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Studying nuclei with medium energy protons : University of Alberta/TRIUMF Workshop, Edmonton, Alberta,… Greben, J. M. Jul 31, 1983

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TRIUMFSt u d y i n g  Nu c l e i w i t h  Me d i u m En e r g y Pr o t o n sUNIVERSITY OF ALBERTA/TRIUMF WORKSHOP Edmonton, Alberta, Canada 11 - 13 July 1983Edited by J.M. GREBENMESON F A C I L I T Y  OF:U N I V E R S I T Y  OF ALBERTA  S I MON FRASER  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  COLUMBI ASTUDYING NUCLEI WITH MEDIUM ENERGY PROTONSUniversity of Alberta/TRIUMF Workshop Edmonton, Alberta, Canada, 11 - 13 July 1983Edited b y :J.M. GREBENDepartment of Physics, University of Alberta Edmonton, Alberta, Canada T6G 2J1Organizing Committee:J.M. GREBEN P. KITCHINGPrefaceThe University of Alberta/TRIUMF Workshop on "Studying Nuclei with Medium Energy Protons" was held at the Westridge Park Lodge in Devon, about 25 km from Edmonton. The idea for this Workshop had been around for some time, when, in early 1983, it was formed into a concrete pro­posal as a result of the apparent need for an assessment of the futureexperimental facilities for proton physics at TRIUMF.These proceedings contain all but one of the invited talks. Wehave attempted to limit the publication time by allowing contributors leniency in manuscript format. This has resulted in some style incon­sistencies, for which we apologize.We would like to express our sincere thanks to all those who have contributed to the success of this Workshop. Special thanks are due to Dr. J.M. Cameron and to Dr. H.S. Sherif who provided valuable advice in establishing the scientific program, and to Greta Tratt who, as no other person, dedicated her time to the organization of the Workshop and the preparation of the proceedings. Financial assistance is acknowledged as follows:TRIUMF Science DivisionUniversity of Alberta Conference Committee FundTRIUMF Users Executive Committee (TUEC)J.M. GREBEN P. KITCHINGCONTENTSTHE EFFECTIVE INTERACTION IN NUCLEISurvey Study of an Effective Interaction in Nucleon-Nucleus Scattering ................................................H.V. von GERAMBEffective Interactions and the Interpretation of Nucleon- Nucleus Scattering ........................................W.G. LOVE ELASTIC AND INELASTIC SCATTERINGMicroscopic Description of Intermediate Energy Proton Scattering ................................................L. RAYImpulse Approximation Dirac Optical Potential . . . .  J.A. McNEILExperimental Observations on the Quenching of the GT Strength J. RAPAPORTGiant Resonances - Why Protons? . . . . . . .F.E. BERTRANDQUASI-FREE SCATTERING AND REACTIONSQuasifree Scattering and Knockout ........................N.S. CHANT(p,d)-Reactions at Intermediate Energies ................J.M. GREBENOverview and Systematics of the (N, ir) and (N,y) Reactions P. COUVERTA-Isobar Effects in Quasi-Free Scattering . . . .  M. DILLIGMedium Resolution Spectrometer ........................C.A. MILLEREXOTIC CONSTITUENTS OF NUCLEINon-Nucleon Degrees of Freedom in Nuclei . . . .F.C. KHANNAFrom QCD to Short Range Nuclear Physics. . . . .A.W. THOMASFUTURE DIRECTIONS AND EXPERIMENTAL POSSIBILITIESPolarization Phenomena in N-Nucleus Scattering .J.M. MOSSFuture Directions in Proton Physics....................G.E. WALKERRAPPORTEUR TALKS AND SUMMARYTheory of Effective Interaction and Multiple Scattering. P.C. TANDYNuclear Reactions ............................P. KITCHINGConference Summary . . . . . . .E.F. REDISHList of participants ............................Un i v e r s i t y  o f A l b e r t a /Tr i u m f Wo r k s h o pI N V I T E D  P A P E R SI*I. THE EFFECTIVE INTERACTION IN NUCLEI1SURVEY STUDY OF AN EFFECTIVE INTERACTION IN NUCLEON-NUCLEUS SCATTERING§H.V. von GerambTheoretische Kernphysik Universitat Hamburg, Luruper Chaussee 149, 2000 Hamburg 50W. -GermanyAbstractFirst principle analyses of nucleon-nucleus scattering is presented with a Brueckner reaction matrix as driving two body effective interaction. The basic input elements and theoretical models underlying the scattering are outlined with several case study applications in an energy region between 100 and 400 MeV. Medium effects are the central theme.The work reported here was done in collaboration with K. Nakano’*' and L. Rikus of the Theoretische Kernphysik, Universitat Hamburg and A. Scott of the University of Georgia, Athens, Georgia, USA.^Supported by Bundesministerium fiir Forschung und Technologie,06 HH 746.21. IntroductionMicroscopic studies of intermediate energy, 100-400 MeV, proton scattering are a fine tool to study many body aspects of the atomic nucleus. They illuminate nuclear structure deep inside the nucleus together with aspects of the hadronic interaction mediating the scattering .1 In this energy regime it is known that the NN reaction cross section has a wide minimum and therefore nuclear transparency is at a maximum? In addition at these energies, the effects of pion production are still minimal and we expect that elastic and inelastic scattering, to low lying excited states, is describable as a direct reaction which knows only of nucleons, although certain mesonic degrees of freedom may occ u r . The unconfirmed conjecture over critical opalescence confirms this view that the explicit mesonic effects are difficult to isolate. Excitation of nuclear isobars, in particular the A 33 resonance, is feasible and such excitations could behave like doorway states resulting in collective enhancements or quenching in inelastic transitions^ Along this line developments of the microscopic optical potentials of nonrelativistic or relativistic origin provide evidence that interference effects between low and high momentum transfer mechanism are crucial at intermediate energies?The microscopic understanding of medium to high energy elastic scattering has made great progress. At high energy approaches based on multiple scattering theory, use the free NN scattering amplitude as driving operator on the elementary NN level6. In the most commonly used approximation the scattering mechanism is assumed to be a coherent superposition of elementary NN interactions in which the rest of the target nucleon?play the role of spectators preserving the centre of mass motion. In this respect it is of course interesting to restrict the analyses not only to the forward angle region but also into kinematic regions not allowed if the scattering is off a single stationary nucleon. It is not clear at this moment how far shell model wave function can supply sufficient Fermi motion to account for what is seen.Towards the end of this talk I'll come back to this problem and trigger possible new experiments.3The present status of first principle calculations and its interconnection with other disciplines can be seen from the flow diagram in Fig. 1.In the following we present the salient features which enter into the definition of the effective interaction and its representation? It makes essential use of the concept of an interaction zone which is small as compared to nuclear dimensions. To be least specific we take it as nuclear matter describable in terms of a non-interacting Fermi gas in its ground state. Thus any given point in the nucleus is characterized by a local Fermi momentum. In computing the effective interaction this nuclear matter approach provides the realm in which all practical calculations can be performed without relying on further approxima­tions and in particular reference to a particular nucleus. This latter aspect is very important as it permits to separate nuclear structure from nuclear reactions. The computational advantage is obvious. Recent emphasis on full relativistic treatments of the many-body problem at various levels of sophistication for elastic and inelastic scattering cause us to expect that the now classique non-relativistic treatment presented herein will be superseded in the near future. This new approach will ultimately combine the microscopic understanding of nuclear forces on the level of QCD with the relativistic many—fermion theory®In the next chapter the background to the effective interaction in nuclear matter (El) is given followed by some considerations regarding the local density approximation (LDA). The energy and density dependence of the complex interaction will then concludeFig. 1: Flow diagram to the concept of first principle analyses.4the principle input. Some applications in Chapt. 3 help to obtain some understanding on a quantitative level for elastic and inelastic scattering. In Chapt. 4 we present theoretical predictions for large angle (p,p) scattering and large momentum transfers, respectively.2, Effective Interaction in the Nuclear Matter ApproachMicroscopic description aim to connect knowledge about the nucleon-nucleon (NN) scattering with many-body theories. This link is establishing with Brueckner's perturbation treatment which is pursued most often in the theoretical medium of symmetric nuclear matter? In finite nuclei a harmonic oscillator shell model yieldsa practical basis}0The disadvantage of the latter approach is the suppression of scattering channels and therewith the suppression of the imaginary part of the effective interaction. The methods of Bertsch et a l . yield a real density independent interaction whose high energy limit is not the free NN scattering amplitude. It is our under­standing that their effective interaction is suitable for bound state problems.The microscopic optical potential follows the infinite nuclear matter approach which was initiated by Hiifner and Mahaux and has been reviewed and applied by several other authors 1 ^ h i s  approach identifies the single particle mass operator with the optical model in infinite nuclear matter in the lowest order of the hole- line expansion= X H > » a r J t(“ ) I V *  <1)|m|<kFt(co) in the anti symmetrized plane wave matrix element satisfies the Bethe-Goldstone equation (BG),t(u>) = V + VG^+) (w) t(u) (2)wherein V is the free NN Paris potentiali2The Green's-function5Gq  ^(u>) contain outgoing wave boundary conditions and medium effects such as the requirement of propagation in unoccupied intermediate states under the influence of an average potential acting on the single particlesG^+) (co) = 5 ---------    1 ^ be><^be 1q Z.--_---- - co-e (b)-e (c)+ie ' 'b|, 1c|>k FWe further identify the starting energy as the sum of the projectile energy e(a) and the energy of the struck single particle in the medium go = e(a) + e (m) .NUCLEAR MATTER(a)FERMI SURFACEFig. 2: Schematic representation of starting situation for scattering a nucleon (a) from symmetric nuclear matter in its ground state.There are a number of methods available to compute the matrix elements of Eq. (1). Since the techniques for the solution of wave equations are well known one introduces, with the identify,<<f> 1 1  (g o )  | 4> >  =  <<j> | v  I ip >am Tam ya m 1 • yam (4)6The correlated wave function ^ satisfies a related BGamequationip = 4* +  ^(u))Vtjj (8)Tam Tam Q amTo obtain the matrix elements, Eq. (4), one may either solve for t (o>) or ip. We solve E q . (5) in coordinate representation for thecorrelated wave function with the standard matrix techniques for Fredholm integral equations of the second kind.To summarize salient features of the procedure, we introduce centre of mass and relative coordinatesR + K  = *b + Eca - i  <?a + ?m> = ?  <?b + ?=>s . I  (S?a - sn > («>3 - j <Eb Ro>r = ra ” rm = r b “ rcAll wave functions are decomposed into partial waves and classified with respect to good total spin/isospin channels. The Pauli projection functionQ(K,q,k„) = |S,c><S,c (7)where | lb | , |c|>kp ensures that the two particles in the intermediate states propagate only in unoccupied momentum states above the Fermi momentum kp . In praxi the monopole part Q(K,q,kp ) is computed and used. The single particle energies e(k) in the propagator contain the kinetic energy and a self-consistent energy dependent potential energye (k) = k 2 + U (k) (8)7Various restrictions and analytic and/or numerical choices of this potential energy result in different forms of t-matrix elements representing alternative levels of approximation. The ultimate choice for U(k) is the fully self consistent complex mass operator itself but due to the numerical complexities involved has never been used. For the calculations described herein the real part of the lowest order nuclear matter mass operator as defined by E q . (1) was used. For energies above 100 MeV,this isa rather good approximation to the final result since the key effect there stems from Pauli blocking. For lower energies more iterations are necessary to achieve self consistency. The enormous amount of computer rime required is, however, daunting.Note that when kp = 0, U(k) = 0 ,  the Pauli function,Q(K,q,kp=0) -*■ 1, and the resulting matrix elements are those of the free t-matrix (on the energy shell) which can be directly compared with experimental phase shifts. The numerical accuracy can be checked herewith. The BG, Eq. (5), is transformed into a system of linear equations by replacing the integral by a trapezoidal rule integration.The correlated wave functions which are the solution of Eq. (5) then enable us to generate a complex energy and density dependent effective interaction in form of a two nucleon potential.t (r) = I t?T (r)PSPT + JtT(r) (£•§) *PT + £t?(r)Si 2PT = I (Rv -S, ) (9)ST T T kThis leads to a prescription first used by Siemens and whose details, . 1314nave been given elsewhere. Averaging the struck particle momentum m: 0<|m|<kp 5 defining a partial wave averaged version, reference to the projectile momentum and Fermi momentum is the only parameter left to distinguish the complex, energy and density dependent interaction with central, spin orbit and tensor component. Tables of this effective interaction are given in Ref.13 and they refer to the forms4 'yi*rcentral t?T (r) = £ tfT ------- (10)i= 1 rspin orbit t t (r)Ttensori=13 (air)(a2r)  -2------As is well known, an alternative approach to obtain an effectivethe general invariant structure of the NN scattering amplitude.An equivalent ansatz to E q . (9) is then used together with acriterium to reproduce this amplitudes. This approach is very appealing as it makes direct use of NN informations without relying on any NN potential. The major disadvantage lies in the limitation to kp = 0. Medium correction of any sort are not included a feature which we believe is important at all energies. We expect preponderance of dispersion effects and Pauli blocking next to higher order contributions in the hole expansion.Smaller medium corrections are expected due to many-body isobar effects which do not contribute to the NN problem, or many-body effects on the subnuclear structure level. However, these small medium effects are less likely to show up in global scattering situations as we are presently investigating but they are rather of a fundamental nature. It is the motivation of our present studies to obtain a solid understanding of dominant medium effects, before the next level may be investigated with confidence.To obtain some inside into the density dependence we display in figures 3 to 10 the Fourier transforms for the central inter­action separated by real and imaginary parts. The densities are indicated with the corresponding Fermi momenta, (0.5, 1.0, 1.4 fm ) which correspond to typically 10%, 50%, 100% of nuclear saturation. All figures refer to 200 MeV.15interaction has been pursued by Love and Franey. They start fromVlk) |M«V lm*| VlkllMeVfm’l9Fig. 3 Fig. 4;Vtkl | MeV Im1!10F i g . 7REALSOkltm'M *IMAGINARYSOFig • 8a _ i klfnf4!Fig. 9Fig. 103. Local Density Approximation and Optical Model PotentialAccurate scattering data are now available for a rich sample of nuclei and energies .6 Some data cover an angular region up to 160 and therefore represent a momentum transfer study up to 1200 MeV/c. Most data are severely more restrictive but comprise differential cross sections and analyzing powers. The situation is quite unique and represents a challenge to optical model calculations with the nuclear ground state properties known from other sources i.e. high precision electron scattering measurements or Hartree-Fock predictions. Here we stress studies with the local non-relativistic form of the OMP which has also been used previously .7 Some aspects associated with the nonlocal OMP have been addressed recently but practical applications are still11The local OMP is obtained by folding the single particle density of the target ground state with the complex effective interactionpending.