TRIUMF: Canada's national laboratory for particle and nuclear physics

Proceedings : workshop on the future of pion-nucleus interactions, TRIUMF, Vancouver, July 22-August… Lee, H. C. (Hoong-Chien), 1941-; Saharia, A. N. (Aditya N.); Thomas, A. W. (Anthony William), 1949- 1979

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T R I U M FPROCEEDINGSWORKSHOP ON THE  FUTURE OF P ION -NUCLEUS  INTERACT IONS  TR IUMF ,  V a n c o u v e r ,  J u l y  2 2 - A u g u s t  3 ,  1 9 79Ed i tors H.C. LeeChalk River Nuclear LaboratoriesA.N. Saharia and A.W. Thomas TRIUMFMESON FACILITY OF:UNIVERSITY OF ALBERTA SIMON FRASER UNIVERSITY UNIVERSITY OF VICTORIA UNIVERSITY OF BRITISH COLUMBIA T R 1-79-2ERRATUMThe following attendees from TRIUMF were inadvertently omitted from the official list of participants:H.W. Fearing D. Gill R.M. WoloshynTRI-79-2TRIUMFPROCEEDINGSWORKSHOP ON THE FUTURE OF PION-NUCLEUS INTERACTIONS TRIUMF, Vancouver, July 22-August 3, 1979Ed i tors H.C. LeeChalk River Nuclear LaboratoriesA.N. Saharia and A.W. Thomas TRIUMFPostal address:TRIUMFAOOA Wesbrook Mall Vancouver, B.C.Canada V6T 2A3 December 1979P R O G R A M M EJuly 23 QCD and the weak PPRR vertexH.C. LeeJuly 2k Pionic effects in weak interactions involving finite nucleiF. KhannaJuly 25 Pion-nucleus interaction: Multiple-scattering approachR.H. LandauJuly 26 Pion-nucleus interaction: Isobar-doorway approachK. KlingenbeckJuly 27 Discussion session on pion-nucleus elastic scatteringChairman, H. PilkuhnJuly 30 Phenomenology of non-elastic reactions within the isobar­doorway picture R.M. WoloshynJuly 31 Discussion session on reactions involving pionsChairman, B. KeisterAugust 1 Pion-nucleus interaction: Field theoretic approachG. MillerAugust 2 Discussion session on new theoretical approachesChairman, J. LagetAugust 3 Quark models for pion-nucleon and pion-nucleus interactionsM. RhoSummaryA.W. Thomasi i iPARTICIPANTSJ. ALSTER, Tel-Aviv University, Ramat Aviv, Tel-Aviv, IsraelD. ASHERY, Tel-Aviv University, Ramat Aviv, Tel-Aviv, IsraelB.S. BHAKAR, University of Manitoba, Winnipeg, Manitoba, CanadaPolytechnic Institute and State University, Blacksburg, VA, USA n OO Univers i tat Karlsruhe, Karlsruhe, Federal Republic of GermanyG. BROOKFIELD, University of British Columbia and TRIUMF, Vancouver, B.C., Canada T. COOPER, University of Alberta, Edmonton, Alberta, CanadaG.N. EPSTEIN, Massachusetts Institute of Technology, Cambridge, MA, USAE. FERREIRA, Pontificia Universidade Catolica, Rio de Janeiro, BrazilR. FREEDMAN, University of Washington, Seattle, WA, USAA. FUJI I, TRIUMF/Sophia University, Tokyo, JapanK. GOTOW, Virginia Polytechnic Institute and State University, Blacksburq. VA USAJ.M. GREBEN, TRIUMF and University of British Columbia, Vancouver, B.C., Canada W. GYLES, University of British Columbia, Vancouver, B.C., Canada R.R. JOHNSON, University of British Columbia, Vancouver, B.C., CanadaB. KEISTER, Carnegie-MelIon University, Pittsburgh, PA, USAF.C. KHANNA, Chalk River Nuclear Laboratories, Chalk River, Ontario, Canada • K U “ ECK> Universit3t Erlangen-Nurnberg, Erlangen, Federal Republ ic of GermanyJ.M. LAGET, Centre d'Etudes Nucleaires, Saclay, Gif-sur-Yvette, France R.H. LANDAU, Oregon State University, Corvallis, OR, USAH.C. LEE, Chalk River Nuclear Laboratories, Chalk River, Ontario, CanadaG.A. MILLER, University of Washington, Seattle, WA, USAH. PILKUHN, Universitat Karlsruhe, Karlsruhe, Federal Republic of Germany M. RHO, Centre d'Etudes Nucleaires, Saclay, Gif-sur-Yvette, FranceE. ROST, University of Colorado, Boulder, CO, USAA.N. SAHARIA, TRIUMF and University of British Columbia, Vancouver, B.C., Canada SHERIF, University of Alberta, Edmonton, Alberta, Canada N. SHRIMPTON, University of British Columbia and TRIUMF, Vancouver, B.C., CanadaS. THEBERGE, University of British Columbia and TRIUMF, Vancouver, B.C., Canada A.W. THOMAS, TRIUMF, Vancouver, B.C., Canada J.D. VERGADOS, University of loannina, loannina, GreeceE.W. VOGT, University of British Columbia, Vancouver, B.C., Canada Chi-shiang WU, University of Victoria, Victoria, B.C., Canada A. YAVIN, Tel-Aviv University, Ramat Aviv, Tel-Aviv, IsraelC O N T E N T SPageProgramme jjiParticipants jv1. Introduction 12. The Invited Talks 22.) Quantum chromodynamics and the weak RRPP vertex 2H.C. Lee2.2 Pionic effects in the weak decays of nuclei 3F.C. Khanna2.3 Isobar-doorway approach to the pion-nucleus interaction kK. Klingenbecki.k Future of ir-nucleus physics— Multiple scattering approaches 5R.H. Landau2.5 Phenomenology of non-elastic reactions within the isobar­doorway picture 7R.M. Woloshyn2.6 A field theory of pion-nucleus interactions 8G.A. Mi 1ler2.7 Quark structure of the nucleon in nuclei 10M. Rho3. Summary 13A.W. Thomas3.1 Comparison with elastic data 153.2 Nuclear ground state parameters from elastic scattering 183.3 Effects of absorption on elastic scattering 183.A Pion photoproduction 193.5 Single charge exchange 203.6 Nuclear structure— Inelastic pion scattering 213.7 Pion quasi-elastic scattering 213.8 Conclusion 21Bibliography IkvINTRODUCTIONThe Workshop on the Future of Pion-Nucleus Interactions was held at TRIUMF from July 22 to August 3, 1979. Financial support was provided by NSERC, AECL and TRIUMF.We would like to thank all of these organizations for their assistance and support.The overwhelming feeling of all present was that the funds were well spent.The format of the workshop was very simple. Each speaker had a morning to develop his topic in an atmosphere where discussion was encouraged. The afternoons and even­ings were free for spontaneous small group discussions and collaborations. With little exception the speakers were willing to explain not only the advantages of their pet approaches but also the problems. Thus we were all led to a better understanding of the future theoretical developments, and also of the possible experimental tests of existing theory. All of us present take this opportunity to thank the invited speakers, and session chairmen, for their efforts.It is a pleasure to thank Joan Thomas for her support, and particularly for her efforts in arranging the reception on July 22. As well, we would like to thank the staff at the Vancouver School of Theology (and particularly Donna Dale Jones) for their willing assistance with all aspects of accommodation, and Ada Strathdee for her assistance in producing the proceedings.-  2 -2. THE INVITED TALKSEach invited speaker was asked to provide a short summary of his talk, indicat­ing the most interesting directions for future research in his field— as well as summarizing the progress so far. These summaries were distributed to participants at the workshop, but are also reproduced below.2 •1 Quantum chromodynamics and the weak RRPP vertexSeveral recent developments in our understanding of the interplay between strong and weak interactions have put a new significance to parity violation in nuclear sys­tems. These developments include the recent SLAC experiment1 on parity violation in e-p and e-d scattering which confirms the standard model of weak interactions between leptons and quarks, the growing belief that quantum chromodynamics (QCD)2 could be a real theory for the strong interaction, and calculations,3 based on the renormalization by QCD of the weak quark-quark interaction, that has provided as yet the best explana­tion of all strangeness-changing (AS=1), non-leptonic weak decays.The key to the explanation of these decays is the appearance of operators of thetypeCED I NGSdit t o r Nt Dst Hl) ,which are generated entirely through the renormalization