI, ST and S2. The beam line elements to be used for kaon momentum analysis in the future are also indicated.169The collaboration studied a series of target nuclei, ranging from 6Li to 209Bi at 0°. Good agreement was found between measured production cross sections7 and distorted-wave impulse approximation calculations.10 These calculations give a rather successful account of the data for transition probabilities to hypernuclear states with simple particle-hole configurations. A one-step reaction mechanism seems to be well estab­lished for the lower excited states seen.The same experiment also emphasized the usefulness of the (K~ ,tt") reaction for the investigation of deep-lying neutron hole states at very low momentum transfers.8 This feature could be even more exploited at the new lower momentum kaon beam line at CERN.11At BNL the study of hypernuclear states in 12C, ^C, ^ N  and ^ 0  has been finished.12’13 The experiments were done by a BNL-CMU-Houston- MIT-Torino-Vassar collaboration at the low energy separated beam LESB I using 800 MeV/c kaons. Basically the same missing-mass technique was used as at CERN. Since the beam line itself did not have any momentum analysis incorporated, the momentum of the incident kaon had to be measured in a separate spectrometer. For both kaons and pions very simi­lar QQDQQ spectrometers were used, see fig. 2. The pion section had an angular acceptance of about 10-11 msr and a useful momentum bite of 'v ±3%. The K" flux at the experimental target was typically 2 x 104 per beam burst (approximately 104/sec) with a ir“/K“ ratio of about 13. More details about the set-up can be found in ref. 13.The new ingredient in these BNL measurements is the variation of the angle of the emitted pion with respect to the incident kaon from 0° to 25“. For 12C and 13C the momentum transfer was thus varied from 'v 50 MeV/c to 'v 330 MeV/c. This turned out to be very important for a reliable assignment of the different states observed. The ^ C  spectrum, in particular, proved to be very rich in structure. Fig. 3 shows some of the results. As the momentum transfer is varied states of different configuration are preferentially excited. The observed excitation spec­tra could be interpreted in a consistent shell model involving a A- hyperon coupled to a strangeness-zero nuclear core.13’14 In this model a A in either the Is or the lp shell is coupled to those core nucleus states which have the strongest one neutron hole strength. The location and strength of these core states is taken from cfp calculations and from single neutron pick-up reactions, like (p,d). The 1^C results are consistent with a very small A-nucleus spin-orbit interaction. This was deduced from upper limits on shifts of levels as the angle is varied.This conclusion had been independently arrived at by the Heidelberg- Saclay-Strasbourg collaboration at CERN.15 A detailed shell model coupled with a distorted wave calculation yielded very good agreement with the experimental angular distributions in ^ C . 14Based on the existing A-hypernuclear spectra more angular distri­butions should certainly be encouraged, both for different target nuclei and at lower kaon momenta.RECENT EXPERIMENTS ON Z-HYPERNUCLEIThe unexpected observation of relatively narrow Z-hypernuclear states at CERN16 has caused much excitement among experimentalists and theorists. The strong ZN AN conversion in nuclear matter was generally expected to lead to the nonexistence of narrow states.(Wdfl/dE (/tbtr-'MeV'170E X C I T A T I O N  ( M « V )171To further investigate these interesting aspects at BNL the same collaboration mentioned previously undertook a search for narrow E-- hypemuclear states in 6Li and 160. The (K-,ir+) reaction at PK=720 MeV/c was chosen, resulting in very clean excitation spectra with no back­ground from kaon decay events as is always the case in (K_ ,tt“) reactions. Only isospin 3/2 levels in the residual E“-core hypemucleus are popu­lated in this reaction proceeding via the K~p E-ir+ elementary inter­action. The same beam line and spectrometer at the Brookhaven AGS was used as for the A-hypemuclear studies.The 6Li results at 0° show clear indication of structure, see fig. 4, For reasons of kaon flux the experiment could not be done below a> 700 MeV/c kaon momentum. The kinematics then resulted in a larger momentum transfer to the E~ 130 MeV/c at 0°) than to a A and therefore a larger contribution from the quasifree continuum in the spectra. A comparison of the excitation spectrum of |_He(=5He+E") with the ®Li and ^Be results from CERN suggests an interpretation in terms of simple particle-hole states in the Is and lp shell.17A main motivation behind the 160 target was the hope to learn something about the E-nucleus spin-orbit interaction by studying the splitting of the P3/2 ancl ^1/2 substitutional states, if they could be clearly identified. Preliminary results, taken with a water target, showed an indication of two peaks at rather high excitation energies.More data have been taken with a liquid oxygen target in order to get rid of the strong peak from the elementary K“p -*■ E"ir+ reaction. Analysis of this measurement is still in progress and an interpretation with respect to the E-nucleus spin-orbit interaction is being worked on.It seems clear from these recent BNL results that much more data ought to be accumulated on E-hypernuclei at lower kaon momenta (P^~ 400-500 MeV/c). A new CERN experiment is setting out to do just that and I will come back to it later.EXPERIMENTAL LIMITATIONSThe following features are common to the recent generation of hyper­nuclear experiments at CERN and BNL: ratio of 'v 12-15, ^ 2 x 104K" per beam burst (or ^ 101* K”/sec) at P^ = 700-800 MeV/c, and a reso­lution of 2-3 MeV FWHM for targets of ^ 2 g/cm2 .It is clear that the most relevant experimental limitation at present is the available kaon flux. It has forced the use of relatively thick targets which contribute significantly to the obtainable energy resolution due to straggling and differences in ir and K energy losses in the target. In addition most differential cross sections decrease with angle and so far the angular distributions tend to be limited bystatistics at the larger angles.Obviously a factor of 10-100 increase in kaon flux would be oftremendous importance in hypernuclear physics. However at this pointa significant improvement in the ir/K ratio becomes necessary in order to keep the counting rates in the upstream detectors at a reasonable level. These detectors normally consist of multiwire proportional or drift chambers for trajectory determination, scintillators for time of flight measurements and Cerenkov detectors for the kaon identification.In a typical set-up they are located between the mass slit and theEvents/MeV Events / 1.5 MeV8 n - B A (MeV)4. Comparison of preliminary pion spectra observed fora) 6Li(K",it" )jjLi to b) that for 6Li(K“,Tr+)|i_He at 6 = 0° and p^ = 790 and 720 MeV/c respectively as a function of Bn - By (MeV).173analyzing section of the beam line. The challenge for the design of new beam lines then consists in keeping them short for the sake of flux and yet long enough to get good ir/K separation. A possible ap­proach towards an improved tt/K ratio might be a system of two separators and two mass slits with some refocussing elements in between. This concept is part of a new antiproton beam line built at KEK in Japan.18NEW EXPERIMENTSIn this section I want to briefly describe new experiments that are being started or actively prepared.At CERN experiment PS166, a search for E-hypernuclear states using the strangeness exchange (K~,ir-) reactions, has just begun.19 In order to enhance recoilless E production kaon momenta around 450 MeV/c are needed and a new shorter beam line has been built for this purpose.11 Its length is around 10 m as compared to ^ 18 m for the previous kaon beam line used at CERN and 'v 15 m for LESBI at BNL. The same SPES II spectrometer is used as for the A-hypemuclear experiment. The aim of the experiment is a systematic investigation of E-hypemuclear levels in the lp shell. The production cross sections for E“, E^, z+ on deuterium are being studied and 12C and 160 are the next targets planned.19For the next generation of hypernuclear experiments at BNL, which will be coincidence experiments, work has started to effectively shorten the distance from the production target to the experimental target by ^ 8 m. The last QDQ elements of the beam line will be used for momentum analysis and the old kaon spectrometer will now serve as the pion spectrometer, see fig. 2. A drift chamber and a Cerenkov detector will be installed between the mass slit and Q5. They will have to handle a rate of > 3 x 106 particles/beam burst. It is hoped that this con­figuration will result in a factor of 4 to 8 increase in usable kaon flux.Experiment 760 at BNL will study the spin dependence of the A-nucleus interaction by observing hypernuclear y-rays in a experiment. A typical energy difference measurement will ensurethe formation of a hypemucleus and the y-rays from the de-excitation of various hypernuclear levels will be detected in several Nal sur­rounding the target. Much better energy resolution than in the (K-,ir-) experiments will be achieved. Therefore many interesting multiplets corresponding to different spin orientations of the A should be resolved. The hypemuclei to be studied are ^Li, 9Be and 180.2°Experiment 759 at BNL will measure the lifetime and the weak decay modes of ^ C  in a counter experiment. Again a measurement willtag the formation of the ground state of ^ C 12 &nd charged particles,i.e. pions and protons, from its weak decay will be detected in a large solid angle O  4 sr) scintillator range telescope.21 The A bound in the Is orbit can only decay through a strangeness nonconserving weak current. In addition to the mesonic decay A -*■ p+ir", like the free A, the nuclear matter introduces two new nonmesonic decay modes A + P ->■ n + P. Pauli blocking due to the low Q-value in the mesonic decay leads to an expected dominance of the nonmesonic decay modes in all but the lightest hypemuclei. The energy distributions and rates174for both charged particle decay modes will be measured at the same time. Using high timing resolution scintillators it is hoped to measure the lifetime of 12C with an overall accuracy of cr ~ 120-180 ps.If the technique and the counting rates turn out to be satisfactory other target nuclei could be studied.Another BNL experiment22 will investigate the possibility of producing A-hypemuclei