( 11 )local momentum is given (self consistently) byand the complex*  k <r > = ^ U ( E CM - U(r) ( 1 2 )The linear combination of the nuclear matter central interactiont 0 required are given by(13)In this equation ST refers to the two body spin-isospin channels in which the effective interaction matrix elements are developed.The spin orbit potentials are computed in a manner equivalent to that of Scheerbaum and Brieva and Rook or in a folding expression similar to the central potential but here involving the LS- potential.These microscopic optical potentials have been calculatedbetween 150 and 400 MeV for “°Ca with density distributions17 .determined at 800 MeV and 1 G e V . Figs. 11 and 12 give an impressionof the radial shapes and energy dependences. The bottle bottom shapes of the real potential are the result of low and high momentum transfer interference effects together with density dependence in the interaction. The microscopic imaginary potential shows a typical Fermi distribution. A close inspection reveals also a doubling of the surface thickness as compared with the underlying density. The central values are larger than in phenomenological potentials. Figs. 13 to 25 compare the prediction of the micros­copic OMP with experimental data.After studying elasting scattering with the nuclear matter t-matrix approach inelastic studies represent a natural extension. The purpose of these studies may again be considered a test of the effective interaction putting different weight on the individual components as compared to the elastic channel. The transition amplitudes are computed with the fully antisymmetrized DWTA where the exchange is treated exactly . We distinguish the DWIA from DWTA by the sole use of the free t-matrix in the former whilst the latter is based on the density dependent t-matrix.T = 5  ! t  ( | r0- r  i | ;LDA) | [x ( + ) 4)^  "4>-; X ( + ) } > ( 14>DWTA “h-T-* □ i D 2 D 2 ‘ L 3 i 3 l J1 l 3 2SJ 'T are spectroscopic amplitudes, which are easily expressed when the initial and final state shell model wave functions are known. The notation for the transition operator emphasises the density dependence and the use of the LDA. Similar to the elastic case, t (|ro-r! |;LDA) in Eq. (14) requires a recipe for handling the dependence on the two coordinates r 0 and ri which point into different density regions. We have chosen the geometric meant (| r 0-ri | ;LDA) = jt ( |ro-r i | ;kp (ro) ) t (|r0-r i | ;kp (ri) ) j 1 / (15)12REAL-OMP [MeV)13dd/dfl (mb/sr)14w110 \E  10’o-OJET3Cq 181.3 MeVI  Schwoodt *t ol.—  9 * L. Roy • 9 * » 9f* Choumaoux0 10 20 30 CO 50 60 70Fig. 13a: Density dependent versus density independent.Fig. 13b Choice of densitiesFla. 14: Density dependent versus independent.[TTTTTTPOLARIZATIONF i g .  1516Fig. 17: Prediction of the energy dependence between 150 and 400 MeV.C/o/tfiz 'im'D/'sr;0 (mbarn/sr J18Fia. 21F i g .  2019F i g .(da/dn)/{da/dQ)R(JTH V(R) I MeV ]20Fig. 23Rlfm]Fig. 24Fig. 25and alternatively the arithmetvio mearij21t (|r o-r! I;LDA) t ( | r o-r j fkp (r o)) + t ( | r o -r j fkp (rj)) (16)In practice these two representations are not distinguishable. Forthe computation we have used the program DWBA82 which is a modifiedversion of Raynal's most recently developed DWBA791 9 . This programcontains the same formalism as used in DWBA70 but is now equivalentin programming structure to ECIS. It facilitates computationincluding all the complications of exchange and density dependenceup to 1 GeV with sufficient numerical accuracy. There are nolimitations in the use of phenomenological or microscopic opticalpotentials or in the number of partial waves and multipoles. Therelevant tensor algebra remains unchanged and can be found in the 1 8literatureThe new aspect in these inelastic transition studies is a consistent use of microscopic distorted waves calculated with the same effective interaction as used for the transition operator.In Figs. 26 to 31 case studies are presented for the isoscalar and isovector non­normal parity transitions in2 012C . These two states are strongly excited by inelastic proton scattering and they are considered selective to various components of the effective interaction. Particular sensi­tivity is found in the tensor and spin orbit components. We have analyzed available data between 120 and 400 MeV, which comprises of differential cross sections, analyzing powers, polarization - analyzing power differences and spin flip probabilities. The structure information required for theseFig. 26da/dQ (mb/sr)22transitions are spectroscopic amplitudestogether with the shell model basiswhich is chosen to be a harmonic oscillator(the oscillator parameter was taken forall inelastic calculations as a=0.61 fm )which is known to reproduce best thetransition rates as yet available in astructure calculation and possiblyreproduces electron scattering formfactors. For the complete inelasticanalyses we used the spectroscopy of21Cohen and Kurath . In view of several existing experimental data for the J 71, T = 1 + f1 state and the failure of the Cohen-Kurath structure to reproduce this data, we should not expect perfect agreement for the inelastic proton scattering, particularly the higher Fig. 27 momentum part. The analyses can more orless only be understood to establish consistency between the microscopic approach to the optical model, use of the same t-matrix as transition operator and the application of the antisymmetrized DWBA model in the right energy _I—mrange. \JE c4. Focusing and Large Ang le (?,p) ^SeatteringTheoretical predictions for elastic scattering into a momentum transfer region which cannot be reached by scattering off a stationary nucleon test various aspects of the optical model potential. To mention a few, nuclear charge distributions areFig. 28-  " c i p . p 1) 15.11 M*V. J .T » 1*,1 _  M ICR O SC O P IC  j  J122 M«V200 MtVX 30 409w,(d«g)known from electron scattering k:0 < k < 600 MeV/c; proton scattering may easily reach momentum transfers of 1500 MeV/c; the local ^-independent OMP is an approximation; the inner region of the OMP is strongly affected by density dependent effects; limitation to the lowest order in the hole-line expansion is a truncation whose validity must be verified; spin orbit potentials determine differential cross sections as well as spin observables, they contain presently the sole explicit angular dependence.Fig. 29The differential cross sections show, for heavy nuclei in particular, a large angle enhancement as compared to the expected exponential fall off. Fig. 21 gives an impression of what is meant. For angles beyond 90° an unexpected behaviour of the polarization goes alongBernikFig. 310cm (deg)Fig. 30with the cross section enhancement.In Figs. 32-37 we show the theoretical polarization prediction for 135 and 200 MeV. At both energies is a smooth trend towards P = +1 observable, from forward angles P=0 it reaches saturation around 70°. For larger angles the diffraction pattern is again resumed and the average polari­zation tends towards zero or even negative values. The enhancement of the differential cross section and the outspoken polarization phenomena are related. We have investigatedPOLARIZATIONF i g , 32verification is highly desireable. understand the enhancement with a focusing effect of the optical potential. The polarization carries the signature of flux.To this point we remember that the imaginary part of the spin orbit potential induces a spin flip mechanism.this effect with phenomenological Woods-Saxon optical potentialsf with microscopic potentialswhich were generated with different nuclear ground state densities. There exists a smooth mass and energy dependence which favours heavy nuclei, 4°Ca is a lower limit, 200 MeV 208Pb is suited best.The explanation of this back- angle phenomenon is presently tentative and an experimental Theoretically it is possible toFig. 33Nucleons moving in the nuclear medium will therefore assume a polarization, P=+1 (or - 1 ),after they have been exposed to this potential long enough. The relative sign of the imaginary spin orbit potential determines the saturation with P = + 1 . Experi­mental data confirm this feature for angles < 60°.iW _f (r) • Jl;.tOl---------  -------- ------Fig. 3425Fig. 35 Fig. 36^  iWS0(lrlfiW„Mr)lf 0)^  - I W  t ( r ) U . I )J - / * 1 / 2  J ■ /  -1 /2D ISTAN CE  IN N U C LEA R  M ATTERFig. 37 Fig. 38Schematic representation of the effect of the imaginary spin orbit potential on the observable polarization (analyzing power).With this background we may now visualize different trajectories, Fig. 39, which contribute in various scattering directions. (1 ) is a small angle trajectory which touches only the peripheral region of the nucleus. Inter­ference effects determine the formost scattering angles.(2) The projectile penetrates into the medium and is strongly affected from the imaginary spin orbit absorption P -*■ +1 . (3) leadsto large momentum transfers and samples the innermost region of the nucleus. (4 ) is a projectile which is focused (orbits) from the real and imaginary potentials around the backside of the nucleus into the scattering region of (3). Trajectory (4) carries particles whose polarization is saturated with P = - 1 . Interference effects between (3) + (4) lead to the calculated interference pattern. Tosummarize this in brief: Large angle cross sections are enhanced due to a multiple scattering mechanism mediated by the optical model potential. The polarization carries a signature of the different fluxes contributing and may therefore be used to verify the outspoken ker behaviour. We are fully aware of the extrapolations which enter our calculations, and absolute magnitude predictions may be over/under estimated. Whatever experiment will tell to be the truth, large momentum transfer mechanism in elastic and inelastic scattering should be investigated with great vigour.2 6  N U C L E A R - S U R F A C EReferences1) W.G. Love in Proc. LAMPF Workshop an Nuclear Structure Studies with Intermediate Energy Probes, Los Alamos (1980);H.J. Weber, Fortschr. Physik 24 (1 976)12) R.M. De Vries and J.C. Peng, Phys. Rev. C 2 2 (1980)10553) J. Delorme, A. Figureau and N. Giraurd, Phys. Lett. 91B (1980)328; Phys. Lett. 89B (1 980)3274) C. Gaarde, Nucl. Phys. A 3 9 6 (1983)127c;Ch. Goodman, Nucl. Phys. A 3 7 4 (1982)241c5) S.J. Wallace, Advances in Nuclear Physics, Vol. 12, e d .J.W. Negele and E. Vogt6 ) A.K. Kerman, H. McManus and R.M. Thaler, Ann. Phys. (NY) 8 (1 959)5577) J.P. Jeukenne, A. Lejeune and Cl. Mahaux, Phys. Rev. C25(1976)83F.A. Brieva and J.R. Rook, Nucl. Phys. A291 (1 977) 21 9,317 Microscopic Optical Potentials, Hamburg (1 978), e d . H.V. von Geramb, Lecture Notes in Physics 8J3, Springer (1979)8 ) For a recent status report see: The Interaction Between Medium Energy Nucleons in Nuclei 1982, e d . H.O. Meyer, Vol. 97 AIP (1983) and contributions to this conference9) An exhaustive guide to the literature of this field containing all backreferences can be found in:Effective Interactions and Operators in Nuclei, Tucson Int. Conference - 1975, Lecture Notes in Physics 40, Springer (1975) Effective Interactions in Nuclear Models and Nuclear Forces.Suppl. Prog. Theor. Phys. 65 (1 979)S.J. Wallace, High Energy Proton Scattering, Adv. in Nuclear Physics 1_2 (1981) Plenum PressTelluride Conference on Spin Excitations in Nuclei (1982)Plenum PressCl. Mahaux, Workshop on the Interaction Between Medium Energy Nucleons in Nuclei - 1982 Indiana., e d . H.O. Meyer, 97 AIP Conf. Proc. (1983)International Conf. on Nucl. Structure 1982, Nucl. Phys. A396 (1 983 ) 9c .10) N„ Anantaraman, H. Toki and G.F. Bertsch, Nucl. Phys. A398(1983)2692711) J. Hufner and Cl. Mahaux, Ann. Phys. 73 (1 972)52512) M. Lacombe, B. Loiseau, J.M. Richard, R. Vinh Mau, J. Cote,P. Pires and R. de Tourreil, Phys. Rev. C21 (1 980) 86913) H.V. von Geramb and K. Nakano, Workshop on the Interaction Between Medium Energy NucZeons in NucZei — 1982 Indianas e d . H.O. Meyer, 91_ AIP Conf. Proc. (1 983)14) P.J. Siemens, Nucl. Phys. A 1 4 1 (1970)225 and see Cl. Mahaux, Ref. 915) W.G. Love and M. A . Franey, Phys. Rev. C24 (1 981 ) 1 07316) P. Schwandt, IUCF-Annual Report (1982),any reference to experimental data are taken from this source and IUCF-WORKSHOP (1982)17) A. Chaumeaux, V. Layly and R. Schaeffer, Ann. PhyS. (NY)11b (1978)247;L. Ray et a l ., Phys. Rev. C18 (1978) 1756L. Ray, W.R. Coker and G.W. Hoffmann, Phys. Rev. C18(1978)2641G. Igo et al., Phys. Lett. 81B (1979)151L. Zamick and G.K. Varma, Comm. Nucl. Part. Phys. 8(1979)135 L. Ray, Phys. Rev. C1_9 (1 97 9) 1 8 55 , C20 (1 979) 1 857G.W. Hoffmann et al., Phys. Rev. C 2 1 (1980)1488D .A . Hutcheon et a l ., Phys. Rev. Lett. 47(1981)31518) H.V. von Geramb and K.A. Amos, Nucl. Phys. A 1 6 3 (1971)337 R. Schaeffer, Thesis (1969)J. Raynal in Computing as a Language of Physics, IAEA - W i e n (1972)97219) J. Raynal, Saclay (1979); this version of DWBA is a new develop­ment which permits to use density dependent forces, less restrictions on a computation level and includes also other very useful options. The Hamburg—version is a modification of Raynal's routine and is internally addressed as DWBA8220) L. Rikus, K. Nakano and H.V. von Geramb, submitted to Nucl.Phys. (1 983)21) S. Cohen and D. Kurath, Nucl. Phys. 73(1965)129EFFECTIVE INTERACTIONS AND THE INTERPRETATION OF NUCLEON-NUCLEUS SCATTERINGW. G. LoveDepartment of Physics and Astronomy University of Georgia, Athens, GA 306021. INTRODUCTIONAn essential element for studying different modes of excitation of the nucleus is a knowledge of the coupling between the probing projectile and the target nucleus. In the case of electron scattering, this coupling is both weak and well understood so that it may be used reliably in a relatively straightforward way to study a variety of types of nuclear excitations.Because of its spin and isospin structure, nucleon scattering is potentially an even richer probe of nuclear structure. The reaction mechanism for nucleon-nucleus scattering is not, however, nearly as well understood as in the case of electron scattering and this clearly limits the quantitative reliability of nucleon-nucleus scattering for extracting dynamical nuclear structure information. One of the most significant uncertainties in the reaction mechanism for nucleon scattering is an incomplete knowledge of the underlying nucleon-nucleon coupling itself. In the absence of a complete and calculable theory of strong interactions (especially at small intemucleon separations), progress interpreting nucleon-nucleus scattering has been made largely by integrating a few theoretical constraints into an otherwise phenomenological approach for representing the coupling between the projec­tile and target nucleons. This situation together with the strong short- range repulsion in the bare nucleon-nucleon interaction and the inevitable truncation necessary in nuclear structure and nuclear reaction calculations has led naturally to the introduction of effective interactions in nuclear physics. The details of any effective interaction are dictated in principle by the context in which it is to be used. In the present context we are specifically interested in effective nucleon-nucleon (N-N) interactions which when used in a non-relativistic single-scattering distorted-wave approximation30provide sufficiently accurate descriptions of inelastic scattering and charge exchange reactions to permit a meaningful extraction of nuclear structure information. Even within this limited focus the term meaningful is rather subjective. It would be particularly appealing if the effective N-N inter­action should, in a folding-model context, also yield an optical potential for describing the distorted waves; in this work this constraint willfrequently be relaxed or untested.Another very desirable property of an effective interaction is that it be simple enough to permit systematic comparisons between calculated and measured observables and yet be flexible enough to reliably represent the variety of important characteristics of the N-N coupling which make it such a rich probe. Three recent and excellent overviews of searches for and developments of effective interactions of the above type have been given by Satchler^ and Mahaux.