procedure. Here qL R stand respectively for left- and right-handed quarks. Although 0LR appears with a small coef­ficient its matrix element is proportional to ? = m2/mums . If one uses the light quark masses mu ~  m^ c* 5 MeV and ms o; 150 MeV, then £ = 26, thereby allowing 0|_R to provide the dominant contribution to the decay amplitude. This proposal can, in' principle, be tested in parity-violating reactions involving the nucleus.For the strangeness-conserving, parity-violating (pv) NNtt amplitude, the operator 0|_R appears with a large coefficient, even without renormalization. Renormal­ization increases the coefficient by a factor 2. Calculation1* shows that, when one expresses the pv R R PP coupling asLNNTT = fr ^ 3 N  .f£V ~  5 x 10-7. (If one uses the effective quark mass mM ~  300 MeV, then fpv is oneu ITorder of magnitude smaller.)One way to measure fpv experimentally is to measure the asymmetry in the cross section, near the threshold, of the reaction Ypol + N N + PP. , with circularly polarized photons. The asymmetry is given byA ( Kv) ~ f P V  ,yir aY++(V  mNwhere f® ~  1 is the strong NNtt coupling constant. The asymmetry remains the same order of magnitude5 as AyW in the reaction y + Np0 ] -*■ N + 2ki where the nucleonis polarized instead of y or in the ir-capture reactions LPe + Np0 j N + y and LPe h R alkN + Ypol- The last reaction appears to have the least background problem and would be very attractive if a low-energy PPv beam of high intensity were available.The physics becomes less clear for ypo, + N N + LP1, say, in the (3,3) resonance region because effects of the weak NNp, NAir, etc. amplitudes then also come into play. (The reason that the effect of the pv RRPP amplitude decreases with increasing energy is because it is an s-wave amplitude.) These effects have not yet been calculated. Even so, measurement of Ay^ as a function of Ey would clearly be of great interest. In fact, an experimental value of Ay^ for any one of the reactions mentioned at any energy will be the first piece of data on the strangeness-conserving, non-leptonic weak interaction of elementary particles.2.2 Pionic effects in the weak decays of nucleiMeson-exchange current effects in nuclei have been considered for some time. It is only in recent years that accurate measurements of Gamow-Teller transitions and the electromagnetic properties in finite nuclei have made it necessary to do better calcula­tions, and to include the meson-exchange current effects.Gamow-Teller transition rates in simple "doubly closed LS shell ± 1 nucleon" mirror nuclei are slower than those predicted by zero-order shell-model wave functions, and an axial-vector coupling constant g^ derived from neutron B-decay. This quenching is attributed to an interplay between core-polarization and meson-exchange current effects. It is believed6 that there is considerable cancellation between core- polarization and meson-exchange current effects, the extent of which can only be judged by calculating both the contributions in a consistent manner. In this talk such a con­sistent calculation^ is described. The effects of isobars are included by considering that in a particle-hole picture the particle can be either a nucleon or a A (1232). The perturbative calculation of the Gamow-Teller matrix element includes all the diagrams in the number-conserving set (NCS), random-phase approximation (RPA) diagrams, with the final B-decay vertex being a transition between A-particle nuc1eon-hole. In RPA, the effect of nucleon p-h bubbles is included. The main correction from exchange currents arises from the p-ir diagram.8 Furthermore, the p-rr diagram is iterated to include NCS and RPA corrections. In addition to all this, relativistic corrections to order 1/M2 are i ncluded.The result of all these corrections is that the quenching of g^ and the magnitude of Gamow-Teller matrix elements in nuclei with A = 3, 15, 17, 39 and ^1 can be explained quant i tati vely.Another interesting example is to look at thermal neutron capture by 8He to a final state ‘‘He + y. Due to symmetry reasons, the impulse approximation result gives a very small value for the cross section. The exchange currents give the entire capture cross section. The calculated value of (52±10) pb is to be compared with the experi­mental value of (60±12) pb.- 3 --  1* -In the immediate future, it will be interesting to evaluate the role of meson- exchange currents in the following processes:1) to investigate the time component of the exchange currents in the first forbidden B-decays (o~ -*■ o+) .2) to extend the analysis to finite values of q2 and o>. This would help to understand the role of meson-exchange currents in the y-capture by nuclei.3) to study the role of meson-exchange currents in the form factors for states of arbitary spin excited in inelastic electron scattering.2.3 Isobar-doorway approach to the pion nucleus interactionBased on the u N3,3) dominance in irN scattering (or less restrictive, the isobar­doorway hypothesis) the isobar-doorway-model (IDM) constitutes the general frame to study the behaviour and the properties of a generalized A-baryon system, consisting of 1A and (A-l) nucleons. Taking into account the A-isobar as an individual baryon, we have to regard the nucleus as a many-baryon system with the usual external many-body degrees of freedom, the internal degrees of freedom of its constituents and their respective coupling. In medium-energy physics the excitation spectrum of this system, involving the internal baryon excitation, will be the outstanding feature to be investi­gated. Once the corresponding eigenmodes— A* resonances— are known, various pion- induced nuclear reactions can be described consistently as a pionic resonance fluores­cence phenomenom.From this general framework several models have been constructed to study this A*-phenomenon on a microscopic basis. In such a microscopic approach we are immediately faced with the full complexity of many-body physics, including in addition the internal baryonic degrees of freedom. Starting out from a shell model-like description all those models are presently restricted to a lplh (ANf) basis. Therefore, most models introduce some more or less refined phenomenology, to approximate the effects of the more complicated ph configurations. Recent studies indicate a promising step to relate those parameters to microscopic contributions.The main result of applications to elastic tt-A scattering (4He,12C ,160) is that each nucleus exhibits a characteristic excitation spectrum at medium energies, composed of broad and overlapping multiple resonances. For each multipolarity a few collective (with respect to the elastic channel) A* resonances were found— characterized by a large elastic width— which consequently dominate elastic irA scattering. The overall compari­son with experimental data indicates that our present A* excitation strength distribu­tion represents quite a realistic picture of the physical situation.In a consequent continuation and as further stringent tests, we also looked into inelastic PPc reactions. Generally the interference pattern of A* multiple resonances happens to be much richer for inelastic reactions than for elastic scattering. From this point of view we have a sensitive test on the A* excitation spectrum under quite-  5 -different conditions. The available experimental data on the low-lying 2+ (k.b MeV) and 3“ (9.6 MeV) excitations in inelastic tt-12C scattering could be reproduced satisfactorily, both from their structure as well as their