with energetic pions (P^ = 1-1.5 GeV/c) via the (tt+ ,K+) reaction. The elementary interaction is ir+n -* AK+ in this case. In contrast to (K~,tt-) the momentum transfer involved is rather high (q = 300 MeV/c), even in the forward direction. Preferential population of high spin states is expected,23 yielding information which is complementary to where low spin states dominate atforward angles. Predicted cross sections at 0° for the strong states in (it+ ,K+) are around 5-20 yb/sr,23 as compared to a. 1-2 mb/sr for the strong states in However the much higher pion fluxesavailable should make the (tt+ ,K+) experiment quite feasible, for instance at the BNL LESBI.SUMMARY AND OUTLOOKIn this section I would like to present some ideas about a pos­sible initial program in hypernuclear physics at a kaon factory, based on the information that comes from the present generation of experiments.An obvious extension of the available hypernuclear data could be foreseen in 'standard' (K~,ir) experiments. Different target nuclei, measurements at different kaon momenta, good statistics not just in the dominant peaks - all that would be within easy reach given kaon beams that are around a factor of ^ 100 more intense than the present ones.Special emphasis could be put on better resolution and more ex­tensive angular distributions. The first could be achieved by using thinner targets and high resolution (and usually small solid angle) spectrometers. The lower counting rates in these experiments would be compensated by the higher fluxes. The usefulness and importance of angular distributions in (K",ir) is clearly demonstrated in the recent BNL results. Together with improved resolution (< 1 MeV FWHM) they would allow further exploration of the A-nucleon and A-nucleus interactions. Besides reliable assignment of levels more detailed information on important issues like spin-orbit and residual interaction would be obtained. Once again the limiting factor so far has been the statistics at the larger angles and a high flux kaon beam is a neces­sity.Apart from A-hypernuclei a kaon factory could address the exciting new spectroscopy of E-hypemuclei in much greater detail. Among the possibilities are systematic studies involving different target nuclei in the kinematically favorable region of low momentum transfer, i.e. around P]( = 400-500 MeV/c. Because of the kaon decays at this low momentum higher fluxes would be particularly welcome. If enough narrow states should be seen around 0° then angular distributions would again provide important information on the levels and E-nuclear inter­actions. Undoubtedly the present experiment at CERN will shed some light on these questions and at the same time point out new aspects to be investigated at a kaon factory.175Given significantly higher kaon fluxes more ambitious and compli­cated coincidence experiments of the CK~,i t x) type become much more feasible. As already indicated in the section on new experiments x can be gamma rays, charged particles or neutrons resulting from various decays of the hypemucleus. These experiments have the potential of giving much more detailed information. Among the possibilities are level schemes with higher resolution and spin assignments from angular correlations of the deexcitation y's.21t>25 Interesting aspects of weak interaction physics can be addressed by studying the ultimate weak decay of hypemuclei. A systematic study of the lifetime and the mesonic and non-mesonic decay modes of different hypemuclei is needed.A prototype experiment on which is in preparation for BNL has been mentioned earlier.21 The non-mesonic decay mode AN + NN could be used to study in detail this four-fermion weak interaction by detecting both nucleons in coincidence, i.e. in a (K“,tt~NN) experiment. This however would require the highest possible fluxes even at a kaon factory.A new dimension would be added to hypernuclear physics by studying strangeness S = -2 systems, i.e. 5- and AA-hypemuclei produced in (K”,K ) or (K“,K®) double strangeness exchange reactions. It is not known whether the E-hyperon will live long enough in the nuclear envi­ronment to form narrow hypernuclear states. The strong conversion SN->-AA might prevent this. AA-hypemuclei, however, do exist26 and their investigation would yield valuable information on the hyperon- hyperon interaction. The predicted cross sections27 for both E~- and AA-hypemucleus formation are around 5-10 yb/sr for the summed cross section and in the nanobam region for discrete low-lying states. Incident kaon momenta would be around 1-2 GeV/c. Only with the highest expected fluxes from a kaon factory and very large solid angle detectors would most of these experiments become feasible.Radiative kaon capture K"N -> Yy (Y = A or E) either at rest or in flight is a yet unexplored possibility for production of both A- and E- hypemuclei. A good low energy kaon channel would provide a high stopping rate for K~ and make the experiments at rest particularly attractive. Large solid angle Nal arrays or pair spectrometers for better resolution could be envisaged for the detection of the y ’s in the few hundred MeV region.At one extreme end of the spectrum of hypemuclei are the possible dibaryons with strangeness S / 0, i.e. YN and YY systems (Y = A,E,5). Since the advent of QCD a great deal of interest has been devoted to states with more than three quarks bound by colour forces rather than by mesonic forces. A kaon factory could address these questions in detail and look for bound states of different systems, for instance E"n, E“n, AA.The above list of possible hypernuclear experiments is certainly not complete and only a starting point for such a program at a kaon factory. It shows, however, that there are many exciting experiments in this field waiting for the promised land of higher kaon intensities.176REFERENCES1. Proceedings of the Kaon Factory Workshop, Vancouver, 1979,TRIUMF Report TRI-79-1.2. Proceedings of the 1979 International Conference on Hypernuclear and Low Energy Kaon Physics, Jablonna, Poland, Nukleonika, Vol. 25 No. 3-4 (1980).3. B. Povh, Nucl. Phys. A335, 233 (1980).4. R. H. Dalitz, Nucl. Phys. A354, 101c (1981).5. P. D. Barnes in Proceedings of the Workshop on Nuclear and ParticlePhysics at Energies up to 31 GeV. Los Alamos, January 1981, LASL Report LA-8775-C, p. 413.6. P. D. Barnes, Invited Talk at the Ninth Int. Conference on High Energy Physics and Nuclear Structure., Versailles, France, July 1981.7. R. Bertini et al., Nucl. Phys. A360 315 (1981),8. R. Bertini et al., preprint CERN-EP/81-14, March 1981, submittedto Nucl. Phys. A.9. E. Aslanides et al., in Abstracts of papers submitted to the 7th Int. Conf. on High Energy Physics and Nuclear Structure, Zurich 1977, p. 376.10. A. Bouyssy, Phys. Lett. 99B, 373 (1981).11. R, Bertini et al., CERN proposal, CERN/PSSC/79-37, Geneva, 1979.12. R. E, Chrien et al,, Phys. Lett. 89B, 31 (1979).13. M. May et al,, Phys. Rev. Lett. 47, 1106 (1981).14. E. H. Auerbach et al,, Phys. Rev. Lett. 47, 1110 (1981).15. W. Brtlckner et al., Phys. Lett. 79B, 157 (1978).16. R. Bertini et al., Phys. Lett, 90B, 375 (1980).17. E. Hungerford et al., to be published.18. F, Takeutchi, private communication.19. P, D, Barnes, private communication from the Heidelberg-Saclay collaboration,20. M. Deutsch et al., BNL AGS proposal #760, 1980,21. P. D. Barnes et al,, BNL AGS proposal #759, 1981.22. H, A. Thiessen et al,, BNL AGS proposal #758, 1980.23. C, B. Dover et al., Phys. Rev, C22, 2073 (1980).24. M. Bedjidian et al., Phys. Lett, 94B, 480 (1980).25. R. H. Dalitz and A. Gal, Ann. Phys, (NY) 116, 167 (1978).26. P. Mandal and M, Saha, Can. J, of Phys, 58, 300 (1980) andreferences therein,27. C. B. Dover in ref. 2.177D . AxenTRIUMF, Vancouver, B.C., Canada V6T 2A3 INTRODUCTIONThis section contains summaries of reports by J. Beveridge andA. Yamamoto on charged kaon yields and a report by J. Doornbos on existing neutral kaon beams. The data from the CERN proton synchrotron on negative pion and kaon and antiproton yields at three energies from carbon, copper and tungsten targets are extremely preliminary. Data from KEK are restricted to one incident proton energy. The neutral kaon data are from a number of laboratories ranging in energy from 6.2 GeV at Berkeley to 400 GeV at Fermilab.PRELIMINARY RESULTS OF CERN MEASUREMENTSREPORT ON KAON PRODUCTION AND NEUTRAL KAONS WORKSHOPIn early July 1981 a collaboration of groups from CERN, Saclay, Rome, LANL and TRIUMF carried out the measurement of particle production cross sections on the K24 beam line at the P.S. at CERN, Geneva. For these mea­surements all beam line elements except the bending magnets were turned off and the solid angle and momentum acceptance were determined by sets of slits and scintillation counters. Particles were identified by time of flight over a 7 m flight path and by two Cerenkov counters, one aerogel coun­ter to distinguish kaons from pions and one gas counter to distinguish pions from electrons. Measurements were carried out at primary proton energies of 10, 18 and 24 GeV for negative secondary particles, tt”, K“ and p, of momenta 1.0 and 1.4 GeV/c.Negative pion production was also measured at 0.4 GeV/c to allow a normalization of yield data which were taken simultaneously on the beam line K26• Five targets were used in the course of these measurements:3 mm and 1 cm Cu, 1 cm L and 3 mm and 1 cm W. A very preliminary analysis of the results of these measurements for kaon and antiproton production is shown in Figs. 1 and 2. These results are extremely preliminary as a number of checks remain to be done.Figs. 1 and 2. Negative kaon and antiproton production cross sec­tions for 1.0 and 1.4 GeV/c particles from carbon, copper and tungsten as a function of incident momentum p.p (GeV/c )178The K2 beam line used for the production measurements is shown in Fig. 3 and the parameters of this line are tabulated in Table I. Target details are given in Table II. Measured differential production cross sections for beryllium are given in Table III and shown graphically inPRODUCTION DATA FROM KEKFig. 4. Pion, kaon and antiproton production cross sections from beryllium.179Fig. 5. Comparison of KEK and CERN production cross sections from beryllium.180Table I. Performances of the beam K2 (at July ’80).Momentum range < 1 - 2  GeV/cTarget 6 mm diam x 60 mm ptCentral production angle 0°Beam length 28.9 mSolid angle acceptance 1.02 msraHorizontal acceptance ±50 mraVertical acceptance ±6.5 mraMomentum bite ±3% Ap/pSolid angle momentum acceptance 6.25 msr% Ap/paSeparator voltage 600 ~  700 kVSeparator gap 10 cmSeparator length 6 mBeam end characteristicsHorizontal magnification 2.4Dispersion 0Angular dispersion 0aVertical magnification 2.5Horizontal image size (FWHM) 2 cmVertical image size (FWHM) 2 cmHorizontal divergence <±27 mrVertical divergence <±3.6 mrParticle yields for 1012 13 GeV/c ppp2.0 GeV/c K+ 5.0 x io5K“ 1 . 