^ Somewhat more detailed derivations of effective interactions for nucleon scattering are described in Refs. 3-13.In section 2 some of the primary elements necessary for describing nucleon-nucleus scattering are discussed briefly. In section 3 several types of effective interactions are considered and some of their most important characteristics are described. In section 4 the effective interactions of section 3 are applied to the excitation of several natural and unnatural parity states. From these examples we can identify some of the major successes and failures of various effective interactions and these should indicate where further developments are most critical.2. SOME GENERAL CONSIDERATIONSThe calculation and interpretation of nucleon-nucleus scattering observables usually involves the construction of a nucleon-nucleus scattering amplitude (or T-matrix) denoted here byt fi = = ^ 1 *  r M '’ V ’M V  ™ *  s pv> (1)where k is the initial relative momentum, (IM) corresponds to the initialAtarget angular momentum and v is the spin projection of the incident nucleon of spin 8^ = h.Once this T-matrix has been calculated the nucleon-nucleus observables may be constructed. For example, the differential cross section is given by:31° k  < v i)1<2i+i> « V <f|i|i>|2 ■ j v .o^ . v  (2)V v' *and the analyzing power by:Ir(IFl V “ Tir>A (9)------------+ (3)Tr(T T )FI FIwhere n is a unit vector in the direction of k xk' and the trace is over theA Aspin projections of the target and projectile. This readily leads toa An (0) = (C+f + C+_) - (o_+ + a ) (4)which is the difference between cross sections obtained with a spin-up pro­jectile beam and a spin-down projectile beam. (Here, up is in the direction of n.) Other observables such as polarization, and polarization transfer may be obtained similarly.In general T in Eq. (1) is a many-body operator; in the single scatter­ing distorted-wave approximation Tpi takes the formT™  * <I'M ’* v ' |J i vipiIM’V > x<+>(iv V  <5>where the represent the effects of distortion before and after the in­elastic event mediated by and is the effective interaction between projectile and target nucleons described above. One of the major advantages of the single scattering approxmation is its transparency in that specific terms in may be identified with the population of nuclear states of particular symmetries. Eq. (5) is oversimplified in that no explicit allowance has been made for exchange effects. In actual calculations knock-on exchange effects are included by replacing V. by V?4"5 = V. [1-P. ] whereip xp ip ipP is the operator which exchanges nucleons i and p. It has been shown-*-P -j /\elsewhere ' that it is often adequate for E >75 MeV to regard V04"*1 as aP iplocal operator of the same form as and we assume that is the case here.It is convenient to identify the role of nuclear structure in the cal- DWculation of more explicitly. At this point we suppress spin and isospin indices for simplicity. From Eq. (5) it is seen that the quantity32AU (r ) = <I'M'| I V(r ) |IM> (6)P i=i lpcontains all the information about nuclear structure and the effective inter­action. This is called the transition potential; from Eq. (5) it is the potential or interaction seen by the inelastically scattered nucleon. This can be rewritten as'M’ljd? V(?p-?)j6(?-?i)|lM> - Jdr T(?p-t)pI ,I(?) (7)° F I < V  ' <ICwhere Pj-t-j- is the nuclear transition density defined byAp , (r) = <X,M I | I 6( r-r.)|IM> (8)i=lIn a single scattering approximation this transition density contains and displays all of the participating nuclear structure information. (This is not completely correct when, for example, the optical potentials which generate the distorted waves in Eq. (5) are calculated15  ^ using thenuclear ground state density.) Even when several inelastic channels are coupled the transition densities between each pair of states contain the essential nuclear structure input.PWIn the plane wave (PW) approximation T is just the Fourier transform of the transition potential evaluated at the asymptotic momentum transfer q = k -lc' giving the especially transparent form:A AT™(?) = V(q)bIf][(q), q = 2kAsin0/2 (9)where V and p denote Fourier transforms of V andp, 0 is the nucleon-nucleus scattering angle andA i** rp_,T(q) .= <I*M* | I e q ±|IM>. (10)1 1 i=lThe inclusion of distortion introduces a weighted distribution of momentum transfers at any asymptotic momentum transfer which may be described by„DWTFIdq,D(q';^A ,kA) T^(q') (11)33where the distortion function D is given formally byD<5 ’=SA-S;> ■ ^ 3  X<+ V A ,?) <12,and becomes 6(q —(k^—k^)) in the plane wave limit. Although quantitativelyunreliable, the plane wave results of Eqs. (9 and 10) serve as extremelyuseful guides for understanding the roles of the effective interaction andthe transition densities in more accurate distorted wave calculations.PWMore complete formulae for Tpj which include spin and isospin degrees of freedom are given in Ref. 16.3. TYPES OF EFFECTIVE INTERACTIONSRegardless of origin, method of derivation etc. effective N-N inter­actions for nucleon scattering are usually constructed to be of the following (or an equivalent) form:Vip ' V?p(r> + ^ ( r ) £ . S  + ^ p(r)S.p (13)withVJP " Vo(r) + Va<r> V ° p  + V5<r> V ^ p  + V V i - ?P (U)Vip = (vLS<r> + VxS(r)TV ^ p ) <15)Vip " (VT(r) + V^(r)t.-Tp) . (16)C, LS and T stand for central, spin-orbit and tensor respectively; p denotesthe projectile and i a target nucleon, r = r. the internucleon separation, •+_->- -> -^PS - s^Sp and Sip is the usual tensor operator. Apart from the relativelytrivial non-locality implied by the relative angular momentum operator (L) VinC LS T *is a local interaction. The various V , V , V , etc. are typically depen—12 13}dent on the incident projectile energy ’ and may also depend on the localdensity etc. Also, the interaction given by Eqs. (13-16) is most oftendesigned for use in an antisymmetrized formalism so that, for example, V inJEq. (1) represents the strength for transferring 1 unit of isospin and 0 units of spin in the direct amplitude. The knock-on exchange amplitudes associated34with V. introduce a well-known type of non-locality; when this non-locality IPis relatively unimportant, these exchange terms may be calculated ratherreliably in a short-range approximation,5>14|17,18) especia;Qy above -75 MeV.19)Although progress has been made calculating the bare N-N interaction in terms of single and multiple boson exchanges etc., the short-range behavior of the N-N interaction must still be obtained phenomenologically at present. Consequently, the effective interactions presently used are either calibrated directly in the nucleon-nucleus system or are derived largely from N-N scattering and bound-state data. The latter approach which attempts to unify nucleon-nucleus and N-N scattering will be emphasized here.3.1. Free N-N t-matrix interactions3 20 21)One of the oldest and simplest approaches ’ ’ to the problem offinding an effective N-N interaction for nucleon-nucleus scattering is the impulse approximation (IA). In the impulse approximation the effective inter­action between the incident nucleon and each of the target nucleons is taken to be the free N-N t-matrix. When the N-N data is sufficiently complete to pin down the most interesting properties of the N-N t-matrix, this approach is quite appealing, especially to those who are primarily interested in using nucleon scattering as a probe of nuclear structure. This method bypasses(in an approximate way) many of the technical difficulties associated with13)the strong short-range repulsion present in N—N potentials. Unfortunately,this method is not expected to be reliable at nucleon bombarding energies (E ) below ~100 MeV; a number of failures of the method have also been noted13,15  ^ above this energy. Despite their limited realm of quantitative validity, effective interactions based on the free N-N t-matrix continue to provide useful insights into trends which may be expected in nucleon-nucleus scattering and provide an appealing point of departure for improving theeffective interaction.The precise connection between N-N data (or scattering amplitudes) andan effective interaction (Vip) for nucleon-nucleus scattering is not unique.20 2 1 )In the simplest approach * Is taken to be:vip - <17)where t° Is the free N-N t-matrix12) evaluated at the Incident energy E and NN35asymptotic momentum transfer q = kA - ^  where kA (kA) is the incident (final) momentum in the nucleon-nucleus system. This asymptotic kinematic approxi­mation should be best for energies Ep £ 100 MeV where refractive effects (due to distortion) are less important. Here we consider an alternative scheme which, in principle, treats the finite-range of the effective inter­action more precisely. Each of these approaches is discussed in more detail in Refs. 3, 12, 20 and 21,The N-N scattering amplitude can be writtenM(E ,0) = A + Bo. a + C(o. +o ) + Eo. a + Fa.„a . (1 8 )cm* in pn xn pn iq pq iQ pQwhere A, B, C, E and F are functions of the N-N center-of-mass energy Ec , the scattering angle 0 and the two-body isospin; a. =o.• n etc. where n is a unit vector in the direction of kxk' and k(k') is the initial (final) momentum of either particle in the N-N c.m. system. The unit vectors £q, Q, n] form a right-handed coordinate system with q = tc - $ = tc + lc*.For the purpose of identifying the spin and spatial ranks of the N-N inter- is U!M = A'Pg + B ’PX + C(oin + 0pn) + E'S12(q) + F ' S ^ Q )  (19)where Fg(P^ ,) is the singlet (triplet) spin-projection operator andA' = A -(B + E + F), B' = A + -^ -+ ^-+ - F), E' = F T = (20)12)A practical form of t-matrix interaction (^p) obtained from the empirically determined amplitude M by assuming some local functional form for V^p and then adjusting its elements in momentum spaceo f 3tNN “ nM ~ Jd r e ”ipl" AipJ" * “ " E12)action, if useful to rewrite M as:parameters until its antisymmetrized N-N matrix net “)■ -)■ 2«-° - i k *r ,7 M t> i ik-r -4Tr(hc)h m  n  = jd r e v-i«I3L “ t,)e » H = — ir— —  (21)cmmatch those of the on-shell N-N t-matrix in each spin and isospin channel at the energies of interest. Guided by one-boson-exchange models and com­putational considerations, the radial parts of the central and spin-orbit 12)parts of V were taken to be a sum of Yukawa terms; the radial form of2 rthe tensor part was taken to be r times a sum of Yukawa terms. In V' theIPYukawa term of longest range was constrained to match the OPEP; the Yukawa36terms of shorter range were then adjusted to match t^. Because of thestatic ansatz for V. , the F* term in Eq. (19) is attributable exclusivelyipto the exchange terms which in this procedure must also be includedexplicitly in the nucleon-nucleus scattering calculations.Although the effective interaction derived in the above way has beenshown to be unreliable for certain quantitative considerations, it stillserves as a simple and useful qualitative or semiquantitative guide for whatto expect in nucleon-nucleus scattering. In particular, some of the mostimportant characteristics of the t-matrix effective interaction V±p may beillustrated by plotting the moduli of its anti-symmetrized momentum space12)matrix elements (t^) in the nucleon-nucleus system as a function ofmomentum transfer (q), projectile energy (Ep) and spin and isospin transfers(S and T). See Refs. 11, 12 and 16 for more detail.Figure 1 shows a plot for the central parts of the force at q = 0 for100<E (MeV)<800. The subscripts a and t refer to spin and isospin transfersof one unit. The most striking feature of these curves is the strongdominance of the scalar-isoscalar part of t^N at all energies consxdered.The very small (and poorly determined) tQ suggests that the central part ofthe force is ineffective for exciting isoscalar spin modes. In strikingcontrast, we see that for isovector excitations t ^  domxnates over t^ atsmall q in this energy regime. This is emphasized in Fxg. 1 where the ratio|t /t | is plotted versus Ep at q=0. It is now well establishedthat this S = 1 dominance of renders proton scattering an especiallysensitive probe of isovector spin modes at intermediate energies. Thisdominance, together with the fact that |t0T|<|tT| below about 60 MeV has beenespecially important for the identification and interpretation of Gamow-11,12,16,22)Teller (GT) resonances using the (p,n) reaction.Figure 2 illustrates the relative importance of the spin-orbit and tensor parts of the interaction as a function of bombarding energy at a momentum transfer of q = 1.5 fm"1. This value of q was chosen for illustra­tion since it represents a compromise of the peak positions of the spin-orbit and tensor terms which, from Ref. 12, peak roughly near 2.0 and 1.0 fra respectively. More importantly, these non-central terms tend to dominate in this region of q. Most apparent from Fig. 2 is the near negligible size of the isovector spin-orbit terra so that isovector spin modes at large q are37dominated by the tensor force at all energies. The smallness of t alsoLjTimplies a strong sensitivity of isovector S = 1 analyzing powers to opticalmodel parameters since there is typically little source of asymmetry in theinelastic reaction mechanism. Isoscalar S = 1 excitations are expected to beexcited competitively by the spin-orbit and tensor parts of t and this isborne out in detailed calculations.Figure 3 shows the S = 1 and S = 0 transfer parts of t at E = 140 MeVNN pas a function of momentum transfer q. As described in Ref. 12, tQ and t0T should be multiplied by ~2.0 in order to compare directly with t^ * and t^" for_Tnucleon-nucleus scattering. These latter quantities (t ) have already been normalized to represent the strength of the tensor force in nucleon-nucleus collisions as described in the appendix of Ref. 12. (The left hand sides of equations A5a, A5b and A5c of Ref. 12 should be t*^  , t ^  and t^a respectively.) For both isoscalar and isovector transitions, it is seen to be important to include the tensor force in calculations of nucleon-nucleus scattering for essentially all values of momentum transfer. A significant exception is seen to occur for the excitation of S = T = 1 modes for q<0.5 fnT1 and this is12 i6 22)especially important ’ ’ for interpreting GT excitations.3:2 Density independent G-matrix interactionsIn this low-energy regime the derivation of V^p for scattering processes2 5}has been strongly influenced by the work of Brown and others on the analogous problem for the interaction between two bound nucleons. The key ingredient in this approach is usually (but see Ref. 4) a phenomenological N-N potential which when used in Schrodinger's equation generates an acceptable description of N-N scattering data. A G-matrix is then defined byG* = (22)xtfhere V is the free N-N potential and <J»(^) is the uncorrelated (correlated) relative N-N wave function in a bound nucleus. Alternatively G satisfies^where the sum is over all unoccupied states (a and b), E is the energy of the two interacting nucleons and e is the single particle energy of state |a>.38Although a proper treatment of the boundary conditions for the scattering case in which one particle is in the continuum yields a complex G-matrix, it is usually assumed'*that the real part of V^ should be quite similar to the G-matrix for two bound nucleons provided the energy of the projectile is comparable to or smaller than the Fermi energy. With this assumption V. is then parameterized to represent some of the most important characteristics of the G-matrix.This procedure for obtaining may be summarized schematically byN-N data -*■ free V -* G-matrix -*■ V. (24)iPSince G defined by Eq. (22) is a very complicated operator, the actualdetermination of V. is often carried out in practice by assuming some local*IPform for V and then adjusting its parameters until some selected subset of i-Prelative oscillator or momentum space matrix elements of ate matched tothose of G. This procedure is described in some detail in Ref. 8 whereexplicit interaction strengths are given.25)Some time ago Scott and Moszkowski suggested a separation method forobtaining the even-state (central) part of V which circumvents the need forconstructing an explicit G—matrix via Eq. (23)• In this method the free N—Npotential is set to zero for internucleon separations smaller than a distanced defined such that the strong short-range repulsion is cancelled by a26)portion of the longer-range attraction. Following Kuo and Brown the second-order contribution of the tensor force to the triplet-even interaction was also included.. A simplified version of this interaction in singlet—even and triplet-even states is given byVSE = -83. g(r) MeV, V?E = -110. g(r) MeV (25)xp ipwithR -xg(r) = YCr/R^ - ^  Y(r/R2), Y(x) = \  = 1 fm, R2 = 0.4 fm. (26)This interaction has been used  ^ with reasonable success to describe the excitation of giant resonances in ^ Pb with 61 MeV protons; it must be39supplemented by the non-central (and Imaginary) parts of V when they contribute significantly.3.3 Density dependent G-matrix interactionsThe most sophisticated (and in principle the most reliable) effective interactions constructed to date are those derived from G-matrices based on realistic N-N potentials and calculated in the presence of nuclear matter where one of the two interacting nucleons has energy greater than the Fermi energy. These G-matrices are obtained by solving Eq. (23) (or its equiva­lent) at a number of different values of the nucleon density or Fermi momen- 3 2turn (p = 2kj,/3TT ) with E -* E+iq. The density dependence arises from the limit on the sum over unoccupied states and from the single particle energies2)Ea depend on the Fermi energy through the single particle potentialin which the nucleons move. The density dependence gets weaker with increasing bombarding energy since the fraction of intermediate states ex­cluded by the Pauli principle in Eq. (23) decreases and the kinetic energy dominates the single particle energies.As in the previous section, the calculated G-matrix