magnitude, which is down by almost two orders of magnitude compared to the elastic channel. As a further model study we have applied this pure resonance model also to the radiative pion capture in flight on 12C into low- lying states in the corresponding isobaric analogue nuclei (12N,12B). The main results of those investigations are:1) Per multipolarity the strengths of the various resonances depend sensitively on the final channel. The collective resonances of elastic PPc scattering are no longer the dominant ones.2) The contributions of the different multipole resonances vary considerably for different decay channels. In this sense, the selection of different exit channels plays the role of some multipole filter, suppressing or favouring certain multipole resonances (fi1 ter effect).To summarize, we believe that the nuclear A* excitation spectrum is fairly well known. But still we have to go a long way, hopefully supported by both the theoretical and experimental developments, to test and to understand this A* phenomenon in detail.Outlook1) npnh configurations?2) other reactions:A(g.s.) Nb APCr A(lf) (EA-resonances?)Nn W PPrA ('N), (e,e')3) extension to open-shell nuclei PP. 13C elastic, SCE; ir-180 .....k) extension to other non-strange or strange resonances (A's, E's, ...)2. it Future of irn physics— Multiple scattering approachesIn general, the future can be predicted by extrapolating the present efforts forward in time, or by examining the reasons and goals we have for doing it- nucleus (n) physics and assuming they will be met in the future. Most of the talk dealt with the first, rather mechanical approach. As for the second more difficult point, 1 believe we all want to learn something new with pions. Nuclear size and structure is the most obvious area, and knowledge of the reaction mechanism is a prerequisite for all else. Certainly we shall continue study of irn states, be they bound states or resonances, and continue developing our understanding of the influence of pion annihilation on elastic scatter i ng.Since the multiple scattering series is not solvable for A > 2 at present, we are all concerned with approximations. The use of an optical potential in a wave-  6 -equation is attractive since it automatically solves an infinite number of multiple scatterings. If, in turn, the series expansion of the potential is rapidly convergent and it is possible to correct the impulse approximations for binding (medium) effects, the theory will be on solid ground. Of course, the inclusion of annihilation effects, which are not described by a two-body potential, requires extension of the theory and one can argue that field theory is more fundamental.The connection between the field theory (Chew-Low) and potential theory (inverse scattering problem) description of the elementary ttN amplitude was discussed, and it was concluded that t h e ~ 0 .2 fm range of the vertex functions of field theory are com­patible with the ~0.6 fm range of the form factors in potential theory. The different analytic structure of the two theories accounts for the different meanings of "ranges" in each.A discussion of the three-body formulation (ir,N core) of the optical potential was given and the approximations made in practical calculations were indicated. Although we are only using the first iteration of the three-body equations as input, this lowest order approximation (three-body energy) does introduce elastic unitarity into the theory and helps in reproducing low-energy scattering. Since the active nucleon-core inter­action is not included exactly, the effective nuclear binding energy is treated as a parameter— yet found to have a relatively minor effect after the dominant kinematic shift is included. Work by Faldt, Silver and Austern, Amado, Lenz and Yazaki lends sup­port to this formulation, and a parallel effect in the isobar hole formulation (A propagation via T^) is also found. The conclusion here is that much more physics is being placed into than was ever done before, and that the momentum space approacheshave the "potential" for future advances.The comparison of the first-order theory with resonance energy elastic scattering data is qualitatively good (all the main features are reproduced) with the careful treat­ment of kinematics providing much of the back-angle structure. On a quantitative basis, there are regions of dcr/dfi where up to factors of 2 deviations occur (minima, e.g.) and regions of 0tot where 20-30% deviations are found. At lower energies the first-order theories certainly need to be supplemented by semi-phenomenological (or phenomenological) rho-squared terms to account for annihilation. Several calculations of and fullFermi averaging indicate significant effects, yet also a fair degree of cancellation in the correction terms, so that only a very complete calculation would be believable.A number of calculations indicate that accounting for the symmetry of the nuclear wave function has important effects on elastic cross-sections, the T m W PPRr reaction and the 13C(ir+ ,TT0) 13N charge exchange reaction. Since these effects are so important (Pauli correlations dominate other correlations for light nuclei), future calculations should include more correctly the antisymmetry of the nuclear wave function, and a symmetric form of multiple scattering theory.Phenomenologically, low-energy (30-50 MeV) irq experiments have proven that the pion annihilation channel couples strongly to elastic scattering. The inclusion of this-  7 -effect into the optical potential via p2 terms is clearly crude, and the progress madeon this problem was described. In particular, the techniques to avoid double countingin the PPU problem appear to have applicability to the irn problem as well.A further test of our theories is given by the inherent prediction they containof various pion reactions. It is straightforward to calculate ae ', and the inclusive atot and areaction_ However, decomposing a r into its quasi-elastic and annihilation (absorption) pieces is more approximate (it also should contain some and o'^EL, al­though explicit coupling to these channels is not usually included). Some findings include 1) a(ir,7rN) is grossly overestimated by models not including elastic unitarity and Pauli blocking; 2) if the impulse approximation is not made, the unitarity relations yield further information on a r, 3) annihilation shadows other channels, yet other channels don't fully shadow the annihilation one; therefore, a different, more statisti­cal theory would be necessary to truly decompose ar.2.5 Phenomenology of non-elastic reactions within the isobar-doorway pictureA number of models based on the isobar-doorway hypothesis have been constructed for pion-nucleus elastic scattering. Given these as a starting point two types of ex­tensions can be contemplated. First consider inelastic pion reactions such as cNPPALPrcMA NPPWPPRrA etc. It is clear that application of the present models which restrict the doorway space to A-h states cannot give a complete description of such reactions. To do so requires an extension of the doorway space to include more complicated isobar plus particle-hole configurations which couple to the final nuclear states. In a multiple- scattering picture these would be the intermediate states of the pion-residual nucleus final state interaction.The other type of extension is to reactions involving another kind of particle in addition to the pion, e.g. Nb APPrA (p,irN), etc. Now if the initial and final nuclear states are the same or belong to the same isospin