0  x 1 0 5? 1.5 x 10^3  j  •  i181Table II. Parameters of the production targets,Materialst a (cm)t/Aa b cnBe 1.91 0.0506 0.0481Al 1.93 0.0533 0.0505Cu 0.77 0.0541 0.0513Pt 0.50 0.0593 0.0559aTarget thickness.^Normalized absorption length.cProduction efficiency when t << Ap ,As (see text).Table III. Measured differential production cross sections/        .. .. . ;      - —_ d2a/d^dp [mb/(sr*GeV/c)/nucleons]P [GeV/c] w+ ir- K+ K- p p0.525 137 ± 50.735 177 ± 2 152 ± 2 7.5 ±1.1 1.98 ± 0.27 49.6 ± 1.0 0.Q072 ± 0.00150.945 202 ± 1 177 ± 1 11.8 ± 1.4 3.25 ± 0.26 65.3 ± 0.5 0.028 ± 0.0031.16 214 ± 1 188 ± 1 13.4 ±0.9 4.38 ± 0.29 73.1± 0.5 0.058 ± 0.0051.47 237 ± 1 199 ± 1 14.4 ± 1.6 4.70 ± 0.39 81.8 ± 0.4 0.120 ± 0.0091.79 255 ± 1 200 ± 1 18.1± 0.4 5.78 ±0.46 85.3 ±0.3 0.172 ± 0.0122.10 265 ± 1 190 ± 1 18.6 ± 0.5 5.78 ± 0.40 90.3 ±0.3 0.214 ± 0.012aPrimary proton momentum: 12.9 GeV/c; target: Be; production angle: zero degrees. Systematic errors are not included. Systematic errors are estimated to be -$±20%. They are mainly due to the uncertainty of pri­mary proton flux and solid angle.NEUTRAL KAON BEAMSAn incomplete list of neutral kaon beam lines is given in Table IV. Neutron contamination is always a problem in any neutral beam. Neutrons being heavier, particles tend to have higher yields in the forward direc­tion, hence neutral kaon lines usually have small non-zero production angles to reduce the neutron contamination.The Kg lifetime of 0.089 ns and decay length of P(GeV/c) x 5.37 cm renders experiments with Kg beam from initial production targets impos­sible. K2 beam can be regenerated by utilizing the fact that Kq and Kg interact differently with nuclei. Regeneration has been discussed by Myron L. Good.1REFERENCE1. M.L. Good, Phys. Rev. 106, 591 (1957).Table IV. Parameters of typical neutral kaon beam lines.LabProtonenergy(GeV)Target NP nkdfi(msr)TakeoffAngleLengthchannel(m)LengthdecayregionN(neutrons) N(kaons)Berkeley 6.2 cu . 1012 0.7 X 106 0.7 3.7° 7.6 5.0 «200ANL 12.0 10.2 cm CU 2.5 x 1011 14 X 10b 0.7 4.0° 6.0 10.4CERN 1 24.0 Pt 0.6 4.3° 6.6 10.0CERN 2 24.0 4.5 cm Pt 0.002 8.0° 30.0 4.0BNL 1 28.5 10.2 cm Pt 6 x io10 2 X 10b 0.1 6.0° 7.0 5.0 3-5BNL 2 28.5 8.9 cm Pt 0.1 3.0° 3.0 3.6BNL 3 28.5 8.9 cm Ir 1010 2 X 10b 0.4 4.0° 2.6 15Fermilab 400 3 x io12 2.5 X 10b 10" 5 7.19 mr 500 m 10.0 m 4-5Mi+ 7.32 mrFermilab 400 3 x IQ12 7.5 X 10b 0.7 x io~3 0.25 mr 500 m 50 m «200m3Fermilab 300 7.3 10.0M2Note: Length of channel is the distance between production target and beginning of the decay region.183D.A. Bryman TRIUMF, Vancouver, B.C., Canada V6T 2A3It is apparent that we are now embarking on a long road which will eventually lead to an understanding of the weak interaction and of the basic nature of the neutrino. Planning for neutrino physics will play a major role in the development of a new high-intensity, high-energy accel­erator at TRIUMF since neutrino fluxes are expected to be roughly two orders of magnitude greater than at existing facilities. In this work­shop we have attempted to outline the issues and important problems re­lated to 1) neutrino physics at medium energy, 2) neutrino beams, 3) neu­trino detectors, and 4) accelerator design.1. NEUTRINO PHYSICSThe physics potential of a neutrino factory lies in the ability of probing new structures or extensions of the standard Weinberg-Salam SU(2)xU(l) theory of electroweak interactions. In particular the grand unified theory (GUT) of SU(5) with the usual 5- and 24-dimensional Higgs gives a definite prediction for sin20w as well as for the lifetime of the proton. Hence, a precise measurement of sin2^  to 1% will be immensely valuable to testing GUTs. Crucial experiments are the following neutral current measurements: .1) Vy + e” -> Vy + e~2) ^Vy + p -*■  ^Vy + p(_) -L. * ^ -L ~3) ve + e ve + eThe last experiment also allows us to study the charge and neutral current interference. A precise measurement of (3) could reveal or limit the ex­istence of extra neutral gauge bosons beyond that of the basic SU(2)xU(l) theory.Another class of experiments involves the search for neutrino oscil­lations. A careful study of oscillation phenomena is warranted for the understanding of the neutrino mass spectrum which also has important cosmological implications.Although neutrino-nuclei interactions are of limited value to the study of nuclear structure, several key experiments have to be scruti­nized since they are important for the determination of sin2^, and for the interpretation of the v-oscillation experiments. These include:ve+ 12C -> JT+12N ve+D -> £-+p+pThe coherent scattering of neutrinos on nuclei, e.g. ^Vy+He -*■ ^Vy+He ,will also be of great interest to astrophysics and will enable the deter­mination of the weak neutral current in nuclei.The above experiments will require clean neutrino beams with the highest possible energies and intensities.REPORT ON THE NEUTRINO WORKSHOP1842. NEUTRINO BEAMSA. Sources of neutrinos at proton acceleratorsThe two main sources of neutrino beams are the two-body decaysir4 -*■ y ±+v(V)K± y±+v(v) .There is also a small contribution fromK -*■ Tr+y+Vy -»■ r+e+ve .Another source comes fromy+ + e++ve+vyeither at rest or possibly in flight in a y storage device.At this meeting, we also considered the possibility of producing copious fluxes of ve from k£ decay. Pions transfer only 40% of their momentum to the Vy whereas K transfer almost 99% of their momentum, so K-induced Vy are of higher average energy.B . Elements of high energy v beams1*21) proton beam, production target, production cross sections2) momentum and sign selection3) decay region4) shield5) detector and flux monitoring devices Figure 1 shows two typical set-ups.Fig. 1. A schematic drawing of the Fermilab (a) and the BNL (b) neutrino set-up.1851) Hadron production cross sectionsInclusive tt production cross section can be parametrized by- Cocioni-Koester-Perkins distribution- or Sanford-Wang distribution.3Experimentally there are few 0° measurements and the normalization of the various data sets is uncertain. The phenomenological parametrization of Sanford and Wang seems to have restricted validity as different param­eter sets are obtained in different energy ranges. Preliminary data from a recent CERN experiment are not consistent with KEK data by a normaliza­tion factor of order 2. Scaling for zero degree data has not been estab­lished because of the scarcity of the data. It was claimed that the Wang parametrization did not work for.K” at low p energies (in the tens of GeV range).2) Sign and momentum selectionWideband beams:The focusing element in these beams is generally an achromatic device such as the Van der Meer magnetic horn.14 A toroidal field is produced around the secondary hadron beam axis which focuses hadrons of one charge and large momentum band while defocusing the other charged state. These beams provide sign selection and maximum flux; the v energy spectrum is a steeply falling function of Ev [Fig. 2(a)], which is difficult to monitor in practice, and the maximum flux peaks at low energy.Horns are essentially pulsed devices because of the large currents involved and the associated cooling problems. Some contamination remains from wrong sign particles emitted near the axis of the horn. As an ex­ample, the CERN PS horn optimized for 6 GeV/c particles produces the gain indicated in Fig. 2(b).Narrow momentum beams:a) High band beam. The focusing device is generally a quadrupole triplet optimized for transmission of high energy hadrons. These beams can accom­modate a dc duty cycle. The flux of high energy v is enhanced and one gets a better understanding of it. The total flux is lower compared to the broadband beam and also there is no vv selection. See Fig. 3.Fig. 2. (a) Vy,Vp and ve ,ve fluxes for the CERN PS wideband (horn- focused) beam, (b) gain due to the horn device for the CERN PS v beam.186SPS NEUTRINO FLUXESFig. 3. Comparison of narrowband and wideband fluxes through CDHS detector (CERN SPS).Fig. 4. Anti-neutrino flux estimates for the beam tuned to select negative particles com­pared with the flux from a bare target. The flux of background neutrinos is also shown. Ordinate: flux/GeV m 2*101+ incident protons.b) Dichromatic beam.5 Here the secondary beam consists of both dipoles and quadrupoles, which provide a beam of sign-selected hadrons with nar­row momentum bite. To reduce the contamination from wrong sign hadrons decaying before the first dipole, the beam line has to be kept short.The neutrino detector is used as a measuring device for the decay angle of the hadron and the v energy can be reconstructed within two narrow bands corresponding to the n or K decay. The v energy resolution depends on- momentum acceptance of the parents- angular divergence of the parent beam- length of the decay section.Figure 4 describes, the Fermilab dichromatic beam.C . Neutrino beams at meson facilitiesOnly LAMPF has presently done v experiments, mainly because of the favourable duty cycle there. We will briefly review their present v facility as well as some of the proposed developments.The v facility at LAMPF is centred around the beam stop for the 800 MeV, 630 yA beam. The neutrinos come from tt+  decay at rest ( v y )  and from y +  decay at rest (ve and " V y ) . Figure 5 shows the energy spectrum and the schematic of the experimental area. The contamination of "ve is very small, and typical fluxes are 107/cm2/sec at 7 m from the beam stop for a 670 yA beam. < " v y >  energy is always below the y  production threshold but is only typically 37 MeV.ENERGY GeV187Fig. 5. (a) Neutrino spectra, (b) Experimental area.Several proposals at LAMPF call for decay-in-flight channels. Experi­ment 645 considered a 20 m decay tunnel off the main proton beam dump.