is much too compli­cated for nucleon-nucleus calculations so that a local effective interaction (V ) is introduced which reproduces some of the most important matrix elements of G. What finally emerges from this procedure is an effectiveinteraction whiqh depends not only on r. but also on the local density atxpwhich the particles interact. This is called the local density approxi­mation  ^ (LDA). Distorted wave programs now exist which can treat density dependence.28}Figure 4 shows a comparison ' of effective interactions at 140 MeV derived from the free t—matrix of Ref. 12 and from density—dependent G— matrices  ^ based on the Paris'^ and Hamada-Johnston"^ (HJ) potentials. This figure suggests that density dependent effects should be quite strong over a large range of momentum transfers for S=0, T=0 excitations especially when the HJ based effective interaction is used. Even at low density there are large differences between the HJ effective interaction and the free t-matrix at this energy; it has not been determined to what extent this can be attri­buted to changes in N-N phase shifts etc. over the past twenty years.The two-body spin-orbit parts of the effective interaction are calculated to be considerably less density dependent.404. NUCLEON-NUCLEUS SCATTERING4.1. Elastic scattering in a folding modelIn the folding model, the optical potential is calculated in a single- scattering-approximation analogous to that for the transition potential (see Eq. 7):where p is the nuclear ground state density constructed to be consistent gswith elastic electron—nucleus scattering. This potential (with central and spin-orbit parts) is then used in a Schrodinger equation to generate the amplitude for elastic scattering and, in addition, distorted waves for reaction calculations. Most calculations to date have used either a zero- range pseudo—potential for the exchange terms or an approximation similar to that implied by Eq. (17). Where V has been obtained from an explicitly density-dependent G-matrix, the density in V(p;irp-r) has been evaluated at rp.Figure 5 (from Ref. 28) gives some indication of the present status of non-relativistic folded optical potentials for elastic scattering near 150 MeV. The proton density was obtained from electron scattering and = P^ was assumed. The free t-matrix (Ref. 12) calculation (IA) is in only qualitative agreement with the differential cross section; the calculated analyzing powers are in poor agreement with the data. The density—dependent G-matrix (Ref. 13) calculation based on the Paris potential (LDAP) is in better agreement with the analyzing power than is the IA calculation. The Hamada-Johnston G-matrix (Ref. 13) calculation is superior to the IA for analyzing power but inferior to the IA for the differential cross section especially for q > 2fm_1. The overprediction of the cross section can be at­tributed to the, large q. behavior of the HJ G—matrix as illustrated in Fig. 4. Kelly2 has noted that this behavior is due to the real central part of the HJ G-matrix.Figure 6 gives some indication of the status of the simple folding model for elastic scattering at somewhat higher energies. The t-matrix of Ref. 12O Q \was folded with the 5^Ni densities provided by L. Ray; no second-order corrections were included. The agreement between calculated and measured differential cross sections is semi-quantitative and of comparable quality(7‘)41at 333,500 and 800 MeV incident energies. Below -500 MeV medium corrections 29)have been shown to be important, especially for the elastic scattering spin observables A and Q. Relativistic formulations29,30  ^ via the Dirac equation have been shown to be important for a simultaneous description of a, A and Q.4.2. Natural Parity ExcitationsWith few exceptions (such as the isovector 2+ excitation in 12C at 16.1MeV) natural parity states (A ir = (-)J) of spin J in nuclei with ground statespins of zero are known to be excited by the central (S=0) and spin-orbitD"f*E(sn term) parts of V through the spin- and current-independent transition . 16) pdensity as given by Eq. (8). Even so, there are, in general, both protonand neutron densities. When possible, the proton transition density,together with the charge distribution of the proton itself,is'usually chosento describe either the corresponding inelastic electron scattering formfactor or the B(EJ) value. For N=Z nuclei the neutron transition density (p )■p nis then taken to be (-) times the proton transition density. For collectiveexcitations in heavier nuclei one often assumes p = (N/Z)p or searches on e„.n p nTo make the above connections it' is convenient to rewrite the transitiondensities in Eqs. (8 and 10) in terms of reduced matrix elements. Using themultipole expansion of SCr-r^) we soon find:Pl»I^> = -r 1 I <IJMp=M,-M|l’M ’> Y*(r) p (r) (27)/2I’+1 J JM JwhereS(r-r )Pj(r) = <I*| II  (r )||I> (28)i ris the radial transition density and the reduced matrix elements are in the convention of Ref. 31. We define the analogous "radial" part of Pjtj^q) in Eq. (10) asf °° 2pj(q) = Jo r dr jj(qr) pj(r) ' (29)42In terms of these quantities the square of the longitudinal form factor for inelastic electron scattering is given by (pjp is the proton part of Pj):|F (q)|2 „ P^J ae1__!—  . (30)I V q;‘ (21+1)Similarly,B ( E J ; M ' )  _ L & j  lJ +2pj , p ( r ) l  Lim |X2J±11U.P („ ) I2 ( 3i )—  J -  (2I+1) ^21+1) q-K) I qJ PJ,PW IIn a fully microscopic shell model treatment Pj(r) is given byp ,(r) = — I  R. (r)R (r) < j 2 ! lYjl I j <I' I lAt i <32>’J i/2J+l 12 2 1 2 1where R. is the full radial part of the single particle wave function andA^ " creates a particle hole (j^) pair coupled to angular momentum J.For very collective states where the use of a fully microscopic tran-32)sition density is impractical, the deformed density model is often used in which the radial part of the transition density p± (i = p or n) is given byp = 5_ = ground state density (33)and 6 is obtained from the B(EJ) value or from electron scattering.P4.2.1. Primarily isoscalar, S=0 excitationsFor (S=0) natural parity transitions Fig. 3 suggests that near 140 MeVthe small (large) momentum transfer part of the differential cross sectionshould be dominated by the central (spin-orbit) part of the interaction.From Fig. 4 medium corrections tend to enhance the central contribution some-C LSwhat at large q. This change in the relative importance of V vs V ^as a function of q is illustrated by considering the inelastic excitation of a sequence of natural parity levels in 208Pb with spins ranging from J=2 toj=12 at E =135 MeV. Figure 7 shows the proton point transition densities ofP . 34)Eq. (10) inferred from inelastic electron scattering. Assuming Pn=Pp wesee that this sequence of transitions (J=0 to J=10) should be sensitive to43IH*E -ithe momentum components of V. between q=0 and q=2.4fm . From Figs. 3 and4 we see that the central part of t^q) has a sharp minimum near q - 2fm justwhere t ^  is reaching its full strength. This sharp minimum in t arisesoprimarily from a sign change in Imt0* This anticipated transition fromcentral to spin-orbit dominated cross sections is borne out by theoreticalcalculations and experimental data for these transitions which are comparedin Fig. 7; the signature of this transition is the change in shape fromweakly oscillatory to bell-shaped angular distributions near J=8.Another striking manifestation of the zero in Imt is illustrated by28 °the excitation of the 5 , T=0 state in Si at E =134 MeV. Figure 8 shows^24)DWIA calculations compared with experimental data for the observables a,A and aA. The N-N spin orbit contribution to the differential cross section is seen to dominate beyond o ~30° which for this nucleus and projectile energy, corresponds to q - 1.4fm \  Even more striking is the sign change in A and oA near 45° (q - 2fm ) which may be traced directly to the signchange in Imt . To understand this, recall that in the PWIA A(q) is given, 12) by2 T l s .c LS ClEr ci  ~ ci ^A(q) - / ---- !— §■* (34)|tC | +  Jt1-3 !LSwhere t is the real part of the spin-orbit component of the N-N t-matrix. LS LS LS Cetc. Since tR >>tI > the tR t^. term tends to dominate A(q) and the signchange in tj. results in a sign change in A(q). This is emphasized by thec cdashed curve in Fig. 8 for A obtained by replacing the true t^ by a t^ whichgives a good fit to the differential cross section but does not have a zerolike that of the actual t-matrix. It should be noted that even after thetransition density is normalized to (e,e') data the DWIA calculations arestill too large by a factor of -1.5 when the t-matrix of Ref. 11 is used35)as is the case here. Olmer has shown that the t-matrix interaction re­quires essentially the same renormalization for 80<E (MeV)<180 as does theP 13)Hamburg (Paris potential based) and HJ G-matrix interactions. This is notLStoo surprising in view of the fact that the density dependence of t is rela­tively weak and the cross sections for this transition are dominated by it.35)The Hamburg G-matrix does, however, track the shape of the cross section better than the t-matrix does in the above energy range. Below -100 MeV none44of the above interactions yields satisfactory analyzing powers. Franey andco-workers3^  have shown using the t-matrix interaction of Ref. 12 that DWIAcross sections using RPA wave functions which describe the longitudinal(e,e') form factor for this transition, require renormalization factors whichrange smoothly from -0.55 at 135 MeV to -0.9 at 800 MeV.Some of the same aspects of natural parity excitations are illustrated+ 12in Fig. 9 for the excitation of the 2 , T=0 state in C at 4.44 MeV using200 MeV polarized protons.3^  The transition density was constructed fromthe 1-p shell wave functions3^  of Cohen and Kurath (CKWF) renormalized soas to agree with the longitudinal (e,e*) form factor out to q = 2.5 - 3.0 fm .36)A standard Woods-Saxon shaped optical potential was used in the calcu­lations shown; the use of a double Woods—Saxon shaped optical potential reduced36  ^ the forward peak only slightly. Using the 20Q MeV Hamburg G-matrix also reduced the forward angle cross section only slightly. Theanalyzing powers calculated with the t-matrix interaction are in qualitativecagreement with the data out to -40°; the pivotal role of t^. for analyzingpowers is again illustrated in Fig. 9 where its omission completely destroysany agreement with the data. However, the omission of tj significantlyimproves the agreement between the calculated and observed cross sections.What this means is not presently clear. The DWIA calculated cross section0£\for this same transition is larger than the data by a similar factor near120 MeV. When the distorted waves generated by a phenomenological opticalpotential are replaced by those generated by a folded G—matrix opticalpotential as in Eq. (71) the magnitudes of the calculated and experimentalcross sections agree better.It is instructive to consider the excitation of the 2+ state at 4.44 12MeV in C at a significantly higher proton energy where medium effects are38) 39)expected to be much smaller. Both cross section and analyzing powerdata are available for this transition at Ep = 800 MeV and are compared with DWIA calculations in Fig. 10. Without any renormalization the DWIA cross section is seen to be in quite reasonable agreement with the data out to q ~2fm_1 when the CKWF transition density is adjusted to reproduce the lon­gitudinal form factor from (e,e') scattering. Although a slightly smaller value of the oscillator length parameter would improve the agreement for (p,pf) such an alteration would be inconsistent with the (e,ef) data and is45therefore unjustified. Near 400 MeV the required renormalization of the calculated cross section (0.8) lies between those at 200 and 800 MeV (-0.6 and 1.0 respectively) suggesting that significant medium corrections may be required up to at least 400 MeV. A comparison of Figs. 9 and 10 illustrates the relatively greater importance of the N-N spin-orbit interaction at 200i f *  T Qversus 800 MeV. This reflects the increase in the ratio of |to/to | suggestedby Figs. 1 and 2 where t*1® is seen to be roughly constant as a function of E C ° Pwhereas t increases dramatically in going from 200 to 800 MeV. Although Ct in Fig. 1 is for q=0, the same conclusion holds as may be seen in Fig. 1 of Ref. 12. The calculated analyzing power is seen to be in reasonable agreement with the data only for q £ lfm Since the transition density used is known from (e,e') data to be reliable for q<3.0fm_1, the present results suggest a significant deficiency in the t-matrix for large momentum transfers. A likely candidate is the isoscalar N-N spin-orbit interaction whose phase disagrees with those of phenomenological optical potentials at this energy.— 208The situation for the excitation of the low-lying 3 state in Pb at122.61 MeV is qualitatively similar to that for C in that the cross sectionnear the main peak is overpredicted at E = 200 MeV^1  ^ using either the t- orPG-matrix interactions. Curiously, when the distorted waves generated by thephenomenological optical potential at 200 MeV are replaced by those obtainedfrom a folded G-matrix optical potential as in Eq. (7'), the magnitudes ofthe calculated and experimental cross sections agree much better. At 800 MeV12)the DWIA gives a very reasonable description ' of both the shape and magni­tude of the differential cross section for q < 2fm 1. The RPA transition densities used for this transition were provided by J. Speth^^ and yield a2 3 oo\B(E3t) value of 0.62 e b in good agreement with quoted values.4.2.2. Neutron transition densitiesOne of the objectives of proton inelastic scattering is that of extract­ing neutron transition densities. In the present context this is done by incorporating the information on the charge density obtained from (e,e') measurements. The charge distribution of the proton is first unfolded from the charge transition density to fix the point proton transition density; the unknown neutron transition density is then adjusted until the calculated (p»p') cross section agrees with the (p,p') data.40)46The technique is illustrated by the excitation of the low-lying natural208 3 2) A3)parity states in Pb by 800 MeV protons. Recent (e,ef) experimentshave provided transition charge densities for a number of these levels. At this proton energy medium modifications to the effective interaction are known to be relatively small, reducing considerably the uncertainty in this procedure present at lower energies. In the present application the point neutron transition density has been assumed proportional to that for the protons according to:p (r) = a y  p (r). (35)J y TTt Z J jPThe constant of proportionality a is then adjusted until the (p,p’) data isreasonably well described. In a more sophisticated treatment p^ . ^ would beadjusted independently of pT . For present illustrative purposes Eq. (35)J ,pwill be used. Figure 11 shows the results including the adjusted values of32)a obtained by the University of Minnesota group for the low-lying positive208 . parity states of spins 2 through 8 in Pb. With the exception of the 8^state a very good description of the cross section data is obtained out to q ~ 2fm 3 - 18° using the simple scaling procedure together with the t-matrix interaction of Ref. 12. Apart from the phenomenological optical model para­meters determined by the elastic scattering, a is the only adjustable para­meter in the calculations. For the well known collective 3 state at 2.61 MeV a is found32  ^ to be 1.09 so that the positive parity states (1.15<a<l.38) appear to be less "collective" in the hydrodynamical sense. For a pure massvibration p = ^  p . For the first two 5~ excitations32  ^ a = 1.40 and n Z p xa2 = 1.17 indicating the greater participation of neutrons in the 5]Lexcitation. ^The same general type of analysis has been carried out for the exci—90tation of low-lying positive parity states in Zr by 160 MeV protons. Although the uncertainties in the effective interaction and overall reaction mechanism are larger at this lower energy, some curious results are emerging.43)Using recent charge transition densities of Heisenberg together with Eq.