multiplet, one can use fairly directly information gained from elastic scattering. Perhaps the best example of this kind of reaction is cNb APPCrcW Below 500 MeV photon energy this reaction takes place essentially entirely through A production. This would not be the case for charged pion photoproduc­tion or nucleon-induced reactions.The first Nb An°) isobar-doorway calculation used the phenomenological Kisslinger- Wang model. This model uses factorization and a modified closure approximation to parametrize the pion-nucleus elastic amplitude in terms of the pion-nucleon amplitude, an average isobar-doorway propagator and an isobar-nuclear form factor. The photoproduction cross section is obtained by replacing the pion-nucleon elastic amplitude with the single nucleon photoproduction amplitude. The resulting Nb WF0) cross section was found to be considerably larger than the result of a standard DWIA calculation.A more elaborate calculation was carried out by Koch and Moniz within an isobar- hole model for 160 Nb APPCr160. The A-h doorway states were the same ones used to analyse elastic scattering from le0. In the usual multiple scattering language this calculation-  8 -differs from DWIA by including higher-order effects in both the distorting optical potential and the production operator. In the final results these effects tend to com­pensate each other, and the calculated cross section is very similar to DWIA with a first-order optical potential.For isospin non-zero targets one has the possibility of analogue NPPAPPr and Nb APPr transitions. In this case the possibility of isospin-channel-dependent isobar-doorway parameters must be confronted. It has been found that 7Li (ir+ ,Tr°)7Be and 13C U + ,ir°) 13N cross sections are very sensitive to these isospin-dependent effects. Detailed non­charge exchange elastic scattering data on these targets are necessary to determine the size of these effects.The application of the isobar-doorway picture to Nn ALPr and NLPARr reactions is still largely unexplored. Hirata has done a calculation of ^ C U . p ) 1^  in the isobar- hole model, but doorway states other than A-h states were ignored. In principle one might be able to apply the A-h approximation to "coherent" production, i.e., A(p,irN)A, but then interference with non-resonant pionic bremsstrahlung may be important.To summarize, it is useful to consider some "homework problems" (both experiment­al and theoretical) the solution of which would go a long way toward testing our under­standing of isobar dynamics.Experiment: cNb APPCrc13C(ir± ,7r±) elastic and total cross sections as a function of energy Nb 11r~) or NPP- Ab r analogue transitions, e.g. on 13C or 15NTheory: Microscopic calculation of Q-space couplings, especially for T / 0Nb WPP1) analogue transitions cNb APPCrc for J 0, e.g. 14N ( =  1 + , T = 0)2•6 A field theory of pion-nucleus interactionsTwo important aspects of pi-nuclear interactions are multiple scattering and pion annihilation. To take annihilation into account one includes terms in the Hamiltonian in which the pi-nucleon interaction is given by either a single absorption by, or emis­sion from, a nucleon. Such interactions also generate pi-nucleon scattering, and it is necessary to use a consistent treatment of annihilation and multiple scattering. In this talk we review some progress in achieving a consistent and calculable theory.We adopt the procedure of deriving and attempting to solve the Low equation (non- relativistic dispersion relation) for varying reactions. So far we have studied pi- nucleon scattering,9’10 pion-nucleus scattering11’12 (in an approximation in which annihilation is neglected) and the pp ->• d?r+ reaction.13These results differ from those of other treatments by the inclusion of propa­gator modifications which act as cutoffs for terms involving pions of relatively small momenta. Because of these propagator modifications the use of a pi-nucleon T-matrix of long range is perfectly consistent with the idea that the fundamental pi-nucleon form- 9 -factor is of very short range.The origin of the propagator modification is the proper evaluation of the off- energy shell dependence of the crossed Born graph:In the graph, a> is the energy of a virtual (off-energy 'N / /shell) pion. The values of w (= /p2+m2") tend to be11large because of the pseudoscalar nature of the pion /(p4 terms in numerators), but one must pay a price be­cause the corresponding energy denominator is large. The propagator modifications result from including the correct energy denominators.We review the salient formulae of published work. For pi-nucleon scattering wehaveI ^ V ' (E)) • (,)which is a linear equation for the pi-nucleon transition matrix, t j (E) , equivalent to that of Chew and Low. In (1) hQ includes the kinetic energy (to order 1/m) of the nucleon as well as the total energy of the pion, and i is the ith target nucleon. The term Xvj/E is the crossed Born graph mentioned above. Under some approximations (in which annihilation is thrown out) for the driving term of the pi-nucleus Low equation one can write the following equation for the pi-nucleus transition matrix T:where Hfl includes the pion total and nuclear excitation energies. The difference between (2) and standard equations is the factor (E/Hq)2 , caused by the energy depen­dence of the driving term, in the progagator. The factor E2/Hg is small for virtual pions of high momentum. Hence effects caused by terms involving such pions, such as the Kisslinger singularity and the Lorentz-Lorenz terms, are significantly reduced.As a prelude to including annihilation effects in pi-nucleus scattering we treat the reaction pp dir+ by solving the relevant Low equation. Let ?(E) be the operator for pion production in proton-proton collisions leading to a final pion-deuteron state.We have found thatf(E) ~  2  tj(E) ^  Bi • (3)i/j ho "hoThe operator Bj produces a pion from nucleon i which propagates until scattered by the nucleon j. The -l/h2 term is the standard Yukawa propagator of the pion. The 2hg factor is absorbed by the l//2to factors appearing in Bj and tj(E). The major modifica­tion of our treatment is the E/h0 factor which acts as a cutoff of terms involving mesons of high momenta.The results for total pp -*■ dir+ cross sections and angular distributions in the resonance region are given in Ref. 14, and a good representation of the data is achieved.-  10 -A more recent development is the attempt to include annihilation by removing the approximations on the driving term of the pi-nucleus Low equation. A set of Low equa­tions coupling pion-scattering with pion annihilation results. We have obtained a set of coupled linear equations that, we believe, are equivalent to the Low equations. The feature that off-shell pion scattering is damped remains in this more general treatment.There are several problems for future consideration:1) Evaluation of cross sections using our coupled equations is necessary.2) This set of equations generates also nucleon-nucleon (NN) scattering. Hence one must readjust the NN potential so that the total NN T-matrix is consistent with NN phase shifts. In our framework this is done by solving the Low equations that couple NN scattering with the reactions NN t- NNir.3) A fully relativistic treatment has not been achieved.4) There is no reference to quark degrees of freedom.2.7 Quark structure of the nucleon in nucleiThe large quark confinement size (R =* 1 fm) implied in the MIT bag model raises an intriguing question as to how the fundamental quark structure of the nucleon mani­fests itself in a nuclear medium where nuclear bags are (naively speaking) nearly close packed. In particular, the remarkably simple description of the exchange currents in nuclear electromagnetic and weak processes (and their success) is either a mere accident in this quark picture or else tells us that the model is deficient. In this work15’16 we propose a new bag structure of the nucleon in an attempt to resolve this paradox.