(v> in the range 100 MeV < Ev < 250 MeV would be available with rates107 Vy/sec/cm2 at 18 m and 1.6xl06 "Vy/sec/cm2 at 18 m.Experiment 638 proposed a decay channel coming off beam line D, which feeds the new proton storage ring. Proton intensities of order100 yA could be injected. Predicted fluxes are: bare target 5.8x10sVy/cm2/sec and 0.6xl05 "Vy/cm2/sec at 50 m; with dipole focusing 7.7xl05 Vy/cm2/sec at 50 m.The experimental layout for these two experiments is shown in Fig. 6.Fig. 6. Layout of the LAMPF neutrino experiments, a) Details of the Vy in-flight beam, b) Details of the v-oscillation experiment.188D. New IdeasAn important disadvantage of the existing high energy v facilities is the lack of Vg beams. At the workshop we heard of two new ideas for generating such beams.1) Neuffler6 from Fermilab has proposed a y storage ring fed by the Fermilab booster and has also investigated other machines in the p energy range 3 to 80 GeV. and "vy would be produced simultaneously and detec­ted along the straight sections of the ring. Vy from tt decay would be present only during a it lifetime. Table I gives estimated performances of such a system.Table I. Performance of a muon storage ring for neutrino production.y ring energy (GeV) p energy (GeV) angular acceptance (mR)^2- pion/GeV/c/pve "vy flux per 3x1013 p8 4.5 4.5 1.5 1.580 80 30 30 825 50 50 100 1009 x 1 0 "3 2.2x10"2 1.4xl0“2 1.7xl0-2 0.9x106xl08 5.7xl09 3.6xl09 3.9xl09 1.8x10More realistic numbers for the flux should be generated which would take into account decay sections, detector angular acceptance, etc. Still this represents a very good prospect at a high intensity (100 yA) facility and requires further consideration.2) Hoffmann7 presented his conclu­sion on the possibility of producing ve and \Fe beams from k£ decays. A k£ beam would be produced by bombarding a production target and extracting the neutral beam from it, eliminating charged particles by a sweeping magnet; the neutral beam would be allowed to decay in a decay region, hadron com­ponent removed in a shield region (see Fig. 7).Estimated fluxes were given for 100 yA incident beam at 25 GeV in afiducial area of 2.5m flux7 . 5x108/sec, Ev > 1 GeV (see Fig. 8)Fig. 7. Schematic diagram of the neutrino beam obtained from k£ decay.Fig. 8. Estimated neutrino fluxes from k£ decay in a fiducial area of 2.5 m x 2.5 m with a 100 yA,25 GeV proton beam.189E. Discussion summaryThe discussion following the plenary session tried to address the question of the optimum energy range for a p machine by maximizing the integral of v flux times a cross section as a function of v energy.Chen presented his calculation based on certain tunnel length and shielding thickness assumptions. For the assumption of 110 m total length to the detector and detector size 1.5 m 2, a shoulder appears in the total event rate for 10 GeV protons. The position of this shoulder is presumably very dependent upon the above assumptions, and more optimization should be performed. In any case it seems that the average< Ev> tends to flatten out as the p energy is increased because the fixed decay tunnel length always favours lower energy pion decay (increasing the decay region length has to be balanced against the reduction in solid angle).A consensus developed that a 15 GeV machine was probably a safe bet. The duty factor was considered to be critical for most experiments, and the synchrotron option was favoured for obtaining the "worst" possible duty cycle to reduce cosmic ray backgrounds.Davies reported on new v facilities being proposed in Europe. The new European intense spallation neutron source to be operated in England has provision for v facilities off the beam dump. A new proposal is being developed in Jiilich for a 1.2 GeV 10 mA spallation neutron source which would also be a good source of neutrinos.3. NEUTRINO DETECTORSThe factors which determine detector design are the beams (i.e. fluxes and duty factors) as described in the previous section, the cross sections and the backgrounds. Currently, the first two dominate the de­sign and construction of the detectors.The total cross sections for neutrinos and antineutrinos on nucleonsare:CTTot v = 0.7x10”38 Ev cm2-GeV-1 °Tot = 0.37x10” 38 Ev cm-GeV-1 .While some typical fluxes are:Los Alamos (ve) 2x107 cm2 sec 1BNL ( V y )  106 cm2 sec” 1 .Thus, although the fluxes are large the cross sections are so low that interaction rates are extremely small, typically ~102/day for detector mass ~102 tons, flux ~106 and Ev ~ l  GeV.Important backgrounds are:1. cosmic rays2. neutrals (neutrons and y-rays from the production target)3. muons from the production target.Each of these has to be removed by some form of shielding. This shielding generally must be massive and is extremely costly. The accelerator’s duty factor is also important because very, low values directly reduce the non-machine-associated backgrounds.190The following conclusions can be drawn:1. detectors must be very large (~102 tons)2. the shielding must be large (~100 m water equivalent)3. the duty factor should be as low as possible (~10-6).For typical existing detectors the masses range from ~10 tons (LosAlamos) to ~1000 tons (Fermilab and CERN). The shielding is also massivee.g. ~100 m of earth at BNL. Active shields with pulsed iron to deflect the muons have also been used.Detectors are a challenge to experiment designers since good resolu­tion is required in energy and space. Also, information has to be extrac­ted from a very large mass which often means that many detector elements are needed and poor resolution results due to multiple scattering and coarse segmentation. The nature of and effectiveness of the inevitable compromises are defined by the object of the experiment and the skill of the designers. For the reactions described in Sect. 1, it is anticipated that positron resolution £1 cm and energy resolution a ~5% may be required.As samples of the existing techniques we have chosen four detectors. The first is the neutrino detector at Los Alamos which is a Cerenkov calorimeter, a 6 ton water £eren- kov counter viewed by 96 phototubes. It records the total amplitude of Cerenkov light emitted by electrons in the 25-50 MeV range.There is no directional sensitivity. The detector was designed to observe positrons from the reaction~ve p -* n e+ .The energy resolution was typically a = 12% at 40 MeV. A diagram of the apparatus is shown in Fig. 9.The second example is the neutrino- proton elastic scattering experiment at BNL. Fig. 9. The LAMPF neutrinoA diagram of the apparatus is shown in Fig. detector.10. The detector is made up of cells of liquid scintillator totalling 33 tons.A third detector is the CFRR detector at Fermilab (Fig. 11). It is a typical scintillator, spark chamber iron plate detector. The first part is a hadron calorimeter of 690 tons. The second is a muon detector of iron toroids to measure the muon momentum totalling 420 tons.As a final case the CERN CHARM detector is shown in Fig. 12. It uses marble (CaC03) as its target which is sandwiched with scintillators and proportional drift tubes. The total mass is 100 tons for the target calorimeter.The detectors mentioned above show the magnitude of the effort re­quired to design and build neutrino experiments. The extremely large masses involved indicate the importance of obtaining higher neutrino fluxes. Higher rates would enable construction of more sensitive and com­plex detectors leading to important advances in neutrino physics.Discussions were held after the plenary sessions concerning the devel­opments of new concepts in neutrino detectors. Prof. H. Chen (Univ. of California, Irvine) described his work on large volume liquid Ar detectors. He stated that he was able to drift up to 1 m in liquid Ar with negligibleS C I N T I L L A T O RA N T I -C O U N T E R SD R I F T  C H A M B E R  A N T I - C O U N T E R SC E R E N K O V  D E T E C T O R  ( 6  tons H s O  or D 2 O )191Fig. 10. a) Side view of charged current event. The energies deposited in each cell are indicated (in MeV).b) Typical candidate (top view) for neutrino-proton elastic scattering. The position of the numbers indicates the posi­tion of the track as deduced from the timing information.The value of the numbers indi­cates which cell fired.VETOD R IF T  CH AM BERE -6 1 6  NEUTRINO DETECTOR420 ton p-detectorspark chamber *  every 20 cm690 ton targetscint. every 8 in.spark chamber every 32 in.TOROK) MAGNET CANT: 4 ScMil.3 Sport Cfcomtori 4 . 8 ml of S MI  TO I—  m c A,J ToM of €Fig. 11. Lab E neutrino detector.192Fig. 12. The CHARM detector.loss of charge. A large volume detector of liquid Ar could have ~15 tons of matter and very high efficieny. It could potentially be used as a TPC-type device allowing observation of multiple charged particles over their entire paths and measurements of dE/dx as well. Considerable devel­opment would be required to make a realistic detector with liquid Argon.4. ACCELERATOR DESIGNThe accelerators described in the introduction to this workshop were considered as sources of neutrinos for neutrino research. A consensus developed that the proton energy should be greater than 15 GeV and the duty factor should be at least as good as that available at Brookhaven (1/106) . The only accelerator having these properties in the example list was the 20 GeV superconducting synchrotron. However, it was pointed out that the addition of a storage ring at relatively little additional cost to either of the other examples could give beams with a duty factor of 1/107. In particular, the addition of a superconducting storage ring to the 15 GeV fast-cycling synchrotron would make possible a duty factor of 1/107 at a time average current of 150 yA and would also make possible the same average current at a duty factor of 90% for other types of research.ACKNOWLEDGEMENTThis report was prepared with the collaboration of the workshop dis­cussion leaders, J.N. Ng, J.