(35) three types of distorted wave calculations were made for the excitation13)of the 2^ state using the Hamburg G-matrix interaction and these are com­pared with the experimental data41) in Fig. 12. The dashed curve corresponds to using the density—dependent Hamburg interaction for the inelastic47transition potential with distorted waves generated by a phenomenlogical Woods-44)Saxon potential which provides an excellent fit to the elastic scattering cross section and analyzing power. The shapes of the calculated inelastic cross section and analyzing power (not shown) are in only fair agreement with the data; the extracted value of a = 0.44 would imply that this transition is strongly dominated by the protons. The solid curve corresponds to using the density-dependent Hamburg interaction for calculating both the transition potential (Eq. (7)) and the optical potential (Eq. (71)). Although the fit to the elastic data is clearly inferior to that using the phenomenological potential it is reasonable. The shape of the calculated angular distribution for the 2j| state is in much better agreement with the data with a = 0.85 which is much more consistent with a collective excitation. The third type of cal-:, culation (shown as the dash-dot curve in Fig. 12) used the zero-density Ham­burg interaction for calculating both the optical potential and the transition potential. The results for the cross section with a = 0.85 are very similar to those using the full density-dependent Hamburg interaction. Although the corresponding analyzing powers are not well reproduced by any of the above calculations (not shown) the self-consistent density-dependent calculation does best. Similar self-consistent density-dependent calculations of thecross section for the excitation of the 2* state at 120 MeV are also in very41)good agreement with the data with a = 0.85.32)The Minnesota group has published a somewhat similar analysis of therelative sizes of the neutron and proton densities for transitions to several90 +of the low-lying states in Zr excited by 800 MeV protons. For the 2 state+which we consider here, they find a(2^) = 0.90 which is in much better agree­ment with the results at 160 MeV using either the density-dependent or density-independent folded optical potentials than with the results using a phenomenological optical potential which gives a better description of elas­tic scattering. Consideration of the inelastic analyzing power data then favors the self-consistent density-dependent model.Similar results for the 2^ are less definitive in that the shape of the cross section at 160 MeV is not well reproduced using either folding model or phenomenological distorted waves together with the full Hamburg G-matrix for the inelastic transition density. This may reflect the greater sensitivity to the shape of the neutron transition density at this energy compared to 800MeV. Using a = 1.54 as is obtained at 800 MeV yields a cross section which is clearly too large at 160 MeV when phenomenological distorted waves are used. The overall magnitude of the cross section calculated self-consis- tently with the Hamburg G-matrix and with a = 1.54 is in reasonable agreement with the data. These results suggest the need for a more careful consider­ation of both the effective interaction and the nature of the distorting potential, especially at the lower intermediate energies.4.2.3. Status of effective interactions for natural parity excitationsThe isoscalar central part of the effective interaction (see Fig. 1) dominates this class of excitation (with S=0) at small q; at larger q the spin-orbit part of the effective interaction participates significantly, especially for q > lfm“1 and E < 400 MeV. At 800 MeV the t-matrix inter­action provides a reasonable description of the differential cross sections where good wave functions (transition densities) are available; however, only the qualitative features of analyzing powers are reproduced. As the bombard­ing energy decreases, the need for medium corrections (or something similar) becomes essential for calculating the correct magnitude of differential cross sections. This becomes especially true below -200 MeV where peak cross sections calculated with a t-matrix interaction (and phenomenological dis­torted waves) are typically -50% larger than the data. Moreover, below 200 MeV the shapes of calculated cross sections usually prefer a G-matrix inter­action with its relatively larger high q components (see Fig. 6). A growing number of analyses tentatively appear to favor the use of a folded model optical potential generated by the effective interaction. When analyzing power data are considered such analyses also favor a density—dependent effective interaction such as that provided by the Hamburg G-matrix. The HJ based G-matrix appears somewhat pathological for q > 2fm . Work clearly needs to be done to obtain a simultaneous description of elastic andinelastic scattering.The prospects for obtaining neutron transition densities for this classof transitions is quite appealing. Presently this is done most reliably at 800 MeV where the DWIA works reasonably well. More information on the reaction mechanism and/or the interior shape of the neutron transition density might be obtained at lower energies where the nucleus is more trans­parent. Analyses at lower energies (E^ < 200 MeV) should, when possible,4832)49incorporate the information obtained at higher energies to help avoid spurious results.4.3. Nucleon charge exchange reactionsAlthough measurements of (p,n) cross sections are usually more difficult than (p,p') measurements, the (p,n) reaction is much more selective in that only isovector excitations are allowed and data may be taken as far forward as 0^^ =0°. Since most of the (p,n) data^ ~*^  at intermediate energies(E > 100 MeV) have been taken at forward angles where the non-central partsD4-E 9of 11 = v,-„ are relatively unimportant, the ratio of It /t | shown in Fie. 1x p  1 O  T  T  1 °should, apart from nuclear matrix elements, be a reasonable measure of therelative cross sections for S=1 and S=0 excitations. Parity and angular momentum considerations further restrict the excitations observed in the (p,n) reaction near 0° primarily to Gamow-Teller (GT) and Fermi (F) transitions whose nuclear matrix elements at small q are given by^~^<GT> = ( 2 1 + 1 ) <r||£ t (k)o(k) | |l> (36)kand<F> = (21+1) * <I'||T_||l>, T = I t_(k) (37)krespectively where t_ is the isospin lowering operator in the convention Tz = (N-Z)/2. For Ep > 100 MeV the (p,n) differential cross sections for Fermi and GT type transitions near 0° can to a good approximation be expressed*^ asd^ (0°) = (T 2 )2 IT £NT |tT<F>|2 + N |t <GT>|2] (38)7rn Awhere N and N are calculable distortion factors (N = oDW/aPW) and t andL U Tare evaluated at q=0 as in Fig. 1. Eq. (38) or one of its variantsprovides a practical method for extracting Fermi and GT strengths frommeasurements of forward angle (p,n) cross sections. By comparing (p,n) datafor transitions having known (from 8-decay) Fermi and GT matrix elementswith Eq. (38), empirical values of |t | and |t | have been deduced^*^ near12}E ~ 120 MeV which agree with those derived from the free t-matrix to50within -10%. Roughly this same level of quantitative agreement between empirical (nucleon-nucleus) and t—matrix based values of appearsto the presence of the one pion exchange mechanism operative in b^. For t^ the situation is less clear. The value of t from Ref. 12 is significantly/ r \too large^^ near 200 MeV; however, more recent N-N amplitudes indicate that the t-matrix value for t is in much better agreement with experiment near 200 MeV.7 47)The dominance of b^ _^  over t^ illustrated in Fig. 1 appears to hold down to E - 50-60 MeV where a transition to a less pronounced dominance ofp 11)t takes place. This results in an energy regime (E $ 60 MeV) where the T P(p,n) reaction probes primarily S=0 strength and a regime (E^ > 100 MeV)where it probes primarily S=1 strength.It is convenient to express Fermi and GT strengths for specific tran­sitions in terms of sum rules^^ for the full Fermi and GT strengths. These sum rules may be derived by considering the target ground state expectationi “Vvalue of the commutator [A ,A] with A^ , = £ t_(k) and A ^  = £ t_(k)o(k), the respective operators for Fermi and GT transitions. If the total GT strengths (S) for the (p,n) and (n,p) reactions are denoted byThe factor of 3 in the GT sum rule arises from the intrinsic size of o(o*o = 3). For both Fermi and GT transitions in nuclei with an appreciable neutron excess, S should be small since neither 1 nor o is typicallyable to connect occupied proton states with unoccupied neutron states leaving $^(1) ~ N-Z, ^^(o) - 3(N-Z).valid'1'2,^  between -100 and 800 MeV. This stability is believed to be due2i-*-f(39)then the GT sum rule is(40)The corresponding sum rule for Fermi transitions is(41)np514.3.1 Transitions to isobaric analogue statesThe simplest charge exchange reaction, particularly in even—A nuclei,is the excitation of the isobaric analogue state (IAS) of the ground stateof the target. For reasons discussed above the IAS transitions typicallydominate small angle (p,n) spectra in N>Z nuclei for E S 50 MeV. The IASPtransitions are assumed to exhaust essentially all of the Fermi strength from the target ground state.An example of the excitation of an IAS at relatively low energy is illustrated in Fig. 13 which shows a comparison of calculated11 and experimental50  ^ cross sections for the Sn(p,n) reaction at 22.8 MeV using the M3Y interaction (dashed curve) of Refs. 8 and 11 supplemented by an imaginary coupling obtained from the optical potential of Becchetti and Greenlees.51  ^The non-central (real) and imaginary couplings have a relatively small effect on the differential cross sections; the imaginary coupling increases the cross section by -2.5%. Using simple shell model wave functions for the neutron excess the M3Y density-independent G-matrix interaction is seen to provide a reasonable description of the differential cross section without any adjustment. The isotopic shape changes in the cross sections are not well reproduced at large scattering angles; this may require a more careful treat­ment of the neutron excess.Since the t part of the effective interaction at this energy is expected to be density dependent, calculations were also made using an effec­tive interaction based on the real density-dependent G-matrix of Dav52  ^ fnnnY 116The results for Sn are shown in Fig. 13 (solid curve) which indicate that the density-dependence of this interaction is too strong and this is not understood.Above 100 MeV differential cross sections for IAS transitions in manyeven-even nuclei are difficult to measure because of the dominance of S=1charge exchange excitations suggested by Fig. 1. A four point angular dis-90tribution for the IAS transition in the Zr(p,n) reaction at 120 MeV has 53)been published and is considered here. This type of transition samples primarily the t part of the effective interaction, especially at forward angles. Figure 13 shows a comparison of calculated cross sections with ex­perimental data for this transition. The calculations were made using a phenomenological optical potential and the neutron excess was described by52the (go/0) ^  configuration with an oscillator length of 2.12 fm. The DWIA 9/2calculations using the 140 MeV t-matrix interaction of Ref. 12 are seen to be in excellent agreement with the available data (q < 0.15 fm ) without any adjustment. Calculations using the HJ G-matrix interaction not only under­estimate the cross section by a factor of 4 but also give the wrong shape.13)Calculations using one of the early Hamburg interactions based on the Paris potential yield cross sections too small by a factor of *-0.7 with a shape xn only rough agreement with the data. It should be noted that essentially all G-matrix calculations predict a strong density dependence for the t T part of the effective interaction which in any case is small as a result of delicate cancellations amongst its single-even, triplet-even etc. parts. In addition, this monopole type of transition is extremely sensitive to density depen­dence5^  etc. The situation is not unlike that near 25 MeV for the DDD interaction. Unless the distorted waves are being treated incorrectly (see sec. 4.2.3.) or two-step processes like (p,d;d,n) are important, the present results suggest that the calculated density dependence of the various G- matrix interactions is incorrect in the t channel.4.3.2. Gamow-Teller transitionsOne of the most exciting and significant developments in nuclear physics during the last decade has been the identification and interpretation of large concentrations of GT strength in nuclei throughout the periodic table by using the (p,n) charge exchange reaction. Although GT resonances have been observed earlier55) below Ep = 50 MeV, only recently has it been feasible to make systematic studies of GT strength distributions in a variety of nuclei. This favorable situation has arisen due to the development of atr/-\sophisticated neutron detection system at IUCF where incident proton energies are such that the spin—independent part (^^) the effective inter­action (see Fig. 1) is strongly suppressed. The distribution of GT excita-/ n\tion strength places important constraints on the isovector component of the spin—dependent part of the residual N—N force in nuclei, especially ii.ssmall momentum components.Although the GT strength of a given 1 excitation can be extracted via Eq. (38) from measurements of 0°(p,n) cross sections, measurements of (p,n) cross sections beyond 0° are necessary to establish the associated L=0 nature of the angular distribution. Measurements of differential cross53sections at a number of angles have also permitted^’^ ^  the identification of isovector spin-flip modes of higher multipolarity. These points are illus­trated in Fig. 14 where the calculated (DWIA) and experimental differentialcross sections'*^ are compared for the (p,n) reaction on ^2C near E = 120PMeV. For N=Z nuclei the (p,n) cross section to the analogue of a state in58)the target nucleus should, under the assumption of good isospin, be twicethat of the corresponding (p,p') reaction in the target so that the (p,p*)33)data are also shown. There is excellent agreement between the (p,n) and(p>P*) data as well as between the calculations and the experimental data.23 59)The CKWF wave functions are known ’ ' to provide a good description of thesmall q(q < 1 fra 1) properties of the 1+ excitation; the renormalization■f 12)factor associated with the 2 excitation, which proceeds primarily by the, isovector part of the tensor force, is known from inelastic electron scatter­ing60  ^ to be due largely to deficiencies in the CKWF.12  ^ These and similar results for the 1 transition at other proton energies support the assumption that a single-scattering description of GT excitations is basically correct.Figure 15 from Ref. 61 illustrates just how striking 0° spectra are in revealing concentrations of GT strength above 100 MeV; at 200 MeV the IAS is just barely visible. Figure 16 shows the GT strengths61  ^ as a function of N-Zfor a number of heavy nuclei (where S ~0) obtained by a comparison ofnp g-, \measured 0°(p,n) cross sections with a version of Eq. (38). Excitation energies below ~30 MeV in the residual nucleus were considered. As illus­trated in Fig. 16 only about 50% of the 3(N-Z) strength expected from Eq.(40) is identified in these nuclei. Since the only assumption behind the GT sum rule is that the nucleons t^ithin the nucleus are elementary constituents, the missing strength phenomenon has been interpreted as evidence for A par- ticle-nucleon hole states. Although this interpretation is not universally accepted, the missing strength has helped spark enthusiasm for learning more about the role of the nucleon's structure and mesons in nuclear physics.4.3.3. Isovector monopole resonancesThe existence of an isovector monopole resonance (IVMR) has been pre-63) >dieted for some time and its anticipated properties have been studied ex­tensively. Apart from its intrinsic interest, the strength and location of this "state" could play a crucial role in understanding Coulomb mixing effects in heavy nuclei.