(?)We make three basic assumptions: a) quark confinement; b) a phase transitionbetween the true vacuum and the hadronic bubble (interior of the bag); and c) asymptotic freedom. In terms of QCD, we are supposing that non-perturbative aspects of the gluon fields provide the quark confinement and that as a consequence the inherent phase tran- ition affects the chiral SU(2)xSU(2) symmetry underlying the QCD to manifest in different modes in the interior and in the exterior of the bubble: outside the symmetry is assumed to be spontaneously broken, generatinga col 1ective mode, i.e. Goldstone bosons ir+ , it- and tt° ; inside the symmetry is unbroken so the Goldstone bosons are expelled. Instead of working with a quark-antiquark structure of the collective excita­tion, we treat the pion in terms of a phenomenological field Tra , a = 1,2,3 with the chiral symmetry realized non-linearly as seems to be suggested by the success of the soft-pion theorems of the 19601s . The following set of equations follows from the general conditions stated above (we ignore for simplicity perturbative, quark-gluon coupling inside the bubble):-  11Ins i de: wOn the surface: (5)(6 )(7)Outs i de: (8 )Here fir (= pion decay constant) is taken to be unity, ip the quark field (massless for up and down quarks), Dy = (1+tt2)~1dp, an outward normal unit four-vector, B theenergy density that it costs to create a bubble in the physical vacuum (little is known on this, even the sign is not agreed upon), and the non-linear Lagrangian density of the Goldstone boson. Equation (*t) follows from the asymptotic freedom, Eq. (5) from the requirement that there be no quantum number flow inward or outward through the bubbleenergy-momentum tensor (or equivalently from stability condition). The energy of the nucleon is thenwhere n — number of quarks (—3) and fl = tuR, w being the lowest cavity mode frequencyWe have not succeeded in obtaining a fully general solution to this set of non­linear equations; however, there is one spherically symmetric solution known as "hedge-put no constraint on B, then it can be eliminated from Eqs. (7) and (9), and the resulting set of equations determines the confinement radius R and the quark frequency Jl. Two inequivalent solutions are found: 1) an MIT-like nucleon with R ^  1.7 fm, fl 1.8, with small effects from the pion field; 2) a"little bagisH'nucleon17 withpicture of pion exchanges (exchange of Goldstone bosons), and offers a natural explana­tion for the observed pion-exchange phenomena in nuclei. We conjecture that this is the nucleon realized in nuclei.The large pion field strength implied in the little bag solution poses an interesting question on the pion cloud of the nucleon. The strength would be singular at r < R if extrapolated inward, but this is not physical since the phase transition requires the pion field to vanish for r < R. There may be some physics in this if a nucleon can be uniformly compressed to a size at which the pion field blows up.To obtain a realistic model of the nucleon, it will be necessary to take into consideration the fact that the pion has a size; this would require an explicit accountsurface, Eq. (6) from the axial current conservation, and Eq. (7) from the conserved(9)U = 0 ).hog", e.g. ir(r) = y <j>(r) for which we have found a beautifully simple solution. If weR =* 0.6 fm, n 0.2 with large pion pressure, with the quark (or quasi-quark) behaving (effectively) non-relativistically. This latter solution restores the classical- 12 -of the qq" content of the collective mode. This, together with other degrees of freedom left out in our model, is hoped to reduce the little bag size to R < 0.4 fm.17 This work is in progress.References1. C.Y. Prescott et al., Phys. Lett. 77B, 347 (1978).2. D. Gross and F. Wilczek, Phys. Rev. £8, 3633 (1973);R. Feynman et al., Phys. Rev. D18, 3320 (1978).3. B.W. Lee and M.K. Gaillard, Phys. Rev. Lett. 33., 108 (1974).G. Altarelli and L. Maiani, Phys. Lett. 52B, 351 (1974);A.I. Vainstein et al. , JETP 4£, 670 (1977)";"J. Finjord, Phys. Lett. 76B, 116 (1978).4. J.G. Korner et al. , Phys. Lett. 81B , 365 (1979);B. Guberina et al., Nucl. Phys. B152, 429 (1979);F. Buccella et al., ibid., 461.5. R. Woloshyn, Can. J. Phys. £7, 809 (1979).6. M. Rho, Nucl. Phys. A231, 493 (1974).7. I.S. Towner and F.C. Khanna, Phys. Rev. Lett. 42, 51 (1979).8. M. Chemtob and M. Rho, Nucl. Phys. A 163, 1 (1971).9. G.A. Miller, Phys. Rev. £14., 2230 (1976).10. G.A. Miller, Phys. Rev. ££8, 914 (1978).11. G.A. Miller, Phys. Rev. Lett. 38, 753 (1977); Phys. Rev. £l£, 2325 (1977).12. G.A. Miller, Z. Physik A287, 387 (1978).13. M.A. Alberg, E.M. Henley, G.A. Miller and J.F. Walker, Nucl. Phys. A306, 47 (1978).14. G.A. Miller, in Meson-Nuclear Physics— 1979, ed. E.V. Hungerford III, AIPCP#54(AIP, New York, 1979), P- 561.15- G.E. Brown, J. Delorme, M. Rho and V. Vento, to be published.16. J.-H. Jun, E.M. Nyman, M. Rho and V. Vento, to be published.17. G.E. Brown and M. Rho, Phys. Lett. 82B, 177 (1979).- 13 -3. SUMMARYIt is obviously not possible to give here the details of the presentations and discussions that took place over a period of two weeks. (To some extent the brief sum­maries, and corresponding references, should compensate for this.) Instead, we have tried to put together an overall picture of the present status and possible future thrust in this field. Specific suggestions have been made as to what one may learn from a number of possible experimental measurements.One of the striking features that emerged from our discussions of several approaches to pion-nucleus scattering was the overall unity of the field. This is not necessarily made clear by the language used. Figure 1 illustrates this for a relative­ly simple (double scattering) contribution to w-nucleus elastic scattering. The isobar-doorway-model (IDM) essentially cuts the diagram on the solid lines— so that one is interested in the self-energy of a heavy baryon (the delta-A) in the medium. On the other hand, the dashed lines indicate the optical model (OM) picture, where one calcu­lates the self-energy of the pion. Clearly there is no difference of principle between these two approaches. Indeed, given any IDM one can find an equivalent OM. (This is the basis of the theory of Kisslinger and Wang, which was recently used— at the phenomenological level— by Saharia and Kisslinger.)In practice, of course, the approximations necessary for practical calculations in either the IDM or OM could be quite different. In the former the elastic scattering ampli tude i sTel = A7 92 fO Ne+ " hDD _ WDD - w UUFgUn 9FCFl Nywhere we've introduced the usual projection operators onto the doorway state (D), the elastic channel (P) and everything else (Q). The interaction terms pUO and includethe effects of coupling of the A-hole doorway states to the P- and Q-spaces, respec­tively. Clearly if one can find the eigenstates of S2 OO + W Dp + W^}, namely, | y>(with eigenvalues ey), the elastic scattering problem is solved:Tel = X ]  <k '°l«C + |h> 7— Ol«C |k0> . (2)u t_eyThe standard technique is simply to diagonalize SgOO + Wpp + WQp } in the A-hole basis. The eigenfunctions |y>are therefore given as- Ik -_  Su K  »i‘> • (3>aBFinally we note that the operator <#C in Eq. (2) simply converts a pion and a nucleon to a A— see Fig. 2.7T£Fig. 2 NTable I summarizes the physical effects which have been included by the various groups doing IDM calculations. In principle, all of these effects have been includedTable I. Effects included in various isobar-doorway calculations."C" represents calculated, "P" means parameterized, and nothing means the effect is omitted.m W n r exchange Elastic width Paul i AnnihilationErlangen C C P PErlangen(Hofmann) C C C CMIT-SIN C C PRegensburg C C C Cin one or more OM calculations, but the practical details differ.