-M. Poutissou, C.K. Hargrove and J.R. Richardson.REFERENCES1. D.H. Perkins in Accelerator Neutrino Experiments, Proceedings of Summer Institute on Particle Physics, CONF 780765-SLAC-report 215, November 1978.2. J. Steinberger, High Energy Neutrino Experiments, Proceedings of the 1976 CERN School of Physics, CERN 76-20 (1976) p. 57.3. C.L. Wang, Phys. Rev. D 2609 (1973).4. S. van der Meer, CERN report CERN 61-7 (1961).5. P. Limon et al., Nucl. Instr. & Meth. 116, 317 (1974).6. D. Neuffer, IEEE Trans. NS-28, 2034 (1981).7. C. Hoffmann, LAMPF report LA-8760-MS (1981).100 ton193K.P. Jackson TRIUMF, Vancouver, B.C., Canada V6T 2A3 JIMPORTANT EXPERIMENTSBugg has provided a thorough analysis of this field with emphasis on experiments requiring intense beams of high quality_to investigate the spectrum of S =-1 baryons formed as resonances in K-N interactions. The current status of experiments in hadron spectroscopy has also been reviewed for both baryons1 3 and mesons.11,5 The list of specific experi­ments suggested by Bugg would form the basis of a vital part of the experimental program at a kaon factory. One of the great benefits to be derived from the construction of a high intensity facility would be the possibly unique ability to pursue a wide variety of future initiatives.The experiments mentioned below are current examples which in some cases are not crucial to the basic design of the facility but which should be considered as the details of the proposal are prepared._Thomas and Rosenthal emphasized the need for new studies of both K-N and K-N interactions at low energies. The main motivations for these ex­periments would be a contribution to the eventual understanding of the dynamics in the q^q system and the need for better input data for a micro­scopic analysis of the interactions of kaons with nuclei.Most comprehensive studies of baryon resonances have involved forma­tion as opposed to production experiments. However, some important sectors of the baryons (specifically the S = -2 and S=-3 hyperons) and many of the mesons can only be identified as peaks in the distribution of invariant mass of a subset of the products of a reaction.6 Isgur empha­sized the particular importance of such experiments as a means to search for glueballs. The observations reported by Pauli of structure in the strange dibaryon sector is also a relevant current example. The flexi­bility gained in being able to mount specific production experiments wouldbe a significant asset at a kaon factory.There is a need for improved data on the scattering of hyperons from nucleons at low incident momentum (<1 GeV/c). These data are basic both to a comprehensive description of baryon-baryon interactions7 and an understanding of hypernuclei. It should be noted that the analysis of Nagels e± a l_ -7 predicts a strong anomaly in Ap scattering very close to the invariant mass of the structure reported by Pauli.It was generally agreed that the importance of the next generation of experiments with low to medium energy antiprotons was well established.8 No detailed assessment was presented, however, of the potential impact ofa facility coming into operation 5 to 10 years after LEAR.Although brief reference was made to other possible uses of theprimary proton beam at a kaon factory, none was judged crucial to theplanning of the facility. With the closing of the ZGS at the Argonne National Laboratory a significant program of experiments with polarized protons was terminated.9 The possible use of the intense proton beam toproduce a neutron beam should be investigated.REPORT ON WORKSHOP ON HADRON-NUCLEON INTERACTIONS194PRIMARY BEAM REQUIREMENTSThe program of experiments to investigate hadron-nucleon interactions outlined by Bugg depends critically on the improved intensity and quality of the proton beam available at a kaon factory. Although there is still some uncertainty regarding the cross sections for kaon production, it appears that a proton energy in the range from 10 to 15 GeV would be well suited to this program. This section deals mainly with the extra require­ments of the additional experiments outlined above.Serious consideration of an extensive program of experiments with antiprotons would require primary beam at an energy significantly above 15 GeV. Proton energies in the range from 20 to 30 GeV would also be needed for most experiments involving the study of hadron resonances in production experiments since these typically involve secondary kaon or pion beams at energies above 5 GeV.Mention has been made of the potential use of an external beam of polarized protons. The study of hyperon-nucleon scattering at low ener­gies is severely restricted by the short hyperon decay lengths (7 cm for a A of 1 GeV/c) and might also require the direct use of a proton beam. A hydrogen target could be used to observe both the associated production (p+p -*■ K++p+A) and subsequent interaction (A+p -»• A+p) of the hyperons.SECONDARY CHANNELSBugg has mentioned the requirements for three separate kaon channels for the study of baryon resonances in formation experiments and has stressed the need to consider in detail their design and a possible con­figuration for the facility. In particular the feasibility of supplying several secondary channels from a single primary beam line must be examined.A decision to pursue an active program involving antiprotons would almost certainly involve a major commitment to the construction of an antiproton accumulator and a facility resembling LEAR8 utilizing a much higher primary beam intensity. Of lesser consequence, to facilitate resonance production experiments it would be necessary to include a chan­nel capable of delivering separated kaon and pion beams at momenta up to 10 GeV/c.DETECTORSMany of the future studies of hadron-nucleon interactions will depend on the simultaneous detection of several particles. The role of the con­ventional bubble chamber in such experiments has declined. There is an increasing emphasis on the construction of complex electronic detection systems and particle identification over very large solid angles. Exam­ples of such devices recently developed for studies of hadronic interac­tions are the Omega spectrometer at CERN,10 LASS at SLAC11 and TELAS at KEK.12 There are several related issues that should be addressed in the planning of a kaon factory.In a recent review of "Prospects in Baryon Spectroscopy",2 Ferro- Luzzi made the following observation, "No large acceptance flexible elec­tronic detector capable of the high rates needed for these studies has made its impact on the field." It will be important to understand the195the difficulties and limitations encountered in the early development and use of these systems.In the field of particle physics in general the cost of large detec­tors has become a significant fraction of the cost of the facility and the time required for their development requires early planning. The experi­ence presently being gained at TRIUMF with the TPC will he most valuable and should be augmented by the participation of proponents of a kaon factory in relevant experiments at existing facilities.There is clearly a significant challenge to be faced in designing large acceptance spectrometers to utilize the high intensities available at a kaon factory. During the workshop Comyn emphasized the importance in this context of recent developments in the areas of microprocessors and Fastbus.13As a final comment it should be noted that there have been several recent developments in the technology of bubble chambers, particularly in the directions of rapid cycling chambers and hybrid spectrometers incorporating a bubble chamber as a vertex detector. Consideration should be given to utilizing such devices on a low intensity channel at a kaon factory.ACKNOWLEDGEMENTSWe wish to thank the following for informal contributions to thissession: N. Isgur, J. Doornbos, M. Salomon, B. White, P. Kitching andM. Comyn.REFERENCES1. G.P. Gopal, Baryon 1980, Proc. IV Int. Conf. on Baryon Resonances(Univ. of Toronto, 1981), p. 159.2. M. Ferro-Luzzi, ibid., 415.3. R.L. Kelly, Proc. Workshop on Nuclear and Particle Physics at Energiesup to 31 GeV; New and Future Aspects, Los Alamos (LANL, 1981), p. 166.4. R.J. Cashmore, Experimental Meson Spectroscopy 1980, Brookhaven,AIP Conf. Proc. 67 (AIP, New York, 1981), p. 1.5. A.B. Wicklund, Workshop on the AGS Fixed-Target Research Program,BNL 50947, Nov. 8-9, 1978, p. 262.6. B.T. Meadows, Baryon 1980, op. cit.,. p. 283.7. M.M. Nagels, T.A. Rijken and J.J. de Swart, Phys. Rev. D J5, 2547(1977).8. P. Dalpiaz, Proc. Workshop on Nuclear and Particle Physics at Energiesup to 31 GeV: New and Future Aspects, Los Alamos (LANL, 1981), p. 300.9. R.C. Fernow and A.D. Krisch, Annu. Rev. Nucl. Part. Sci. J^, 107 (1981) .10. C. Evangelista et al., Nucl. Phys. B178, 197 (1981).11. A.K. Honma, SLAC report 235, November 1980;L.S. Durkin, SLAC report 238, December 1980.12. K. Nakajima et al., submitted to Nucl. Instrum. Methods.13. Proceedings of the Conference on the Application of Microprocessors to High-Energy Physics Experiments, Geneva, 1981, CERN report 81-07; R.S. Larsen, IEEE Trans. Nucl. Sci. NS-28, 322 (1981).14. L. Montanet and S. Revcroft, CERN/EP report 81-59, submitted to Phys. Reports.196REPORT ON WORKSHOP ON HADRON NUCLEAR INTERACTIONS,AND HYPERNUCLEI WORKSHOPD.F. MeasdayUniversity of British Columbia, Vancouver, B.C., Canada V6T 2A6INTRODUCTIONThere have been many recent reviews of hypernuclei and of the K-nucleus interaction. In addition to the presentations at this workshop, there are the proceedings of four recent conferences, viz. Zvenigorod 1977,1 Warsaw 1979,2 Rome 1980,3 and Liblice 1981.  ^ In addition there are reviews such as those by Povh5 ’6 and Dalitz.7 These various sources show that there is already a significant body of knowledge on this field, but nevertheless there are probably more questions than answers. The following are broadgoals that one can envisage for future research:(a) Study of the properties of A and E hypernuclei(b) Study of exotic atoms(c) Attempt to extract information on hyperon-nucleon interactions (using specific features of hypernuclear structure or, wherever feasible, using direct hyperon-nucleon experiments)(d) Study of the K-nucleus interaction(e) Experiments on new and unusual systems such as charmed orbeautiful nucleiWe shall first summarize the contribution of the speakers in the ses­sion, with a view to defining potentially useful reactions or types of measurements.HYPERNUCLEAR STRUCTUREThe present knowledge of hypernuclear structure is very sketchy and a more complete body of knowledge would permit the extraction of systematic effects. In particular, binding energies of heavy hypernuclei as seen from the high-energy tail of the tt"  spectrum in ( K “ , i t " )  reactions could better determine the binding of a A in nuclear matter. Also, the strong isospin- violating AN force could be studied by (K",ir°) reactions such as 3Be(K” ,ir°)^Li*. This would involve a large solid angle tt° detector with good energy resolution. The LAMPF design could be used as a first approxi­mation, but it should be noted that they are sorely limited by duty cycle.In the study of hypernuclei, different states can be excited by vary­ing the momentum transfer in the (K~,tt_) or (K~,ir°) reaction, so it is essential tha.t facilities be provided for obtaining an angular distribution.KN and KN data below 60 MeV kinetic energy are lacking. The former would help to clarify the nature of broken chiral SU(3) while the latter would provide information on the very peculiar baryonic resonance A (1405). These would require major advances in beam purification. Also lacking are good