^>63,64)54The IVMR (J11 = 0+ , AT = 1) may be defined63,63  ^ in terms of the operatorTz, y = 0^ ( Tx ± i T )  y - f l(42)and t  , x  and x  are the Pauli operators for isospin. A state tha£ exhausts x  y  za significant portion of the strength of this operator is said to be a giant IVMR. Because of the isovector nature of Q^, there are three components of this excitation corresponding to y = 0(p,p'), y = l(n,p) and y = -l(p,n). Using pions of kinetic energy 164 MeV the y = 1 component of the IVMR has recently been reported66  ^ in the ( it  , tt° )  reaction on Sn and Zr. The chances of seeing the y = 0 component of this excitation with nucleons appear small due to the overwhelming isoscalar part of the nuclear effective inter­action (see Fig. 1) in addition to the Coulomb interaction. Nucleon charge exchange reactions (y = ±1) appear to be more promising probes for observing the IVMR and therefore for corroborating its recent discovery using the (tt ,7r°) reaction.iRecently, microscopic transition densities have been calculated in the HF-RPA approximation for the charge exchange components of isovector S=0 resonances. The transition density for going to a state [n> is defined bypn (r) = /4tT <n| I 6(r-r.)x (i) 10>. y . y(43)The IVM strength exhausted by this state is then given by:i|Qy!0>!2 = |4Tr|°°rAdrp” (r) I2Sn = I<nI (44)Transition densities p^r) and P_1(r) which contain all of the IVM strengthfrom the ground state of 9°Zr are shown in Fig. 17. If we define(45)and neglect the small isovector spin-orbit part of the effective interaction, the differential cross section in the plane wave approximation is given by55i - ' f c - V i r l s w f l K w l 2 < « >irn A nwhere q is the asymptotic momentum transfer. For small q this becomeswhich apart frrom a distortion factor is the IVMR counterpart of Eq. (38) for Fermi and GT transitions. Eq. (47) would imply that the differential cross section should behave like q at small scattering angles* (We are using the fact that t^(q) varies relatively slowly over the small range of qinterest.) Using the transition density p in Fig. 17 a DWIA calculation has67) 90 *been made for the Zr(p,n) reaction to this "state" (Q-value = -42 MeV)using 800 MeV protons to estimate the feasibility of detecting the IVMR inthis reaction and this is shown in Fig.18; E = 800 MeV was selected to 12 Penhance tT relative to t^. Most notable is the variation of the differen­tial cross section with increasing q (or 0) which is opposite that predicted by the simple PWIA formula, Eq. (47). Moreover, calculations for other nuclei show that da/dfi does not scale as S^. This qualitative departure of the DWIA calculation from the PWIA results (Eq. (47)) is in sharp contrast to the situation for the excitation of Fermi and GT modes where renormalized PWIA calculations permit a reasonably reliable extraction^"^ of Fermi and GT strengths. This difference arises from the amplified sensitivity of the small—angle cross section for the IVMR to Q—value and distortion effects (see Eq. 11). Note that for the IVMR dcr/dQ-K) as q + 0  in the PWIA. In con­trast, the 0° PWIA cross sections for Fermi and GT transitions are typically at their maxima. These considerations emphasize that if the giant IVMR is observable in the nucleon charge-exchange reaction, care will be necessary to extract a precise measure of its strength.Because of its smaller Q-value the (n,p) reaction could also be appro­priate for identifying the IVMR at relatively low energies (E £ 60 MeV) where/* n\ n(n,p) measurements have already been reported and the ratio It ft 1 = 1 0t o r 1is relatively favorable. Using the real effective interaction given in Eqs.(25 and 26) distorted wave calculations with phenomenlogical optical poten-90tials were made for the Zr(n,p) reaction (Q = -22.9 MeV) at E = 6 0  MeV.56The calculated cross section for the IVMR (solid curve) is shown in Fig. 19; although reasonably large it is relatively flat compared with that predicted at 800 MeV for both the (p,n) and (n,p) reactions. Since a significant frac­tion of the expected isovector quadrupole strength in the corresponding90 / 69)excitation region of Zr has been reported from an (e,e ) measurement,the cross section for exciting the IVQR in the (n,p) reaction has been calcu­lated at E = 6 0  MeV using a HF-RPA density, by assuming the entire isovector nquadrupole strength is concentrated in a single state near Q ~ -20 MeV. The relatively small calculated cross section for the IVQR is shown in Fig. 19 as the dashed line. This result suggests that the IVMR should dominate at for­ward angles at this energy. The 16° (n,p) spectrum for this target shown in Ref. 68 suggests a significant cross section in this excitation region; it would be interesting to have an angular distribution. In summary, despite the absence of a striking signature of the IVMR in the form of a strongly forward peaked cross section at this energy, the (n,p) reaction near 60 MeV should be considered seriously as a method for searching for isovector mono­pole strength.4.3.4. Status of effective interactions for charge exchange reactionsThe types of transitions considered in section 4.3 are sensitive primarily to the small momentum components of the effective interaction and therefore primarily to t and t^, its isovector central parts.For S=0 transitions only data for IAS transitions have been considered.At low energies the M3Y interaction appears to work well11  ^ when supplemented by *?hat is thought to be a reasonable imaginary part. The simple HJ based interaction of Eqs. (25 and 26) also is similar to purely phenomenological interactions7  ^ in this S=0, T=1 transfer channel below -50 MeV. The only density-dependent interaction (DDD) considered at low energies is that of Day;52) unless the supplementary imaginary part has been greatly under­estimated this Reid-based G-matrix interaction appears much too weak in this channel at low energies. Near 120 MeV the t-matrix interaction of Ref. 12 appears to work well; it has not, however, been thoroughly tested. Near 120MeV both the HJ and Paris based complex G-matrix interactions appear to be too13)weak. It would be desirable to extend the new Hamburg interaction down tothe E =25 MeV regime to see how it works there. Above -140 MeV the t part Pof the t-matrix interaction of Ref. 12 appears to be too strong. A similar57interaction^^ based on newer N-N amplitudesappears to resolve most ofthis discrepancy. Above -200 MeV t has not been tested directly but (p,n)T 71)data at 800 MeV should be available soon. A knowledge of t is clearly critical for making reliable estimates of cross sections for S=0 isovector modes.For S=1 transitions the t-matrix interaction of Ref. 12 appears to pro­vide a good description of t for q * 1 fm 1 from 100 to 800 MeV. This part of the interaction is largely real and is driven by the OPEP. At Ep = 200 MeV it has been verified (not discussed here) that the density-dependent13)Hamburg interaction provides an equally good or better description of the + . 121 , T=1 excitation in C. The density dependence of t is predicted to be° T 12)weak as is suggested by the success of the t-matrix interaction. At lower energies (E^ s 60 MeV) the M3Y interaction has been shown’*‘‘*','*'^,~ ^  to be too large by a factor of ~1.4; this difficulty can be largely rectified empiri­cally by omitting the odd-state parts of the central interaction but there seems little other underlying justification for doing so and this remains apuzzle. Moreover, the long range part of the singlet-odd part of the M3Y73)interaction appears critical for describing heavy ion potentials within a folding model.4.4. Spin excitations4.4.1. Forms of spin couplingsIn order to integrate information from electron and pion inelastic scat­tering into analyses of inelastic proton scattering it is convenient to write couplings of the different probes to spin modes in a common forra.^*^^ The focus here will be primarily on those parts of the couplings relevant for the excitation of unnatural parity states (Air = (-)^+^) where J denotes the total angular momentum transferred to the nucleus. In the case of nucleon-nucleus scattering one complication is the necessity of including the exchange termsassociated with V. of Eq. (13). Above E = 100 MeV there already existlp 3 4  12P14)reliable short-range approximations * * * for the central and spin-orbit3)parts of V^p- The short-range factorization approximation for the tensor part of the force is somewhat less reliable but will suffice for present purposes. The DWIA calculations done here do not use the short-range approximation for the tensor force even where it is used for the central and58spin-orbit forces; this approximation can, however, be conceptually very3 12)helpful. The result of the approximation * mentioned above is, to lowestorder, a local energy dependent N-N interaction for which only direct typematrix elements are to be calculated. We denote this approximate effectiveinteraction by t. where IPV ^ E * t. = tC(r) + tE(r)o.-a + tLS(r)L*S + tT(r)S +  XTS(r) (48)ip xp o l i p  xp•J’where r = r. and X denotes exchange terms arising from the tensor force.xp 6 T TIsospin indices have been suppressed for brevity. If t is taken to be V.11 12) 1Pfrom Eq. (13) then *XT = -Vg(Q)Sip(Q), Q = ( ^  + PA)/2 (49)Twhere V is the Fourier transform of the tensor force of Eq. (13) except thatT 6)the signs of the odd-state parts of V^p have been changed. With theseapproximations the coupling terms for the various probes can be put in a common form by introducing the spin and current tensors defined by:MLSJ(qr,Og) 5 jL (qr)(iLYL W ® O s)J , spin (S = 0 , 1 )  (50a)and•P (qr,L) = — (iJ"1Y T_1(r)®L)J , current (50b)j j J-where 0^ = 1, 0^ = a and i is the orbital angular momentum operator. The longitudinal and transverse combinations of are also useful forunnatural parity excitations and are given by:Longitudinal: M* = / ^  Mj_n j  “ Mj+llj> (51a)Transverse: M* HJ+11J . (51b)59In terms of the above tensors t may be written:£ 2 * 2 1 =  ‘i'p ' f/o ->2“q ^ < - > J W i S W H . gJ<l)-l^(p> (52a)Spin-Orbit: LSi p ^  * I  q2dq^ £LS(ci^ (“)Jv/l § ^  BPJC±>MjCp)-HlJCi)-PjCp)'] (52b)tip Tensor:tTiPV f j T  ’2<J‘>ET(1) J , JiL+L,+2< L ' \ ' S J (i)-MLSJ(!’)> S'l (32<=>where the Fourier transforms (t) of the spatial forms of t. are defined inip jEq. (15) of Ref. 12, the geometrical recoupling coefficients Z , are givenL Lin Ref. 74, and q is to be identified as the momentum transfer in the plane-wave B o m  approximation. Only the unnatural parity part of t. is given for LS ipI- •Apart from kinematic factors'^ arising from the pion-nucleus mass dif­ference, the coupling of pions to spin excitations of unnatural parity isLSgiven in lowest order by the second term in t^. Excluding coupling to the nuclear currents the spin-orbit part of the N-N coupling is (like (it,it’)) only sensitive to the transverse part of the spin-density. This is also true for the magnetic multipole operator for the excitation of unnatural parity states by inelastic electron scattering which is given by^"2^Electromagnetic: Tj38(q,i) = i2 Jgq£y-M*j(i) + 2g^ / (53a)where 3 is the nuclear magneton and g (g ) is the spin (orbital) g-factor.S  XFor natural parity excitations the spin dependent electric multipole_ 75) .operator isA. 2Electromagnetic: T ^ q . i )  = i~JS q-y-M ^(i) . (53b)elThe more complicated convective part of T is not considered here. For completeness, the operator for allowed B-decay in the nucleon space is3-decay: M =   [gv + gAo(i)3 (54)/4tt60where gy(gA) is the vector (axial-vector) coupling constant for Fermi (GT) transitions corresponding to S=0 and S=1 modes respectively, and t_ is the isospin lowering operator. The reduced nuclear matrix element of each of the above tensors defines a corresponding transition density'*'^ in momentum trans­fer space. For example,PL S J ^  <T I ^  I lI>* (55)Aside from differences in isospin selectivity, one of the most notable dynamical differences between electromagnetic, pionic and nucleonic couplings is that the (tt,7r*) and the (e,e') reactions are only sensitive to the trans­verse part of the nuclear spin density for unnatural parity transitions while the (p,p*) reaction is sensitive to both longitudinal and transverse parts. The first point follows from Eq. (52b) and Eq. (53a); the second point will be demonstrated in some detail below. Much has been made of this in thesearch for precursors to pion condensation.To show how the central and tensor components of the N-N interaction couple to both longitudinal and transverse spin densities for unnatural parity transitions, it is convenient to introduce the longitudinal and trans­verse components of the central plus tensor parts of the interaction. ThisC T T ->is done by equating the sum of the Fourier transforms of t S. and X 6 (r)18)in the N-N system tou(56)where18)(57a)(57b)(57c)61The longitudinal, transverse and "exchange transverse"V^(q) = t^(q) - 2t'r(q), longitudinalt ~C -TV (q) = t^(q) + t (q), transverseu 3~TV (Q) = 2"V£(Q)» exchange transversewheretj(q) - v|j<q> + Vg(Q), iT(q) . vj(q) - fv*(Q) <58d)and is from Eq. (13) and is from Eq. (13) but with the signs of6)the odd-state parts of reversed; Q is given in Eq. (49). The staticS=1 central plus tensor parts of t^ may now be written asnatural parity:‘ l V ^ p  + tT s ip  = 7  l0q2dq^ (~yJ+ lv t(q )M J U ( i ) *MJ U (p ) (59a)unnatural parity:t?0 -o + t TS. = —  ( q^dqj(-) J+’L[Vt(q)M^(i) *M^(p) (59b)l i p  i p i r j o j J J+ V*(q)M*(i) Ha (p)]. (59b)The VU term usually contributes to both natural and unnatural parity transitions(and is included in Figures 2 and 3). In the factorization approximation77)without distortion Moss has shown that this term enters the differential cross section multiplied by the square of the transverse nuclear matrix element of Eq. (51b). Since the isovector part of VU is weak (see Fig. 20) and it is without a precise counterpart in the pionic and electromagnetic couplings it will not be discussed further; it is of course included implicitly in the DWIA calculations.Equation (59a) suggests that the N-N transverse coupling can best be studied empirically by examining S=1 modes of natural parity; this is especially true when the spin density is available from measurements of the transverse electric^®) form factor. In practice this is most useful for T=1terms are found to be: (58a) (58b) (58c)62excitations because of the usual dominance (see Fig. 1) of the S=0 terms for T=G excitations. In many ways the longitudinal coupling is even more diffi­cult to isolate since from Eq. (59b) it appears with VC(q). A striking exception is the excitation of 0“ states where M^ =0 and only longitudinal excitation is possible. Unfortunately there is only sparse data * for such excitations.The practical limitation on the extraction of longitudinal transitiondensities, search for precritical phenomena, etc., is determined by theactual size of V4(q) relative to Vfc(q) and VU. In Fig. 20 we illustrate thislimitation for S = 1 transitions in this representation by showing the moduli12\of v£, Vfc and VU (the coefficient of 0 ) for the free t-matrix interactionu tat 140 and 425 MeV. Surprisingly, the N-N isovector transverse coupling V(believed to be dominated by p-exchange) is significantly larger than thelongitudinal coupling (dominated by tt—exchange) for most momentum transfersq<2fm- 1  at each of these energies. This suggests that the really distinctiveinformation obtainable from (p,p*) may be masked by the large transversecoupling. Figure 20 suggests that for isoscalar S = 1 transitions whereV*’>Vt the situation may be quite different. However, the isoscaler terms aremuch more uncertain. In addition, the non-static and less familiar VU term(arising in the present model entirely from the tensor excahnge terms) is0comparable to or larger than V for most of the relevant momentum transfers. For isovector transitions VU is quite small.4.4.2. Longitudinal spin modes: ^^(p.p1)As noted earlier 0+ -*■ 0~ excitations are especially interesting sincethey are only sensitive to V^, the longitudinal part of the N—N coupling.Consequently these transitions are forbidden in (Ti-jit’) and are first-orderforbidden in (e,e’) reactions; isovector 0+ -> 0 transitions are seen in g-decay.79  ^ Similarily, this type of excitation is insensitive to the N-N spin-15)orbit coupling (see Eq. (52b)). Recently data have been obtained for the 0“ T=0, excitation at 10.95 MeV in 160 using 135 MeV protons. Data for the higher lying T=1 state could not be resolved from the background. Figure 21 shows a comparison between the calculated (T=0 and T=l) and experimental (T=0) differential cross sections. Each transition was assumed to be described by a lp, 2s1 configuration. The T=0 calculated cross section is dominated by the exchange amplitudes arising from the tensor force and is63larger than the data by a factor of 1.7. The calculated and observed shapesare in quite reasonable agreement. The relatively structureless differentialcross section for this transition can be understood in terms of the relatively £flat V (q) for T=0 excitations.Data for the 0(p,n) cross section for the 0~, T=1 state should behelpful for studying the more structured isovector part of the longitudinal70)force. Such data have very recently been reported at 35 MeV. Assumingthe same simple configuration as for the T=0 excitation, calculations^8 11}using the M3Y interaction ’ ' are compared with the data in Fig. 21. Whenreduced by a factor of two the calculated cross section is in reasonable agreement with the main peak; the second large angle peak (q ~ 2 fm-1) is in complete disagreement with the calculation. Until more reliable wave func­tions are available, little definitive information can be obtained about the longitudinal part of the effective interaction.124.4.3. Transverse spin modes:____ C(p,pf)As indicated in sec. 4.4.1., the N-N transverse coupling can best bestudied by considering natural parity modes having S=l. The isovector 2+excitation in ^2C at 16.11 MeV is known from electron scattering^^ to be sucha transition. In particular, both longitudinal (S=0) and transverse electricform factors have been m e a s u r e d . A f t e r  scaling the Cohen-Kurath S=0 andS=1 transition densities to agree with the (e,ef) measurements, the S=1transition density dominates. In addition, |t |> |t | at intermediate energiesCFT Tand at larger q t should dominate over t . Figure 22 shows a comparison^ 12) 23 80)between the calculated and measured * differential cross sections at120 and 800 MeV using Cohen-Kurath transition densities scaled to (e,e') measurements. The N-N spin-orbit contribution is negligible, but as seen from Fig. 22 the tensor force is extremely important at each of these energies and is apparently given correctly in the impulse approximation. More specifi­cally, the transverse coupling predicted by the free N-N t-matrix12  ^ appearsadequate at these two energies. There does appear (not shown) to be some 23 AO )difficulty ’ with this transition near 200 and 400 MeV which is not presently understood.The sensitivity of the (p,p') reaction to the S=1 transition density (largely because of the strong isovector tensor force) is in striking con­trast to the (ir,tt') reaction near the (3,3) resonance which has been shown^"^64to go almost entirely by S=0. Consequently, to the proton this excitation is predominantly a spin mode; to the pion it is not.