- One suggestion arising from the workshop was that the best comparison of IDM and OM calculations may be through the corresponding eigenenergies (e^). The details of how to extract (ep)from an OM is an interesting theoretical problem.An excellent illustration of the unity of this field over a wide range of ener­gies was provided by the discussion of the renormalization of the axial current as seenin 0-decay (and p-capture). In particular, the strength of the Gamow-Teller transition matrix is proportional to Mf., wherePs + _ fir 9PPRR | < f |  x±0 [ l  + H (q ,u ,)] | i > j .  WThis is illustrated in Fig. 3- Clearly this renormalization is described by the same set of diagrams which at <o > m^ describe pion elastic scattering.M fi .Fig. 3fdcr/dH (mb/sr)15In the case of infinite nuclear matter, if we call the A-h graph (Fig. 4) "a" (the polarizabi1 ity of the medium), thenand2m„ ^opt1 + a ’< f|T+CTIi > . 1 + a -(5)(6 )N -1Fig. 4That is, the effective axial coupling constant is of the order0.71* gA in nuclear matter. These medium corrections have also been calculated for nuclei with closed shells plus or minus one nucleon (e.g. A = 3, 15, 17, 39 and 41), and the A-h self­energy corrections account for up to 50% of the observed effect.3-1 Comparison with elastic dataThere is now a considerable amount of high quality elastic pion nucleus data.The qualitative features are usually extremely well reproduced by theory with the inclu­sion of one or two "not-so-adjustable" parameters— as shown in Figs. 5-7 . However, a less casual examination reveals that there are places where the discrepancy amounts to a factor of 4 or 5! This is as big as the problems encountered in low-energy pion elastic scattering four years ago.Fig. 5(a). Comparison of the ir— '+He data of Crowe et al. with recent optical model calculations of Landau and Thomas.LAB'Fig. 5(b). Comparison of the ir±-160 data at T^ = 240.2 MeV with preliminary opti­cal model calculations by Landau.- 16 -Fig. 6. Differential cross section for ir-12C elastic scattering in the IDM.-  17 -It is possible that a phase shift analysis of the data either eliminates or severely constrains many theories. Unfortunately the large inelasticities (i.e. n* + 1for most partial waves) render such a phase-shift analysis impossible with presentdata. So-called "model - independent analyses", where the amplitude itself is parame­terized asf(s,t) = f(s.O) eBt n  (1 - t/tj) (7)i=l(with seven real parameters— B real and t; complex), have been able to fit the datavery well. This analytic expression can then be expanded in partial waves in order toobtain (n^.fi^). Unfortunately there is some residual doubt over the extracted numbers because the asymptotic (large-*) behaviour of Eq. (7) is incorrect. From this point of view the phenomenological IDM, which does guarantee the correct asymptotic behaviour, could be the most reliable technique for phase-shift analysis.In comparing the predictions of the IDM and OM far below resonance, it should be remembered that the t-matrix approach to the IDM has severe problems of including back­ground terms (e.g. irN s-waves). Indeed these problems may render the IDM impractical at low energy. Well above the resonance there may also be technical problems in the A-hole calculations performed so far (see Fig. 7) because they do not necessarily reproduce the nuclear form factor at high momentum transfer. Of course, this is not an intrinsic problem of the method.Fig. 7. Comparison of ir±-160 scattering data with optical model and isobar-hole calculations.- 18 -3.2 Nuclear ground state parameters from elastic scatteringWhile there is undoubtedly a strong selectivity of PPh (and ir“) for the proton(and neutron) distributions in the (3,3) effects have been observed for (say) 180Fig. 8. Comparison of the best fit curves using the potential models of Strieker et at. and DiGiacomo et al. with the data of Johnson et al. for the ratio of do/dfi in ir“ 180 and 160 elastic scattering.resonance region, and strong qualitative and 48Ca, theoretical uncertainties have so far precluded quantitative conclusions regarding the differences in the proton and neutron distributions. This is an area deserving of much theoretical work.Low-energy pion scattering offers the same advantages (f^_n : i^r_p = 13:1) with regard to selectivity. Moreover, the inves­tigations so far of the TRIUMF data involving the ratio of the LPv differential cross sections on 13C/12C, and 180/180 (see Fig. 8), show an apparently model-independent determi­nation of the difference in neutron rms radius between the isotopes. For 13C the result is 2.35 ± 0.03 fm (relative to 2.31 fm for 12C), and for 180 2.81 ± 0.03 fm (relative to 160 with 2.60 fm). The real test of this tech­nique involves the use of tr+ to extract the difference of proton radii in neighbouring isotones, so that the answer can be checked us ing electron scattering. The analysis of ir+ data on 12C/31B recently taken at TRIUMF is presently nearing completion.3-3 Effects of absorption on elastic scatteringOne of the major new theoretical problems facing us in the description of pion elastic scattering is the effect of coupling to channels where the pion has been absorbed. In the language of the IDM this is a specific Q-space effect, which has been included in the lowest order at least in some calculations. The presence of such coupled channels raises questions over the consistency of the theory, and specifically the problem of double counting.For the PPRR system, this has been the subject of considerable theoretical work, and there is a general consensus that the full PPRR scattering amplitude can be written asT = TMS + Tabs . (8)Here Tabs is the contribution from those terms in which the pion is absorbed and re­emitted. It involves T^g, which is the usual multiple scattering (or Faddeev) series, calculated with (say) phenomenological t-matrices, with the one constraint (to avoid- 19 -double counting) that the Px1 t-matrix not include the nucleon pole term. Some calcu­lations have been performed for ttD elastic scattering, and the effect of Tabs is parti­cularly apparent in the tensor polarization t20• So far only one experimental point has been measured, and it lies mid-way between the calculations with and without absorption.The future developments in this system should be very interesting. Further tensor polarization measurements will be made at LAHPF, hopefully as a function of both angle and energy. In addition there has been a recent suggestion that the LPU polariza­tion would be very sensitive to the possible coupling of PPU to a dibaryon state. This experiment is already being prepared at SIN. On the theoretical side some rather deep theoretical questions have been raised about the correct relativistic theory to use.In particular, it is possible that the usual Blankenbeclei— Sugar type