low-energy YN scattering data, which are needed as input to calcula­tions of hypernuclear structure and for comparison to meson-exchange and quark model predictions. Here also, beam purity is very important.The S=-2 nuclei (AA,E) could be explored via the (K“ ,K+) reaction, and a kaon factory set up to do the above experiments could, with long but reasonable running time, study this reaction as well.197y-SPECTROSCOPYAs the present resolution of the spectrometers used in hypernuclear research is only 2 MeV or so, there has been an attempt to improve the ef­fective resolution by detecting the de-excitation y-rays of the hypernuc­leus. As there are many other y-rays produced when a K interacts with a nucleus, the experiment must seek coincidences between a y event and a (K",tt-) reaction. This means, however, that, with present fluxes, the anticipated event rate is extremely small (6 per day, for example!!).Of particular interest is the hypernucleus 1 ?C where there are a pair of levels at about 10 MeV, both Vfc but separated by about 300 keV. This difference gives vital information on the £*s coupling of the AN force. These levels are bound so should decay to the ground state. For a stopped K - experiment one might anticipate a rate of 20/day, but for an in-flight measurement with a 2 g/cm2 target an event rate of only 6/day is calculated. This is on the edge of feasibility as any unexpected back­ground (accidentals, for example) will ruin the experiment. Remember there will always be y-rays from the break-up of the hypernucleus. The proposal, however, has been accepted as Expt. 760 at the AGS and should start in January 1982.(A more extensive discussion of older experiments was given byH. Piekarz at Zvenigorod, see p. 162 of proceedings.1)LIGHT SUPERNUCLEIWith the discovery of new types of quarks (charm, bottom, etc.), it becomes feasible to consider nuclei which have one baryon containing one of these heavy quarks, and the term supernuclei will be used to describe such objects. Even simple systems of two or more baryons may be bound. Using SU(4) it is possible to estimate the strong force between charmed baryons and nucleons and then to investigate the two- and three-body sys­tems. (The notation used is CQ=Ac and Ci5Ec .)It is found that the C^N singlet state (I=3^ , J=0) is bound but none of the other two-body systems are bound. The C0NN (1=1) and CiNN (1=2) states are extremely loosely bound, but the states C0NN (1=0, J=1/£ and % )  are quite strongly bound, or in alternative terminology, the system qq11’ the charmed analogue of ^H, will be bound by about 4 MeV and so may be amenable to experiments.Using these two-body interactions it is possible to estimate the bind­ing of C0 in nuclear matter, taking the nucleon-nucleon interaction to be represented by the Reid potential. It is found that a binding of 22 MeV can be anticipated, which is considerably smaller than estimates of Ci binding in heavy nuclei by Dover and Kahana.8The main problem associated with supernuclei is the lifetime of charmed particles, viz. D* t ~2.5 x 10-13, Ac t ~ 7 x 10-13; thus even travel­ling close to the speed of light, their range is of the order of 10 y .Thus identification of the associated particle and of the supernuclei will require detectors of very fine grain. So far emulsions have proved the most convenient for such studies.Further details of supernuclei are given in Ref. 9.198It is interesting to consider the photoproduction of K+ on nuclei as this reaction appears to excite unusual states in the hypernucleus. Esti­mates are that the cross section will be 0.1 pb/sr and that with 50 pA of 2 GeV electrons, one may anticipate 200 counts/h MeV. It would probably be best to use bremsstrahlung difference techniques to obtain the mono- energetic y-rays, but tagged photon facilities have also been discussed. Although a study of this reaction is not possible at a kaon factory, the information will complement experiments which are possible.Further details are given in a study for the 2 GeV National Electron Accelerator.10PHYSICS CONCLUSIONSIt became clear that the workhorse of hypernuclear physics would remain the (K-,tt_) reaction but new possibilities such as (K“,ir°) would have to be tried. It also became clear that the present limitations on the experiments are certainly flux, but that an increase in flux must be accompanied by an improvement in the beam lines. In particular, a better resolution is essential to separate hypernuclear states (^C is an excel­lent example where a resolution of better than 300 keV would give qualita­tively new information on the £*s component of the AN interaction, see Gal's contribution, these proceedings, p. 148, and the discussion of hyperon-nucleon potentials by Nagels ). The point was also made that the it contamination in the beam (normally 10 times the K flux) impedes the experiments so much that at present a higher flux could not be used effec­tively. Thus it is essential that any kaon factory have beam lines which are significantly better in quality than any existing kaon channel in the world. (Note, however, that there are several ideas and proposals and some tests may have been performed before any firm design is needed for channels at a new accelerator.)Although not mentioned above, there were also discussions on the K- nucleus interaction. The K+ interaction with nuclei may lead to a more detailed knowledge of neutron distributions in nuclei,1  ^ and there are important problems concerning low-energy K-nucleus scattering and its re­lation to the low-energy interaction of kaons and nucleons. A recent summary of KN scattering has been given by Martin,13 although a more com­plete knowledge of the K+-nucleon interaction will be required. As the equipment required to study the (K“,tt“) reaction will almost certainly be adaptable for a study of K-nucleus scattering, we shall not go into further details.The discussion now turned to the equipment needed to implement the physics programme. The present channels at CERN and BNL serve as excellent points of reference. Before discussing channels we shall briefly consider exotic atom work.EXOTIC ATOM DETECTORSIn recent work on exotic atoms, the detection of the y-rays has centred on rarer y-rays, and it is now becoming normal to use Compton suppression to lower the background (see Refs. 14 and 15 for examples of TT-mesic studies). A problem with antiproton atoms or even K atoms is that there are always a large number of associated charged particles. With aTHE (y,K+) REACTION199large annulus it is possible to find that many good events are being vetoed by these associated particles. It is therefore necessary to have a small yet efficient Compton suppression, and bismuth germanate seems to be the best available, even though it is expensive.KAON CHANNELSIt became crystal clear that a lot of design effort would have to go into the kaon beam lines at a kaon factory. At the production target the tt/K ratio is about 100 but the lifetime is 12.4 nsec, whereas the lifetime is 26 nsec, so that as the beam comes down the channel the ratio will get worse (200:1 is normal in the experimental area). All existing K lines have therefore included crossed-field separators to improve the proportion of kaons in the beam. In beams intended for counter experiments the tt/K ratio is rarely better than 10:1 even though the beam optics cal­culation gives a far better separation. The characteristics of the kaon lines at KEK are as follows (fluxes are for 1012 protons at 12 GeV):Kla K2 K3Length (m) 85 29 14.5Momentum (GeV/c) 0.5-4.5 1-2 0.55Solid angle (msr) 0.04 1 7.3Ap/p 0.5 3% 2%Flux K+ 30 5 x 105 4.2 x IO1*K 1 x 105 1.0 x io4P 10 b 1.5 x 101* 3.5 x 102Separator length (m) (9m+6m)/9m 6 2tt/K ratio 0.05 at 2 at 5 at3 GeV/c 1.5 GeV/c 0.55 GeV/^bubble chamber two-stage separationFor bubble chambers it has been customary to add a second separator section, but this means that the lines are excessively long (~30 m) and the flux far too small for counter work (—10 sec-1). A discussion of rf separators concluded that their main advantage was at high energy. At low energies the dc separator is still the best (see Ref. 16 for more details).The general conclusion is that the pions which contaminate the beam could be eliminated by refocusing the production target on a slit in as short a length as possible. Then this slit would become the source for the rest of the beam line. There are proposals at the AGS for such a design and this idea holds the most hope. (The initial dipole might be of com­bined function in order to minimize the length, but this would increase the cost.) Other solutions have been discussed by Hoffman17 but do not seem competitive.SPECTROMETERSThe experiments must aim for a resolution of about 100 keV (see above), or Ap/p of 10-1+. To retain any flux it will be necessary to use an energy loss mode, but if various experiments are envisaged (or different K moment) there will have to be a variable dispersion to match the system.200This is complicated but feasible using quadrupoles in the spectrometers.Various facilities were discussed such as EPICS, Enge multi-gap spec­trometers and SPES II. It became clear that the spectrometer must be integrated into the channel and will be a major construction problem. The BNL system is estimated to be about a $7,000,000 facility (in a laboratory which has experience in such facilities and has equipment to pirate).GENERAL CONCLUSIONSThere is a large variety of potentially important experiments that one can foresee in the fLeld of hypernuclei and related topics. Many of these experiments are technologically possible at present accelerators, but the data-taking rate is so low that only a minute sample of nuclei can be studied. Other reactions cannot be studied at all with present beam intensities or the beam contamination makes them impossible. However, enough experience exists to be able to specify facilities with a fair degree of confidence.One will need a beam line and spectrometer system which is at least as sophisticated as the new beam line at CERN. The system should be capable of studying the (K-,ir“) reaction for both A and E hypernuclei, and the spectrometer should also be adaptable to measurements of K-^-nucleus elastic scattering. Thus there should be a beam line with a refocusing section going into a spectrometer-quality section with a dc separator.The goal should be a tt/K ratio of at least 1:1, preferably less. Coupled to the channel there should be a high resolution spectrometer capable of observing various reactions at any forward