+ 124.4.4. 1 Excitations: C(p,p')Although 1+ excitations are in some ways less selective than the transi­tions described above, the isovector ones can be correlated with (p,n) and g-decay measurements of GT strength and have been generally helpful in estab­lishing the DWIA as a quantitative procedure for extracting GT and HI strengths. (See sect. 4.3.2.). The isoscalar 1+ excitations are most reliably compared with Crr.-ir') scattering16  ^where the isoscalar coupling is relatively strong. + 12Data for the excitation of the isoscalar 1 state in C by protons areavailable23’^ 0,8°^  for several proton bombarding energies below 800 MeV.Both (it ,tt*)81 *82  ^ and (e,e')6^  data are also available, with the (e,e')results being especially sensitive60  ^ to T=1 impurities. Since (p,p'> is much23)less sensitive to this admixture, the (e,e*) data are less helpful in pin­ning down the nuclear structure information sampled in the (p,p?) reaction. Results from (ir,r')' studies81  ^ suggest that the CKWF for this transition are adequate for q s 2fm_1. Figure 23 shows a comparison between measured andcalculated (p,p') cross sections for this transition at 120 and 402 MeV. Aton')E = 120 MeV :the agreement is poor. At 402 and 800 MeV, (not shown) the Pagreement between theory and experiment is much improved though still some­what inferior to that found for the 15.1 MeV T=1 transition. The over-12)prediction of the forward angle cross section at 120 MeV can be traced to the large tensor exchange amplitudes. This overprediction at small q is con­sistent with the results for the 0 -> 0~ transition in 0 where the forwardcross section (dominated by the isoscalar tensor force) is overpredicted by a+factor of -1.7. The calculated cross section for this 1 transition at18 83)E = 120 MeV is quite sensitive to current©spin terms * (LSJ=111) whichpare not tested by the (e,e') data. At higher energies where the agreement is much better* the calculated cross sections are much less sensitive to the current(x)spin terms.284.4.5. High spin states: Si(p,p')The study16,24,35,84  ^ of stretched excitations (those having j = fc + h,i = 5. + J* and J = j + j,) in nuclei with different probes has provenh h p h65especially helpful in understanding the high-momentum components of the spin dependent part of both the residual particle-hole interaction and the coupling of the target nucleons to the projectile. As can be seen from Eqs. (50-53), neither the current nor the terms contribute to this type 'ofunnatural parity excitation. Only the single nuclear transition densityp j _ n j ( q )  =  < £ I I X M j _ 1 1 J ( i > t ) x ( 1 > l l i > ;  < ° 0  =  1 »  ° i =  C 6 0 >is sampled in the (e,e'), (tt,tt*) and (p,p') reactions yielding a simple con­nection between the three reactions.28 —In Si the stretched states have Jv=6 and arise primarily from the-1 24 84)lfy^2 “ ^ 5 / 2 Particle-h°le excitation. * For the 6 , T=1 excitationdata is available for all three reactions; for T=0 only (ir,7r?) and (p,p') data24,35,84-86) .. _ . ,are available. Figure 24 shows a comparison between observed(p,p') differential cross sections at E =134 , 333 and 500 MeV, the (e,e')form factor and the corresponding calculated quantities. The T = 1 oscil-Or\lator parameter (b=1.71 fm) was determined by fitting the (e,e') form2factor without recoil corrections. The quantity S is the factor by which thepure particle-hole calculated cross section is multiplied in order for thecalculated and observed cross sections to agree. For the (p,p') reaction the 2 2average S is = 0.27 which is -15% smaller than that for (e,e') wheresi ~ 0.31. The (tt.tt') reaction1^’ gives S2 = 0.31. As has been shown* , 16,24,35) . . ^elsewhere, the (p,p ) cross section is strongly dominated by thetensor force. Therefore, the present results suggest that the isovector partof the tensor force may be -5-10% too large for 1.5 S q(fm_1) 5 2.0.Results for the T=0, 6 excitation are less satisfactory. Particular2problems are the energy dependent values of S extracted and the differencepin shapes of the calculated and observed cross sections forward of q~ 1 . 5  fm~^. 16 86) 2At = 162 MeV * = 0.12 which is in reasonable agreement with theaverage of . Because of the relatively x^ eak electromagnetic coupling toisoscalar modes, there is no (e,e') data for this transition. For thisexcitation the (p,p?) transition is meditated by nearly equal contribu- 12,16,24) c LS , T totlons from z and t at 134 MeV; at 333 and 500 MeV t dominatesC(see Fig. 2). The t contribution is small at all energies considered.TRecall that t arises primarily from exchange terms.6635) —C. Olmer has recently studied these same 6 transitions at = 80,100, 134 and 180 MeV proton energies using several effective interactions.The analysis using the t-matrix interactions of Ref. 12 are shown in Fig. 25 for both T=0 and T=1 states. The results for the 6~ , T=1 state are'in good agreement with those at higher energies in that the renormalization required at each energy is 0.30. There is, however, some deterioration in the cal­culated shape of the cross section and especially the analyzing powers below 100 MeV. Although a common renormalization factor is also obtained for the T=0 state, the deterioration in the shape of the calculated cross section with decreasing energy is even more acute. Figure 25 suggests this is not the fault of a specific component of the force but of the overall reaction mechanism.4.4.6. Status of effective interactions for spin excitationsBased on the use of a few selected transition densities calibrated fromelectron scattering, the isovector component of the spin-dependent part ofthe effective interaction appears to be given reasonably well by the freet—matrix interaction of Ref. 12 between 100 and 800 MeV. The low spinexcitations at small q and the high spin states at larger q test primarilythe central and tensor parts of the interaction respectively. Cross sectionsat intermediate values of q are sensitive to the central-tensor interferenceand this also appears reasonable. The weak isovector spin-orbit interactionpredicted by the free t-matrix appears consistent with cross section data;however, calculations of analyzing powers are more sensitive to this component23)and they are often in only modest agreement (or disagreement) with the data. The transverse isovector coupling also appears correctly given by the t—matrix interactions at 120 and 800 MeV; difficulties near 200 and 400 MeV have, however, been reported. Very little information is directly available on the longitudinal N-N coupling at any energy. Below -100 MeV the t-raatrix approach appears to need some modification for S=T=1 excitations. Recall that below -60 MeV the odd-state part of the M3Y G-matrix interaction is suspect.For S=1 isoscalar excitations the situation is less clear, in part due to an absence of (e,e*) data with which to compare. A few systematic features do emerge, however. Based largely on the 1"*", T=0 excitation at 12.7 MeV in 12C at a number of energies, it appears that the isoscalar tensor force given67by the free t-matrix may be too large near 140 MeV by as much as 40% atsmall q but is roughly correct for = 400 and 800 MeV. Based largely oncomparisons with the excitation of high spin states with pions, the isoscalartensor force appears correct near E = 135 MeV. At lower and higher energies 3 5) _ P Tcthe situation is worse. The isoscalar spin-orbit interaction (t ) appearsto be too strong at 333 and 500 MeV. Definitive tests of t^ ** are difficultcbelow 200 MeV where medium effects on the central part (t ) of the interactiontend to be large and uncertain at large q (for natural parity transitions)LSwhere t is most easily studied. At present there is little definitive information on the spin-dependent part of the isoscalar central interaction; it is masked by the tensor exchange terms at small q and by the tensor and spin-orbit forces at higher q.5. SUMMARYThe motivation for and derivation of effective interactions for calcula­tions of nucleon-nucleus scattering have been described briefly. Particular emphasis has been placed on nucleon-nucleus scattering above E - 100 MeV where complex effective interactions based on the free N-N interaction appears to be reasonable, when a qualitative description is required. A number of different types of excitations have been considered which illustrate some of the current deficiencies in various effective interactions as well as some of of the nuclear structure information (such as neutron transition densities,GT strengths, etc.) which might be extracted from (p,p*), (p,n) and (n,p) studies at different projectile energies. Significant advances in our understanding of medium corrections to free t-matrix interactions appear to have been made through the introduction of effective interactions based on density-dependent nuclear matter G-matrices. 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Love and L. J. Parish, Nucl. Phys. A157, 625 (1970).75. T. deForest, Jr. and J. D. Walecka, Adv. Phys. 15, 1 (1966).76. W. Weise, Comments on Nucl. and Part. Phys. _10, 109 (1981) and references therein.77. J. Moss, in ref. 62.78. H. Orihara e_t jal. , Phys. Rev. Lett. 49, 1318 (1982).79. G. T. Garvey, in ref. 62.7280. M. Haji-Saeid et al., Phys. Rev. C25, 3035 (1982).81. T.S.H. Lee and D. Kurath, Phys. Rev. C21, 293 (1980).82. C. L. Morris, in ref. 62.83. T. Carey et al., Phys. Rev. Lett. 49., 266 (1982).84. G. S. Adams et al., Phys. Rev. Lett. 24, 1387 (1977); S. Krewald andJ. Speth, Phys. Rev. Lett. 4_5, 417 (1980).85. M. Gazzaly, M. A. Franey and N. Hintz, private communication.86. C. Olmer et al., Phys. Rev. Lett. 43, 6l2 (1979).73FIGURE CAPTIONSFig. 1. Energy dependence of the magnitudes of the central (direct +exchange) parts of the N—N t—matrix. On the right is shown the energy de­pendence of the ratio [t^/t^l at zero momentum transfer.EAg» 2. Energy dependence of the spin-orbit and tensor parts of the t—matrixinteraction (t) at q = 1.5 fm-1.Fig. 3. Moduli of S=1 and S=0 parts of t as a function of q at E = 140 MeV.Pi c cFig. 4. Comparison of |to(q) = t^Cq) | at 140 MeV for the t-matrix inter­actions from Ref. 12 (solid curve on both sides) with the effective inter­actions from Ref. 13 based upon the Paris and HJ potentials. Long (short) dashed curves show low (high) density limits.Fig. 5. Elastic scattering of 135 MeV protons by 160.Fig. 6. Elastic scattering of 333, 500 and 800 MeV protons by 58Ni.■Fig. 7. Proton transition densities and (p,p') cross sections for natural 208parity states in Pb. The central (dashed curve) and central plus spin- orbit (solid curve) contributions are shown separately.Fig. 8. Differential cross sections, analyzing powers and their products for2 8 “*• .a ^the Si(p,p’) reaction at 134 MeV for excitation of the 5~, T=0 state at Ex - 9.7 MeV. The central (C), spin-orbit (LS) and tensor (T) contributions to the cross section are shown separately.Eig- 9. Differential cross sections and analyzing powers for the C(p,p')reaction at 200 MeV for excitation of 2+ , T=0 state at E =4.44 MeV.xFig. 10. Differential cross sections and analyzing powers for the ^C(iT,p')reaction at 800 MeV for excitation of 2+ , T=0 state at E =4.44 MeV.xFig. 11. Cross sections for the excitation of some low-lying natural parity 208states in Pb by 800 MeV protons. See the text for more detail.Fig. 12. Differential cross sections for the excitation of the 2* state in90 1Zr at 2.186 MeV by 159.5 MeV protons. The calculations were made with theHamburg-Paris G-matrix interaction from Ref. 13. See the text for moredetail.Fig. 13. Differential cross sections for transitions to the IAS in the 90Sn(p,n) and Zr(p,n) reactions at 22.8 and 120 MeV respectively. See the74Fig. 13. Differential cross sections for transitions to the IAS in theo nSn(p,n) and Zr(p,n) reactions at 22.8 and 120 MeV respectively. See the text for more detail.12 12 90Fig. 14. Cross sections for the C(p,p') and C(p,n) and Zr(p,n)reactions to the 15.1 MeV, l"*", T=1 state in C and its analogue in Nrespectively together with DWIA calculations using the CKWE... On the right+ 12are similar cross sections for the 2 , T=1 state in C at 16.1 MeV and its analogue in ^2N.90 90Fig. 15. Zero-degree Zr(p,n) Nb spectrum at Ep = 200 MeV.2Fig. 16. GT strengths (B(GT) = <GT> ) as a function of N-Z extracted from 0° (p,n) cross sections. 3(N-Z) is a lower bound to the GT sum-rule.Fig. 17. Radial transition densities for excitation of the isovector giantmonopole resonance via the (p,n) reaction (p^(r)) and the (n,p) reaction( M, xx 90 (p^r)) on Zr.Fig. 13. Calculated differential cross section for excitation of the isovec-90tor monopole resonance in the Zr (p,n) reaction at E — 800 MeV. The 90calculated Zr(n,p) cross section is very similar.Fig. 19. Calculated differential cross section for excitation of the isovec-90tor monopole and quadrupole resonances in the Zr(n,p) reaction at En = 60 MeV.Fig. 20. Moduli of V*, V*1 and VU at Ep = 140 and 425 MeV. See the text for details.pig. 21. DWIA calculated (T=0 and T=l) and measured (T=0) cross sections for excitation of 0 states in 0 at 10.95 MeV (T=0) and 12.9 MeV (T=l). On the right are calculated (M3Y interaction) and measured cross sections for the ■^0(p,n) 0+ 0" reaction at 35 MeV.12Fig. 22. Calculated (DWIA) and measured cross sections for the C(p,p')4-reaction at 120 and 800 MeV for excitation of the 2 , T=1 state at Ex = 16.1 MeV.Pig. 23. Measured and calculated (DWIA) cross sections for excitations of the 12.71 MeV state in 12C via the 12C(p,p’) reaction at Ep = 120 and 402 MeV.75Fig. 24. Calculated and observed cross sections (and form factor) for__ 28 excitation of the 6 , T=1 and T=0 states in Si. The plotted T=1 proton(electron) data are too small (large) by the factor 0.9223; the values of S2have been corrected for these renormalizations.Fig. 25. Momentum transfer and energy dependence of the cross sections for the inelastic excitation of the 6~, T=1 state at 14.35 MeV and the 6~, T=0 state at 11.58 MeV. The DWIA calculations used the interaction from Ref. 12; the calculated T=1 (T=0) cross sections have been multiplied by 0.30 (0.15) at each incident energy.11 (q = 0) | MeV-fm76Fig. 1|t(q=1.5fm~1)| MeV-fm77Fig. 278COM•H.u y-A9|A| |(b)| |Fig. 480Fig. 581to_0I3*~oto' I DFig. 68210 Ll.LL III \ f.f- \ --— l0 t 2 3yqtfrrT1)Fig. 783aCMdcr/dXl (mb/sr)840c.m. M eg)2 3q (fm ')2 30 10 20 30ec.m. Meg)/A lo (mb/sr)8610'I O 'b~ o/**to208P b ( P,p')Ep rr 800 MeV» . * }X X X  E x p ----- PWIAJtiP : Ce,e‘)o ( = M S0^=138j----- j----- !----- L0 Z  4- 6 6 1 0  \ z  W© c m  6leo) Fig. ll16 19 10  ZZ 2487Fig. 1288CPcH  >Q)^  zdL o(SJrfi *'o  Q —or L Ui .L1-1-1—I 1 L li l I I(JS/CJUA) P O p ^ poCD(JS/qui) rop/^pFig. 1389(js/quj) (0)H3o8cm (deg)90Es ( M e V )Fig. 15Gamow -TellerCD>91Mio in(19) aFig. 1692Fig. 17q (f m1)0.25 0.5 1.0 1.5 2.0£Wdeg)Fig. 1894i-tn_ QJ3r obQ'CrnFig. 19wj-A9W|(b)A|95Fig. 2096X  oCD(JS/qULl) m p / J D pQcm Fi8- 21dtx/d^ (mb/sr)97q (frrf1)Fig. 22dcr/dfl (mb/sr)98Fig. 23C ( l \  12.71 MeV) : E p = 120 MeV C + L S + T10° k-    C + LS° c .m . (deg),0 10 20 30 401 ' I 1 I ' 1 '=l2C (1+, 12.71 MeV) =E p = 40 2  MeV I  C+LS+T C + LST ~ n  "jrrn rrn  i (in 111 i~ i— |m'n~rr- i |iu 11 m i ro 99oh-£CD~ ii x  LUICDCOCDCM^ ‘/ ^  o  o^  LO** II\ Ol* - t \LU=T M"QIIIOiiCMCD►M-'s/hm ro ro, roM M  11W  Q.LU•f* "N.CMCOOO ’iiCMCO/roTi»-X\w \IIa .LU\CMOiiCMCOCMEcr.1.1 i J m 1 1 1  i i a^ -Llli.u  i i i ^ l i m i  i i i 111M 1 1 io o  o(JS/quu) rop/x>pCM'o oT~1 I |l!i! ! I I I pTTl'T I I I [TTTTTTTii¥<3-M;iixLUH H XD P 'V+-\S‘isHOOmiiClLUJ *9-i >■\✓ S 'roro '  M"ro 1 roiia . ►*-i ,,LU \ ° -  MH LU1 \\CD Q  I ICO CD CMCDCMO'itCMCOinsi-CMoiiCMCO |L L . I  J l l l l.U  I I ^  [ill 11 I I IoroO'iiCMCO1 1 1 I'o o 'oEcr(js/quu) cop/jop |(b) XJ|Fig. 24<r tmb/sr) ... tmb/sr)100.4- .2 ■.1 -  .08 - .0 6 -.0 4 -,02u.01 -  .008 - .006 -.004 -.002-i 1 rEp*80"I 23! . " I 23 .