of reduction to a 3D theory may be unreliable for one light particle far off mass shell.A number of groups have attempted to extend the field theoretic approach to the case of a general nucleus. At this workshop we heard about the extension of the Low equation to the many-body system. Unfortunately this has been put to very little practical use. On the experimental side we could use much more guidance as to the strength of various inelastic channels. The recent Tel-Aviv data are a step in the right direction, but much more systematic data are needed on the various channels coupled to elastic scattering.Thus our study of elastic scattering leads very naturally to a need to understand the reactive content of the OM, and hence to a study of pion reactions. In the follow­ing sections we present a systematic discussion of possible pion reactions, beginningwith the simplest— namely, electroproduction. However, to finish this section we note that there has been theoretical speculation that there could be narrow resonances in specific absorption channels, and the experimental search for these is long overdue.3.k Pion photoproductionA glance at Fig. 9 reveals the essential dif­ference between charged and neutral photoproduction onthe nucleon. The Nb APP0) process is completely dominated, which means that the coherent A(y,ir°)A reaction is an ideal test of the IDM. In particular,the scattering amplitude for this process isT(y,„o, - £  <°t-1 u> <>■ ira,NTiobt> _ (3)y euThus if we define the photon doorway state |D^ .^  asl°y>= A.Ny l0’S >  ’ (,0)what this reaction measures is the over 1 ap <(p | D^ )>.The next few years will undoubtedly see a few angularW(MtV)Fig. 9- I 11ustration of the dif­ference between the elementary yp -+ mr+ (dot-dash) and YP~*"n,°P (solid) processes. [The dashed curve is “ atot(ir+p -*■ PPhn rW:-  20 -distributions measured for Nb APPCr to the ground state. However, low y fluxes, and low 7t° detection efficiency, will probably mean no data will be taken for specific excited states— even though this would be theoretically interesting.Charged pion photoproduction (or pion photoabsorption) is experimentally much more accessible because of the greater ir* detection efficiency. However, as we saw in Fig. 9, the elementary process is never A dominated. This leads to great background problems in the IDM, and it is likely that the DWIA using OM wave functions will be the only possible theoretical approach. In this formalism there is an important question of the effects of the medium on the two-body (yN -*■ ttN) amplitude. However, at least for the a • term which dominates below (50-70) MeV current algebra tells us that the medium effects are negligible. Thus the usual DWIA is probably good below 100 MeV.Indeed a comparison with the recent total cross section measurement for 12C(y,PPMr12Ng _s_ suggests the DWIA may be good even above 100 MeV. However, a definitive test will require angular distributions, too.At first sight the (i^.y) [or (y.ir1)] reaction seems an ideal way to study the off-shel1 pion-nucleus Interaction. However, recent calculations using phase-shift- equivalent transformations have shown little sensitivity. The basic reason seems to be that the transition density is surface peaked, and thus one is less sensitive to the interior wave function. In the IDM model this has also been observed as the filter effect. In fact, whereas elastic scattering (and inelastic scattering to'the 0+ T«=l analog state) in 12C gets its biggest contribution from p-wave, the NPPh Ab r reaction Is dominated by d- and f-waves.Nevertheless, the NPPAy) reaction does contain new information, and it should be exploited in the next few years. From the point of view of TRIUMF, the reaction 13N(tr+ ,y)*50g s could probably be measured now with TINA and MINA, and this is an important priority. As there will be an Ml (AT = 1) contribution to this, it may con­tain information on the precursor to pion condensation— although it is not as clear-cut as the Nb 11t+) reaction on 12C to the 12Bg 5_.3.5 Single charge exchangeSince charge exchange (SCX) , and in particular atot(ir+13C -*■ irol3N), was discussed in terms of the phenomenological IDM and the 0M. It was observed that SCX is extremely sensitive to improvements in the first order 0M— especially Pauli effects— and to differences in the isospin 3/2 and 1/2 optical potentials. In fact a relatively small (phenomenological) shift in the energy dependence of these potentials can resolve the remaining disagreement between theory and experiment. This energy shift can be shown to correspond to the addition of an extra core term in the usual DWIA. The derivation of such a correction term from a microscopic theory is an important theoretical problem. Needless to say, we look forward to the time when the measurement of do/dfl, on a wide range of nuclei, will provide an even stronger test of the theory.-  21 -3.6 Nuclear structure - inelastic pion scatteringThe traditional interpretation of NPPWPPKr in terms of extracted deformation parameters Bn and gp has led to the result that these are generally larger for low-energy pions than other probes. This is rather surprising in view of the relatively weak interaction of low-energy pions, and the apparent lack of sensitivity to the pion wave function as seen in studies using phase-shift-equivalent transformations.It is quite likely on theoretical grounds that the low-energy region could be veryinteresting for studies of inelastic scattering— and this is particularly relevant to TRIUMF— once the theoretical problems are understood. The point was made in the discus­sion that what is needed is not a phenomenological approach to Bn and Bp , but rather one should start with well-known transitions (Bn and Bp fixed) and work to understand theinelastic data there first. Only then can one move to uncover new information.A number of exciting new results are just beginning to emerge from inelastic scattering in the resonance region. At SIN the GQR in ‘♦“Ca has been seen at 18.2 MeV (with PPh at 163 MeV), and there is a hint of the monopole at 20.6 MeV (at 241 MeV).There have also been some spectacular results from EPICS, using a comparison of 7r+/ir' scattering and the best energy resolution it can presently manage (~240 keV FWHM), from which one can extract the isospin mixing of three 4" (stretched) states in 12C (19.25,19.5 and 19-65 MeV). In addition a pure (nn"1) state (signature a ratio 9:1 for PPM,PPhr with j* = 9/2+ has been seen at 9-5 MeV in 13C. Clearly there is much more exciting work to be done.3-7 Pion quasi-elastic scatteringThis is one of the major inelastic channels in pion-nucleus scattering, and as such will be extensively studied experimentally. Traditionally, knock-out reactions have been suggested as a possible means to study the off-shell behaviour of a two-bodyinteraction. Recent work on the NPPAPPRr reaction suggests that while the usual off-shelleffects are far too small to be measured, (tt,ttN) is particularly sensitive to the effect of the medium (e.g. Pauli effects) on the PPR t-matrix. Experimenters who plan to look for these effects should at least consider the possibility of using the so-called fixed condition geometry, where as far as possible distortion and nuclear structure uncer­tainties are kept fixed. The theoretical motivation has been presented in great detail in the literature, and we refer the interested reader there for more details.3-8 Conclus ion3-8.1 Future theoretical developmentsIt became apparent during our discussions that the realistic IDM