angle.There should be considerably more information available soon on beam line performance, and this should be incorporated in any design. Both CERN and BNL are actively trying to improve the performance of their sys­tems in this field.ACKNOWLEDGEMENTSWe wish to thank the following persons for contributing verbal presen­tations in this session: A. Rosenthal, H. Piekarz, G. Bhamathi, T.W. Donnelly, J. Davies, A. Yamamoto and R.R. Johnson.REFERENCES1. Proceedings of Seminar on the Kaon-Nuclear Interaction and Hypernuc­lei, Zvenigorod, September 1977, eds. P.A. Cerenkov et al. (Academy NAUK, Moscow, 1979).2. Proceedings of 1979 International Conference on the Hypernuclear and Low Energy Kaon Physics, Jablonna, September 1979, Nukleonika 25,No. 3-4 (1980).3. Proceedings of Workshop on Low and Intermediate Energy Kaon-NucleusPhysics, Rome, March 1980, eds. E. Ferrari and G. Violini (Reidel,Dordrecht, 1980).4. Proceedings of Symposium on Mesons and Light Nuclei, Liblice, June 1981, to be published, Czech. J. Phys.5. B. Povh, Annu. Rev. Nucl. Part. Sci. 28, 1 (1978).6. B. Povh, Nucl. Phys. A335, 233 (1980).7. R. Dalitz, Nucl. Phys. A354, 101 (1981).2018. C.B. Dover and S.K. Kahana, Phys. Rev. Lett. j39, 1506 (1977).9. G. Bhamathi, University of Alberta preprint Thy-5-81.10. A.M. Bernstein, T.W. Donnelly and G.N. Epstein, p. 363 in Report ofthe Workshop on Future Directions in Electromagnetic Nuclear Physics,Rensselaer Polytechnic Institute, Workshop Chairman P. Stoler.11. M.M. Nagels, T.A. Rijken and J.J. de Swart, Phys. Rev. D 2J), 1633(1979).12. A.W. Thomas, Nucl. Phys. A354, 51c (1981).13. A.D. Martin, Nucl. Phys. B179, 33 (1981).14. J. Konijn et al., Nucl. Phys. A326, 401 (1979).15. C.J. Batty £t^  al., Nucl. Phys. A355, 383 (1981).16. A. Yamamoto ejt al., Jpn. J. Appl. Phys. ±b_, 343 (1977);A. Yamamoto et al., Nucl. Instrum. Methods 148, 203 (1978).17. C.M. Hoffman, Los Alamos report LA-8949-MS (1981).202SUMMARY OF THE WORKSHOPD.V. Bugg*Queen Mary College, Mile End Road, London El 4NS, U.K.There has been a remarkable unanimity on the important physics to be done with a kaon factory, and it is clear that progress in many crucial areas is unlikely (or painfully slow and costly) without the intensity and quality of beams which such an accelerator could produce. Neutrino phys­ics, which has always been a central pillar in particle physics, would gain by a factor 100 in intensity * cross section, and it is therefore appropriate to view a new accelerator as a kaon-neutrino factory.In this summary, an attempt is made to produce a shortlist of the most important experiments, which would probably form the first phase of an experimental programme. Although further study is needed of the tech­nical details, the consensus of the experts at the workshop is that most or all of these experiments are a reasonable extrapolation from current practice. The fact that one can pinpoint 8-10 experimental set-ups, each with a programme of several years contributing to central areas of parti­cle and nuclear physics, is a powerful justification that at least one such accelerator should be built somewhere in the world. It appears financial­ly and technically attractive to use one of the present meson factories as an injector.In brief, the crucial areas of study are as follows:1) CP violation. Is e ' = 0? Is h+_0 = h+_? Can one find further mani­festations of CP violation?2) Rare K decays. Does K° -*■ p±e:j:? What is the magnitude of AS = 1 neutral currents?93) Neutrino physics. Can one detect neutrino oscillations? Is sin 0W universal, and if so what is its precise value? Do neutral current cross sections scale as A2 on nuclei?4) Baryon spectroscopy. Eigenvectors (i.e. branching ratios) are likelyto be a much more revealing test of QCD-inspired models than eigenvalues (masses). Do the [70,2]+ and [70,0]+ exist?5) Hypernuclear spectroscopy. Can one account quantitatively for levels and widths of A, E and AA hypernuclei? Do S hypernuclei exist? Do analogues of the deuteron exist in AN and EN systems at threshold?Other interesting areas which would benefit from a new machine are K~-nuclear scattering, v-nuclear scattering and exotic atoms. The increased intensity of tt" beams would be an asset for radiotherapy and y“SR.CP VIOLATIONThe rate for K° tttt decay as a function of proper time t isf (inr)-t/2TS + ne-t/2TL eiAmt(1)where tg ^ are lifetimes of Kg ^ and Am is their mass difference. Also*SRRC Senior Fellow.203n ( i r + 7r- )  = e + e ' n (ir°T T ° ) = t  -  2 e ' .All current Information is compatible with e ' = 0 ,  and the phase of t  agreeing with the value predicted by superweak theory. It is crucially important to try to pin down the origin of CP violation. Many theories1 such as the Kobayashi-Maskawa parametrisation of the relation between the mass matrix and weak eigenstates of 6 quarks, the Weinberg-Lee model, and technicolour demand or at least accommodate values of |e'| in the range (2-6) x 10-2 |e|, close to the present limit |e'| < 0.06|e|.The phase, <f>, of e r with respect to e is known from the tttt phase shifts:<t> (e) - <f>(e') -  8° .Hence the interference term between Kg and k£ has the ratio:f(7r+ir") | \n t |e ’f(T70Tr°)|intThat is, the detection of e f rests upon finding a different interference term in TT°ir° and Tr+ iT- . Bob Adair has pointed out that one can increase experimental sensitivity to e ' by using a regenerator to add to Eq. (1) a Kg amplitude which interferes destructively with e after about 7xg. Usingsuch a trick, there is hope that one could improve the present limit on e 'by a factor 10. However, even with 4 GeV/c K°, 7 x g  = 140 cm. It seems likely that one will not be able to work so close to a primary beam of 100 yA, so one should probably envisage generating the K° (possibly tagged) with a fierce K + beam by charge exchange. Good time of flight would be ahuge asset in killing the background of K° 3tt°.The same experimental set-up should be used to improve the accuracy of the phase of u+_ by looking at interference between Kg and K^ after about 12xg without a regenerator. Presently the experimental value is 44.6±1.2° compared with 43.7±0.2° predicted by the superweak theory. In addition, one should try to check the prediction ri+_0 ^  u+_ by measuring interference between Kg and K^ in ir+TT_ir° decay. Finally, the same experi­mental set-up should be able to improve substantially the present upper limitk £ ^ y e+ k £ all< 3 * 10-9it might be possible to reach the region 10-12-10-13. As Ng has pointed out1 this would be an exceedingly severe constraint on horizontal gauge bosons.RARE K DECAYSOne of the triumphs of theory in the early 1970s was the prediction of charm and the GIM mechanism for suppressing AS = 1  neutral weak cur­rents. Yet to my mind it is remarkable that this suppression mechanism is so good. The branching ratio for such decays is ^lO-7, making it one of the best selection rules we know. Establishing the level of decays such as204K+ -> tt+v\T -* ir-e+e+-*■ TT+ e + e “-»■ ir+e+y_would provide further powerful constraints on gauge theories of weak inter­actions. Experimentally, it looks attractive to search for decays of a 750-1000 MeV/c K+ beam using a spectrometer magnet to analyse decay prod­ucts. With the same set-up, the equality of the slopes of the Dalitz plots in -* is a further test of CP. [The set-up should also beappropriate for studying K+ -> K* using high momentum K+ and the Primakoff effect, known to be a clean source of natural parity K*'s.]NEUTRINO PHYSICSWith a factor 50-100 increase in intensity * energy over Fermilab andCERN, one is clearly in a position to do over again most of neutrinophysics with much more hygienic equipment. K1 decay is important as a source of high energy ve and v"e . Obvious topics of current interest are as follows:(i) v oscillations(ii) Is sin20w universal ±1%? Currently the number of v^e" scatters is of order 50 in the best experiment with 12 background events, and 300 Vyp+Vyp with 100 background. The scope for improvement is obvious. However,(a) background suppression will be important, (b) absolute normalisation of beam intensity and energy spectrum will be a difficult question. It may therefore be that one gets the best checks on sin20w from the differ­ent interferences in rates and angular distributions invpe" vye”Vye- -* Vye"vee" * vee" and Vee” vee_ •(iii) It would be nice to check that neutral current cross sections scale as A2 by measuring the ratio of Vy elastic scattering from H and say ^He (which scintillates). This is an important component in the theory of supernovae.(iv) It is of interest to measure exclusive Vy and Vy interactions in hydrogen and deuterium bubble chambers.Clearly one versatile neutrino beam (broad and narrow-band, K and tt decays) is needed, with several different detectors in sequence for mea­suring various channels and looking for oscillations.BARYON SPECTROSCOPYThe QCD-inspired model of Isgur and Karl2 is in impressive agreement with known N, A and E masses and branching ratios. But it is worrying that members of the [70,2]+ and [70,0]+ have proved s£ elusive. Isgur has205explained that these multiplets naturally couple rather weakly to the elastic channel. Therefore, it is important to devise specific experiments of the typew &K p -* prominent YiE*TTL* E it, Airwhere (or A*) is predicted to have a large branching ratio to both ini­tial and final states. It is also important to(i) fill the gaps in the [70,1]” and [56,2]+ , [56,0]+*(ii) establish the full pattern of branching ratios. I envisage at leastfour experimental set-ups as follows:(a) a polarised target to studyP(K“p + K°n)P(K"n -> K“n)initially in the 500-1000 MeV/c range, then at higher momenta. With the same equipment one could nail down the important K+N amplitudes below the inelastic threshold by measuringP(K+p ■* K+p)P(K+n + K+n)P (K+n •* K°p)from 400 to 700 MeV/c.(b) an "electronic bubble chamber", i.e. omega-type of device, with liquid hydrogen target and frozen spin target to increase statistics on all K"N (and K+N) channels to ~100 events/yb; this would establish the pattern of Y* branching ratios with precision and settle the issue of whether or not the [70,2]+ and [70,0]+ multiplets exist.(c) K°p -> K°p- *  E ° 7 r + , E + TT° ;the former depends on interference between K+N and K”N amplitudes and is therefore a delicate source of information for phase-shift analysis; the latter is a pure 1 = 1  channel and helps sort out the elusive isospin dependence in KN Ett .