was too compli­cated to allow one to see any really new phenomena. It seemed that it would be usefulto set up a simple model, which permits exact solution, to allow study of new many-bodyeffects e.g. reflection, many-nucleon absorption, etc.?It was also obvious that there is a need to extend and improve the relativisticfew-body calculations— e.g. for PPU elastic, PPU + irNN, NN + ND, etc. However, many of-  22 -Fig. iO. Predictions for the vector polari­zation in irD elastic scattering. The curve "NR" is a three-body prediction, and the other curves show the effect of reasonable couplings to di-baryon resonances.Fig. 11. The predicted ■n,_3He polariza­tion shows a strong sensitivity to the three-body magnetic form factor— curves of Landau.the theoretical problems could be better studied in a less realistic model problem.For example, a comparison of the exact solution of the Bethe-Sa1 peter equation, with the usual Blankenbecler-Sugar result,would be useful-even in a spinless model calculation. This may be particularly relevant to the calculation of pion absorption (e.g. PPh U  + pp), where the intermediate state can involve exchanged pions far off mass shell.For pion-nucleus scattering a number of important priorities have already been discussed. Perhaps the most pressing need is for a better description of the coupling to Q-space. In particular, one needs to improve and test the incorporation of the effects of absorption guided by the reaction content analysis.At the much deeper level we heard about the quark description of hadrons, and particularly the tests of QCD involving parity violation in the yN -> PPR reaction. The phenomenological approach to quark confinement through the bag model was also discussed. It seems highly likely that at usual nuclear densities the MIT bag model would lead to percolation i.e. the formation of bag-chains containing many quarks. Since this is probably not consistent with our knowledge of nuclear structure, one solution is to use a smaller bag radius (~0.3 - 0.4 fm)— the so-called "little bag".It was shown that when the pion field is coupled to the bag, there are two solu­tions to the non-linear field equations. One of these corresponds to the MIT bag radius, the other to the little bag. The latter model has already been extended at TRIUMF to give a new model of the off-shell P33 t-matrix. In the long term one may hope to extend this sub-microscopic approach directly to the many-body system.3.8.2 Experiments to come^ We just mentioned that the measurement of an enhancement of the parity violation in yp -* T7+n (or PPIn -► yn) would provide an important test of some aspects of QCD. It is possible that such a test could be mounted at TRIUMF.Polarized targets offer considerable promise for the near future. We have already mentioned that the asymmetry in PPU elastic scattering is quite sensitive to the presence of a coupled dibaryon resonance (see Fig. 10). The OM calculations for PP3ffe show a great sensitivity to the spin distribution (magnetic form factor) in 3He— asshown in Fig. 11. This is certainly a high-priority experiment.The use of low-energy PPM to measure neutron radii seems very promising, and ifthe Pr+ tests on isotones work, one should proceed with a program of measurements— e.g.on etc_ similarly, pion inelastic scattering to states of well-knownstructure has a high priority.Finally we mention that a complete set of measurements— including (y,ir°)g s ,(y>^_) , (t ,7r ), NPPAPPR r A  Nb APPR r A  NPPA absorption), ( PP , tr') as discussed in detail above— on a few selected targets (e.g. 15N> 160> 40Ca) WQu]d be extreme]y usefu].Without a doubt the next few years hold a great deal of exciting and rewardingwork in pion physics. Let us get on with it!-  23 -- 24 -BIBLIOGRAPHYThis is intended primarily as a very incomplete guide to the recent literature dealing with topics raised at the Workshop. The proceedings of the most recent topical conferences in medium-energy physics are a good source of such material, in particular:1. Proceedings 8th Int. Conf. on High-Energy Physics and Nuclear Structure (8 1COHEPANS),Vancouver, August 1971, eds. D.F. Measday and A.W. Thomas, Nucl. Phys. (in press).2. Proceedings 7th Int. Conf. on High-Energy Physics and Nuclear Structure,ed. M.P. Locher (Birkhauser, Basel, 1977).3. Proceedings 2nd Int. Conf. on Meson-Nuclear Physics, ed. E.V. Hungerford III,AIPCP #54 (AIP, New York, 1979).4. Proceedings 1st Int. Conf. on Meson-Nuclear Physics, eds. P.D. Barnes et al.,AIPCP #33 (AIP, New York, 1976).A. Elastic ScatteringMicroscopic Optical Model:5. R.H. Landau, in Ref. 1.6. A.W. Thomas and R.H. Landau, Phys. Reports (to be published), TRIUMF preprintTRI-PP-79-23.7. J. H'ufner, Phys. Reports 21C , 1 (1975).8. H. McManus, Michigan State University preprint (1979).9. W. Weise and G.E. Brown, Phys. Reports 22C^ , 280 (1975).Microscopic Isobar-Doorway Model:10. H.M. Hofman, Zeit. f. Physik 289., 273 (1978).11. E . Oset, i n Ref. 1.12. E.J. Moniz, p. 288 in Ref. 3.13. M. Dillig, p. 306 in Ref. 3.14. F. Lenz, Ann. Phys. 95, 348 (1975); and p. 175 in Ref. 2.15. L.S. Kisslinger and W. Wang, Ann. Phys. 99., 374 (1976).Phenomenology:16. L.S. Kissiinger and A.N. Saharia, TRIUMF preprint TRI-PP—79-26.17. M.S. Sternheim and R. Silbar, Ann. Rev. Nucl. Sci. 24, 249 (1974).18. R.R. Johnson et al., Phys. Rev. Lett. 43., 844 (197977"B . ReactionsInelastic Scattering:19. H. Thiessen, in Ref. 1:R.J. Peterson, ibid.20. G.E. Walker, p. 206 in Ref. 3;M. Dillig, H.M. Hoffmann and K. Klingenbeck, ibid., p. 306Pion Photoproduction:21. J.M. Laget, in Ref. 1.(y,ir°) :22. R.M. Woloshyn, Phys. Rev. C^8, 1056 (1978).23. J.H. Koch and E.J. Moniz, MIT preprint CTP#765 (1979).Nb WPP-r ,24. M.K. Singham, G.N. Epstein and F. Tabakin, Univ. of Pittsburgh preprint (1979), to be published.- 25 -25. K. Klingenbeck and M .G . Huber, "Nuclear A* excitations in the medium energy range", Erlangen preprint (1979).Charge Exchange:26. D. Bowman, in Ref. 1.27. J. Alster and J. Warszawski, Phys. Reports 52C, 88 (1979).28. A.N. Saharia and R.M. Woloshyn, Phys. Lett.~54B, 401 (1979) and Phys. Rev. C (in press)29. E. Oset, p. 364 in Ref. 3.30. R.H. Landau and A.W. Thomas, Phys. Lett, (in press), TRIUMF/OSU preprint TRI-PP-79-24Quasi-elastic Scattering:31. D.F. Jackson, A. loannides and A.W. Thomas, Nucl. Phys. A322, 493 (1979).Absorption:32. D. Ashery, in Ref. 1.33. H.K. Walter, p. 225 in Ref. 2.C . Few-Body Problems Involving Pions34. F. Myhrer in Ref. 1.35. A.S. Rinat, Y. Starkand, E. Hammel and A.W. Thomas, Nucl. Phys. (in press, 1979).36. A.W. Thomas and R.H. Landau, Ref. 6 , chapters 3 and 4.37. R.H. Landau, Phys. Rev. CJ_5, 2127 (1977).38. M.P. Locher, K. Kubodera, F. Myhrer and A.W. Thomas, J. Phys. G (letters,October 1979)•39- J.M. Laget in Ref. 1.40. J.H. Koch and R.M. Woloshyn, Phys. Rev. C16, 1968 (1977).41. P. Bosted and J.M. Laget, TRIUMF preprint TRI-PP-79-22.D. Miscellaneous Topics Discussed at Workshop42. G.A. Miller, p. 561 in Ref. 3.43. I.S. Towner and F.C. Khanna, Phys. Rev. Lett. 42, 51 (1979).44. G.E. Brown and M. Rho, Phys. Lett. 82B, 177 (1979).45. G.A. Miller, A.W. Thomas and S. Thdberge, TRIUMF preprint TRI-PP-79-16.46. K. Johnson, Acta Phys. Pol. B6^, 865 (1975);T. DeGrand et al. , Phys. Rev. D12, 2060 (1975).47. B.W. Lee and M.K. Gaillard, Phys. Rev. Lett. 33^ , 108 (1974).48. J. Finjord, Phys. Lett. 76B, 116 (1978).49. J.G. Korner et al. , Phys. Lett. 8j_B, 365 (1979).50. B. Guberina et al., Nucl. Phys. B152. 429 (1979);F. Buccella et al., ibid., 461.


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