(d) K-p->-K+"* probably demands a specific set-up, independent of (b) , with a sampling device of the TPC type to identify K+ by dE/dx.HYPERFRAGMENT SPECTROSCOPYIt is a fascinating variety of nuclear physics to be able to implant new species of nucleons into nuclei in the form of A, E and 5 hyperons.From the spectroscopy and the ratios of mesonic and non-mesonic decays (i.e. A -> pir”/AN -*■ NN) one has much to learn about (a) the hyperon-nucleon interaction, (b) many-body effects. Present experiments stretch the limits of available intensity to identify a handful of (very instructive) levels in A and E hypernuclei. The existence and spectra of the latter is a challenging issue. A factor 100 in intensity and beam cleanliness would206open up the opportunity for systematic examination of A, E, AA and S hyper­nuclei, and would probably allow detection of y decays in coincidence, with a consequent huge gain in energy resolution (and angular correlations?). One requires 400-1000 MeV/c K” and 1-1.5 GeV/c tt+ and a high resolution spectrometer. With the same equipment, one can look for deuteron-like states in EN,5N, e.g. K_d -»■ K+(H_n) . This provides delicate information on the long-range part of the hyperon-nucleon interaction, whereas hypernuclei are sensitive mainly to the short-range interaction.It would be of great interest to measure low energy AN and EN scatter­ing; however, lifetimes are so short that nobody has come up with a con­vincing technique for doing this.K1-NUCLEAR PHYSICSThe low cross section of the K+ makes the nucleus semi-transparent to it, raising the hope that one can obtain information from elastic and inelastic scattering without the serious distortions of incident and out­going waves which have proved so confusing in N-nucleus and ir-nucleus interactions. (Although very low energy pions offer similar potential, they are confined to very long wavelengths.) However, one should beware that Fermi-motion and collision-broadening will make intermediate states of K*N and KN* bothersome in nuclei of significant atomic number. A high resolution spectrometer (<100 keV) will be required.Exotic K- and E“ atoms are experimentally entertaining and a source of precise information on scattering lengths, particle masses and magnetic moments.CONCLUSIONSOne can readily identify 8-10 experimental set-ups (according to how many neutrino detectors one can afford) which will make fundamental contri­butions to particle and nuclear physics. A kaon-neutrino factory must be built somewhere, and TRIUMF is an excellent contender.A lower limit on the primary beam energy is 8 GeV, in order to produce good fluxes of K1 up to 2 GeV/c and v above 500 MeV. There are attractions in having 15 GeV primary energy, but above this the cost and demands on space for the accelerator and experimental areas begin to look serious.I suspect the yield of K and v per dollar has a broad peak in the 8-15 GeV range, but this conclusion requires detailed costing. Into this cost it is essential to include shielding, beam dumps and beam transport. To progress further, it is essential to sketch out experimental areas and accelerator, using existing K and v beamline designs for guidance. Previ­ous experience is that one requires K beams covering three momentum ranges, e.g. 400-800 MeV/c, 700-1400 MeV/c, and 1200-2400 MeV/c.No clear distinction has emerged between the potentialities of a cyclotron and a synchrotron. Both are capable of a duty cycle of ~10“1+ for neutrino physics, and could reach <10-6 with the addition of a storage ring. The cyclotron cannot reasonably go above 10 GeV. However, it is likely to have a superior bunch-length (0.25 nsec?). My own experience with both cyclotrons and synchrotrons is that good time-of-flight informa­tion is an enormous asset, sometimes an essential one, in cleaning up an experimental signal. Both cyclotron and synchrotron design should strive to achieve good bunch structure. At the workshop I raised the possibility207of making RF separated beams; the general feeling was that this would not obviously improve on DC separators. However, it perhaps deserves further detailed study, and a workshop of experts on separated beams seems desirable.Should one choose a primary energy high enough to make p? My feeling is that this is not important, but this feeling is not universal. Anti­proton physics at CERN and Fermilab has laboured under the weight of high u backgrounds. LEAR solves this problem, and it is clear that a kaon factory producing p^ would only be competitive if equipped with an accumu­lator and storage ring. The additional cost would be high, of the order of $85M Can. It is conceivable that the accumulator ring could also store as a source of v£ and ve .Finally, the scale of the accelerator and experiments would require and would attract good physicists and technicians. It would be a reward­ing, stimulating challenge to Canadian industry and physics.REFERENCES1. J.N. Ng, in "Kaons for TRIUMF", TRIUMF report TRI-81-2 (1981).2. N. Isgur and G. Karl, Phys. Rev. D lj?, 4187 (1978); ibid. D 1J), 2653 (1979); ibid. D 20, 1191 (1979).208R. ABEGG, TRIUMF, Vancouver, B.C., Canada R.K. ADAIR, Yale University, New Haven, CN, USAK.A. ANIOL, University of British Columbia, Vancouver, B.C., CanadaE.G. AULD, University of British Columbia, Vancouver, B.C., Canada D.A. AXEN, TRIUMF, Vancouver, B.C., CanadaG. AZUELOS, Universite de Montreal, Montreal, Quebec, CanadaA. BAGHERI, University of British Columbia, Vancouver, B.C., CanadaR.C. BARRETT, University of Surrey, Guildford, Surrey, EnglandB. BASSALLECK, Carnegie-Mellon University, Pittsburgh, PA, USAD. BEDER, University of British Columbia, Vancouver, B.C., Canada G.A. BEER, University of Victoria, Victoria, B.C., CanadaM. BETZ, TRIUMF, Vancouver, B.C., CanadaJ.L. BEVERIDGE, TRIUMF, Vancouver, B.C., CanadaG. BHAMATHI, University of Alberta, Edmonton, Alberta, CanadaE.W. BLACKMORE, TRIUMF, Vancouver, B.C., CanadaB. BLANKLEIDER, TRIUMF, Vancouver, B.C., CanadaM. BLECHER, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA J. BREWER, University of British Columbia, Vancouver, B.C., CanadaD. BRYMAN, TRIUMF, Vancouver, B.C., CanadaD. BUGG, Queen Mary College, London, UK W. CAMERON, TRIUMF, Vancouver, B.C., CanadaH.H. CHEN, University of California, Irvine, CA, USA M. COMYN, TRIUMF, Vancouver, B.C., CanadaJ. COOPER-SMITH, University of British Columbia, Vancouver, B.C., Canada M.K. CRADDOCK, TRIUMF, Vancouver, B.C., Canada K. CROWE, University of California, Berkeley, CA, USAB. CUJEC, University Laval, Quebec, P.Qud., Canada J. DAVIES, University of Birmingham, Birmingham, UKC.A. DAVIS, TRIUMF, Vancouver, B.C., CanadaP. DENES, Los Alamos National Laboratory, Los Alamos, NM, USA M.S. DIXIT, National Research Council, Ottawa, CanadaT.W. DONNELLY, Massachusetts Institute of Technology, Cambridge, MA, USA J. DOORNBOS, TRIUMF, Vancouver, B.C., CanadaC.B. DOVER, Brookhaven National Laboratory, Upton, NY, USAG. DUTTO, TRIUMF, Vancouver, B.C., CanadaR.A. EISENSTEIN, Carnegie-Mellon University, Pittsburgh, PA, USAF. ENTEZAMI, University of British Columbia, Vancouver, B.C., CanadaK.L. ERDMAN, University of British Columbia, Vancouver, B.C., CanadaH.W. FEARING, TRIUMF, Vancouver, B.C., CanadaA. GAL, Hebrew University of Jerusalem, Jerusalem, Israel K. GOTOW, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA J. GREBEN, University of Alberta, Edmonton, Alberta, Canada L.G. GREENIAUS, University of Alberta, Edmonton, Alberta, Canada H. GUBLER, University of Manitoba, Winnipeg, Manitoba, CanadaD. GURD, TRIUMF, Vancouver, B.C., CanadaC.K. HARGROVE, National Research Council, Ottawa, Canada M. HASINOFF, University of British Columbia, Vancouver, B.C., CanadaA. HAYNES, TRIUMF, Vancouver, B.C., Canada R. HELMER, Simon Fraser University, Burnaby, B.C., CanadaWORKSHOP PARTICIPANTS209C.M. HOFFMANN, Los Alamos National Laboratory, Los Alamos, NM, USAE.V. HUNGERFORD, University of Houston, Houston, TX, USAD.A. HUTCHEON, TRIUMF, Vancouver, B.C., CanadaN. ISGUR, University of Toronto, Toronto, Ontario, Canada K.P. JACKSON, TRIUMF, Vancouver, B.C., CanadaJ.A. JOHNSTONE, University of British Columbia, Vancouver, B.C., Canada C.Y. KIM, University of Calgary, Calgary, Alberta, CanadaC.J. KOST, TRIUMF, Vancouver, B.C., CanadaM. KRELL, Universite de Sherbrooke, Sherbrooke, Quebec, CanadaL.F. LI, University of California, Santa Barbara, CA, USAJ.A. MACDONALD, TRIUMF, Vancouver, B.C., CanadaG.H. MACKENZIE, TRIUMF, Vancouver, B.C., CanadaA.K. MANN, University of Pennsylvania, Philadelphia, PA, USAG.R. MASON, University of Victoria, Victoria, B.C., CanadaD.F. MEASDAY, University of British Columbia, Vancouver, B.C., CanadaC.A. MILLER, TRIUMF, Vancouver, B.C., CanadaM. MOINESTER, Tel-Aviv University, Tel-Aviv, IsraelL. MORITZ, TRIUMF, Vancouver, B.C., CanadaK. NISHIKAWA, University of Chicago, Chicago, IL, USAJ. NISKANEN, TRIUMF, Vancouver, B.C., CanadaJ.N. NG, TRIUMF, Vancouver, B.C., CanadaT. NUMAO, University of Victoria, Victoria, B.C., CanadaA. OLIN, TRIUMF, Vancouver, B.C., CanadaC. ORAM, University of British Columbia, Vancouver, B.C., CanadaE. PAULI, CERN, Geneva, SwitzerlandJ.C. PENG, Los Alamos National Laboratory, Los Alamos, NM, USAH. PIEKARZ, University of Warsaw, Warsaw, Poland J.M. POUTISSOU, TRIUMF, Vancouver, B.C., CanadaJ.R. RICHARDSON, TRIUMF and University of California, Los Angeles, CA, USA P.J. RILEY, University of Texas, Austin, TX, USAB. ROBERTSON, Queen's University, Kingston, Ontario, Canada L.P. ROBERTSON, University of Victoria, Victoria, B.C.A. ROSENTHAL, TRIUMF, Vancouver, B.C., Canada M. SALOMON, TRIUMF, Vancouver, B.C., Canada0. SHANKER, TRIUMF, Vancouver, B.C., CanadaJ. SPULLER, TRIUMF, Vancouver, B.C., CanadaN. STEIN, Los Alamos National Laboratory, Los Alamos, NM, USAM.W. STROVINK, University of California, Berkeley, CA, USAA.W. THOMAS, TRIUMF, Vancouver, B.C., CanadaG.B. THOMSON, Rutgers University, New Brunswick, NJ, USAG. TOKER, University of Pittsburgh, Pittsburgh, PA, USAW.T.H. van OERS, University of Manitoba, Winnipeg, Manitoba, CanadaE.W. VOGT, TRIUMF, Vancouver, B.C., CanadaP. WALDEN, TRIUMF, Vancouver, B.C., CanadaC. WALTHAM, University of British Columbia, Vancouver, B.C., Canada T. WARD, Indiana University, Bloomington, IN, USAJ.B. WARREN, University of British Columbia, Vancouver, B.C., Canada R.E. WELSH, College of William and Mary, Williamsburg, VA, USAD. WERBECK, Los Alamos National Laboratory, Los Alamos, NM, USAD. WOLFE, Los Alamos National Laboratory, Los Alamos, NM, USA R. WOLOSHYN, TRIUMF, Vancouver, B.C., CanadaA. YAMAMOTO, National Laboratory High Energy Physics (KEK), Ibaraki, Japan


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