* Si(p.p') St100-1— i--- r~6~, T=0 11.577 MeVt 1---1---r  r~OWIA; LOVE-FRANEY133 M«V 180 M.V(00 200 300 400 300 200 300 400 SCO 200 300 400 300 200 300 400 500 600 q(M*V/e> q (MeV/c) q (MeV/c) q(MsV/c)Fig. 25ELASTIC AND INELASTIC SCATTERING101Microscopic Description of Intermediate Energy Proton ScatteringL. RayDepartment of Physics The University of Texas at Austin Austin, Texas 78712AbstractRecent developments in the analysis of proton-nucleus elastic scattering are discussed. The relativistic impulse approximation prescription for the Dirac optical potential is presented and a number of applications to proton-nucleus elastic scattering data given. It is demonstrated that Dirac optical potentials generated by folding nucleon-nucleon invariant amplitudes with realistic, self consistent relativistic nuclear wave functions with no ad justable parameters, provide remarkably good descriptions of proton-nucleus elastic scattering data at and above 400 MeV. The success of the relativistic compared to traditional non-relativistic approaches is most dramatic with respect to predictions for spin observables . The impact which the relativistic calculations have on non-relativistic, multiple scattering models is discussed and practical reasons are offered for continued, although limited use and development of Schrbdinger equation based formalisms. Directions for future theoretical and experimental work are recommended.I. IntroductionSince the close of the IUCF-1982 Workshop last fall, dramatic developments have occurred in proton-nucleus (pA) scattering research which challenges the applicability of several time honored nuclear scattering models and which potentially may redirect the pursuits of experimentalists in the field. I am speaking, of course, of the startling success which the relativistic impulse approximation (RIA) (Refs. 1-5) together with the Dirac equation for proton scattering have demonstrated in the description ofIntermediate energy proton-nucleus elastic scattering observables, particularly those involving the spin of the projectile. The sizeable differences between the RIA and non-relativistic impulse approximation (NRIA) predictions, based on the Schrodinger equation , imply the extreme importance of virtual negative energy states6 which non-relativistic models (such as the Kerman, McManus and Thaler (KMT) multiple scattering formalism^) do not include. The applicability of KMT and other non-relativistic many-body theories to pA physics must be reevaluated and at best, only cautious use of these theories is any longer appropriate. Likewise the success which the RIA approach has with respect to spin observables and spin related phenomena must be viewed, for the time being, with some reservation until a firm theoretical foundation for these calculations has been established and a systematic investigation of corrections carried out. Even so, the success of the RIA will likely rejuvenate experimentalists, causing them to study with renewed vigor proton induced elastic scattering and reactions in energy domains where the spin-dependent parts of the nucleon-nucleon (NN) interaction are relatively strong, i.e. the 200 - 600 MeV region.8’9In the next section the RIA model is discussed and a compilation of the results obtained using accurate NN amplitudes and numerical folding techniques is presented. In section III the impact which the RIAcalculations presently appear to have on non-relativistic analyses isdiscussed. Several very practical advantages which KMT models continue to offer in light of the RIA success are also discussed. Anticipated theoretical developments and the implications for experimental work are discussed in section IV while some tentative conclusions are presented in section V.II. Relativistic Impulse Approximation and ResultsA detailed discussion of the RIA-Dirac equation model forproton-nucleus scattering has been presented in the previous talk by J. A.McNeil,^ so that herein, only a summary of the RIA model is presented.The connection between NN interaction models and pA relativistic optical potentials at low energies has been successfully provided by way of the relativistic Brueckner Hartree Fock theory.6 The significance of the102work under discussion here and in Refs. 2-5 is that for the first time a successful connection between NN and pA scattering observables has been accomplished in a completely covariant manner.The first step in the calculation is the generation of NN invariant amplitudes in the proton-nucleus center-of-momentum (c. m.) frame. The kinematics correspond to those of the Breit frame1 in order that the optical potential in factorized "tp" form best approximate the actual, fully folded optical potential.1 The NN scattering amplitudes in the NN c. m. system areOgiven byf ( q )  = A(q ) + B ( q ) a l n a 2n + C ( q ) ( a l n  + a ^ )  + DCq)^ l q ^ 2q + E ^ I k^ k * (1)where alx " a^x, n = (£*£')/|icx£'| , q = (£-£')/\t-t' | , k = (&+£')/|£+&' | , £(£') is the incident (final) NN c. m. momentum, q = Ic-fe', and (1) and (2) refer to the incident and target nucleons, respectively. Upon division by k the total amplitude f(q) is invariant11, however each of the five individual terms are not.Equation (1) as it stands does not have the correct Lorentz transformation properties to be useful in a covariant equation of motion. A suitable rearrangement of Eq. (1) can be found however such that each termin the new expression is Lorentz invariant. Such is achieved by requiring1   ^ /\US '(k,;) us • (~ k "> F &  u c-io1 2 1 s2= xs+, xs + , ( f / k )  xs X- ( 2)1 2 1 S2where ug(lt) are Dirac spinors12, yg represents two-component spinors, and F is given by1The {Fg, Fp> Fv , Fa , Ft) and {A,B,C,D,E} are related by1104f •>Af Fs 1B FPC B(l) FvD faESBjt T(4)Sg,twhere B(l) Is a 5x5 matrix given explicitly in Ref. 1, while (sB,t) denote the invariant total energy squared and invariant momentum transfer in the Breit frame.The Breit frame kinematic quantities for the pA elastic scattering case are given as follows. For a given proton-nucleus c. m. momentum, kQ, corresponding to an incident laboratory kinetic energy TL , and for a momentum transfer q, we have^SB = fEP + FSN^2 - Fa fl - l/K)2 ’ whereEp = /  k a 2 + q 2/ 4 + m2 , (5b)Esn = /  (ka/A)2 + q2/4 + m2 , (5c)k -  / k  2 - q 2/ 4 , (5d)d Uandt = -q2 . ^In Eq. (5) A represents the number of target nucleons and m is the nucleon mass. The NN laboratory energy corresponding to sB isTLAB,efftNN) = V 2m - 2m ' (6)A feature of the Breit frame kinematics is that sB and thereforeTt *„ **(NN) increase with q. For example, in 800 MeV proton scattering fromLAB,err208Pb over a momentum transfer range, 0 < q < 3 fm , one finds800 < TLAB eff(NN) * 977 MeV‘The local, proton-nucleus optical potential to be used in the DiracO _ Aequation is given in the relativistic impulse approximation by% < «  = ^ o l V ' O l v  . (7)where is the relativistic nuclear ground state wave function andi" ViT^(q) represents the NN invariant t-matrix for the i target nucleon. The0 /T^Cq) are given in the pA Breit frame according to,T.(q, . - k(q) . (8)■to ■» /The antisymmetrized, relativistic nuclear wave function is expanded as, ’V V "  = Deti jI1U{a}(?i ) (5)105where-io-r An£j(r)do)represents the 4-component Dirac single particle wave function for the {a} = ,j) orbital. The set of {ct} include all occupied single particleAsubshells. The spin-angle function /^Vfr) is given as usual by= I (£,y+ms,%,-ms |jy) Yq+ms(r) x ^ _ m • (11)ms sInserting Eqs. (3), (8) and (9) into (7) yields for spin saturatednuclei,^U o p t ( r )  =  -  2 l TV ' - -  \ [  U s ( r )  +  Y l °  U v ( r )  -  2 1 ^ - r  U T ( r )  ]  ,  ( 1 2 a )whereUg(r) = (2tt)'3 I /d3q e~iq’r Fs(l)(q) Ps(l)(q) , (12b)i=p,nUy (r) = (2tt) 3 I fd3q e_iq‘r (q) pv (l) (q) ,i=p,nand(12c)106UT(r) = (2tt) 3 I r /d3q e'iq*rF ^  (q) p (q) . (i2d)i=p,nIn Eq. (12a) the three terras on the right hand side correspond to scalar,vector, and tensor terras while and p ^ ^  represent the scalar,1 A1vector and tensor density form factors, respectively. These are given hy? tiJ(q) = /d>rei?'? ps(i)(r) , (13a)pv (1) tq) - !i3r eiq'r Pv(i)(r) , 03b)and^ ( q )  = /d’r ei?-? i p T fi)(r) . (13c)The superscript (i) denotes target protons or neutrons. In terras of the upper and lower components of the nuclear wave functions these densities are given b y ^ ’^ 4• tl4a) pvCi)W  = j .  T F -  C|W 2+ |Xnl j l 2) • (14b)andPT (l)(r) = 2 K l j K l j  > (14C)where the sums include occupied proton or neutron orbitals. The aboveoptical potential is inserted in the Dirac equation(a^p + B J m  + Uopt(r) + Y1°UCoul (r) ]) <f>(r) = E 4>(r) (15)where tTc0ul^r  ^ represents the spin independent pA Coulomb interaction, 4>(r) is the 4—component pA wave function, and E is the total relativistic energy. The Coulomb interaction also contributes to the tensor term in Eq. (15) (Ref. 15). This arises from the proton anomalous magnetic moment but asyet has not been included in Dirac equation calculations. The correspondingeffect in the KMT approach is discussed in section III where it is seen to be important for several cases.1^,17In all the calculations presented here the SP82 phase shift solutionOof Arndt provides the NN amplitudes needed in Eqs. (1) and (4). The Breit frame invariant NN amplitudes have been computed at each laboratory energyusing Eqs. (4) and (5). The variation in NN c. m. energy with pA momentumtransfer has been included in the calculations by inputing NN c. m. amplitudes at 5 energies ranging from T^ to (TL + 200 MeV) and numerically interpolating for specific13The scalar and vector densities have been computed by Serot usingthe Dirac-Hartree approximation. In the near future use will be made ofexperimental proton vector densities which are readily obtainable from18measured charge distributions. Hartree - Fock - Bogoliubov (HFB) neutron19densities computed by Gogny will provide the neutron vector densities. The scalar densities will be obtained according to,ps ( l ) ( r )  = pv ( i ) ( r )  -  [ p s ( i ] ( r )  -  Pv ( i ) ( r ) ] S e r o t  ( 1 6 )where the quantities enclosed in brackets are the Dirac-Hartree densities of Serot.13The Fourier transforms in Eqs. (12) and (13) have been carried out numerically using an upper momentum transfer (q) cut-off of (2k) or 4 fm-3, whichever is less. The tensor contribution has been omitted in most of the calculations presented below; explicit inclusion of this term (see Fig. 19 below) indicates a negligible effect for elastic scattering from spin saturated nuclei.3^’^The RIA results for proton elastic scattering from ^Ca at 181, 300, 400, 500, 613, 800, and 1040 MeV and from 3 *^3Pb at 500 and 800 MeV are shown in Figs. 1-9, respectively^’3 along with data.3**’33-33 Solid curves indicate the RIA predictions discussed above where no parameter adjustments have been made, while the dashed curves represent the analogous predictions using the first order, spin dependent KMT-IA model discussed in Ref. 18. In these KMT calculations NN Wolfenstein amplitudes in the pA Breit frame have been used which correspond to the invariant amplitudes in the RIA calculations.3 Note that these particular KMT calculations are notrepresentative of the best available KMT predictions. For instance,18 27correlations, non-locality corrections, electromagnetic spin-orbit18 17(EMS0) terms ’ , etc. are routinely included in present KMT107calculations3  ^ and yield significantly improved results at T^ > 800 MeV108Theta(c.m)Fig. 1. Relativistic IA (solid Fig. 2. Same as Fig. 1, exceptcurves) and KMT-IA (dashed curves) for 300 MeV.predictions compared to data for181 MeV p + 40Ca elastic scatteringobservables.I O'-------1--------J------ 10 20 40 60Theta(Deg)L09Theta(c.m)®cmF ig .  3. Same as F ig .  1, excep t F ig .  4 .  Same as F ig .  1, exceptf o r  400 MeV. f o r  497 MeV.110Thetafc.m.)aF ig .  5 .  Same as F ig .  1, except F ig .  6 .  Same as F ig .  1, excep tf o r  613 MeV. f o r  800 MeV.IllTheta(c.m.)®cmF ig .  7. Same as F ig .  1, except F ig .  8. Same as F ig .  1, exceptf o r  1040 MeV. po r  p + 208pb ap 4gy112^cmFig. 9. Same as Fig. 1, except for p + 208pb at 800 MeV. Note that the KMT prediction for the differential cross section at back angles is better than the RIA.113compared to the dashed curves shown in Figs. 6 and 9. However, the KMTdescription of the data shown in Figs. 4 and 8 at 500 MeV is littleimproved when correlation corrections and EMSO terms are added to the first 17 “>3order KMT model. ’" The important role of medium modifications in the KMT approach will he discussed in the next section.For 4^Ca at 181 and 300 MeV, the RIA differential cross sections aretoo large and the analyzing powers are too small. At 400 MeV and above,both the differential cross sections and the analyzing powers agree wellwith the experimental data, with the best agreement occurring at 500 MeV. Predictions for the spin rotation function are also in good agreement with9 Q_30existing data.” On the other hand, the first order KMT-IA predictionsfor d.r/dV' display minima which are too deep for E < 613 MeV but are good at800 and 1040 MeV. The analyzing powers and spin rotation predictions are9 nopoor at all energies. Notice that the RIA predictions for Pb at 500 and 800 MeV do not agree as well with the differential cross sections andanalvzing power data as the corresponding calculations for 4<^ Ca. In the near future extensive calculations which explore the energy and target mass9 ndependence of the RIA will be presented by our collaboration."o iComparison of the RIA with the results of Dirac phenomenologyreveals several interesting features. First, the reactive content, asmeasured by the total reaction cross section, is well reproduced by the RIAas shown in Fig. 10. Phenomenological and RIA agree to within 1% at 300MeV and above; at 181 MeV the difference is 7%. This agreement is3?substantially better than obtained with KMT-IA calculations where differences as large as ^20 % occur below 200 MeV (see Fig. 10).The ratio of the volume integrals of the real vector to scalar31potentials, a quantity well determined by the phenomenology , agrees to within 5% at 300 MeV and above; the values at 181 MeV differ by 7%. The root mean square (rms) radii of the RIA real and imaginary scalar and vector potentials are within 10% of the corresponding phenomenological values at every energy. Comparing the volume integrals of phenomenological and RIA vector and scalar potentials provides another measure of the validity of theO 1IA. Table I gives RIA to Dirac phenomenological volume integral ratios. The agreement for the real potentials is very good in general except at 181 and 800 MeV and is substantially better than for the imaginary potentials. The largest discrepancy, around 300-500 MeV, for the imaginary potentials,114Tl  (MeV)Fig. 10. Total reaction cross sec­tions for p + ®Ca from 180 to 1000 MeV. The dots are obtained from Dirac optical model fits to data. The KMT-IA and RIA predictions are indicated by the dashed and solid curves, respectively.Table I_Ratio of Relattvlstlc IA to Phenomenological Volume IntegralsTL(MeV) VectorReal Imag Real Imag181 1.20 1.35 1.11 1.29300 1.01 0.89 0.96 0.76400 0.99 0.55 0.96 0.38500 0.99 0.66 0.97 0.47800 0.82 0.79 0.77 0.56115mainly reflects differences in the central strengths of the Imaginary RIA and phenomenological potentials.Constructing the Schr&dinger equivalent optical potential corresponding to the RIA and Dirac phenomenological optical potentials according to (omitting the tensor contribution),31U . =  U jrj.+ U a * J  (17)opt eff so /JwhereUeff = 2S t2EUV * 2»US - UV2 * “s' - 2UCoulUV ' 2?A If3 , 8A,2 _+ ( 3^  1 . (18a)(18b)UCoul)/(E + m) * (18c)provides another means for comparison with the KMT-IA model. The volume integrals per nucleon for the phenomenological31, RIA, and KMT-IA optical potentials are shown in Figs. 11-14, by the dots, solid and dashed curves, respectively. The real central potential volume is too repulsive (attractive) in the RIA (KMT-IA) model compared to experiment (see Fig. 11). At high energies the RIA and experiment agree. Both the RIA and KMT-IA imaginary central volumes are similar over the range of energies studied; each being somewhat too large below 400 MeV (see Fig. 12). The volumes of the spin-orbit potentials predicted by the RIA and KMT-IA are all in fairly good agreement with experiment, with slight preference for the RIA calculations being noted. Equation (18b) however implies that important differences in the shapes of the RIA and KMT-IA spin-orbit potentials exist which are a significant factor in the ability of the RIA potential to provide accurate descriptions of pA spin observables. The above discussion illustrates the fact that although the description of data by the RIA is quite impressive above 400 MeV, there remains a need for corrections based on the above comparisons with empirical potentials.Because of its predictive ability and sensitivity to densities, the Dirac approach is potentially a powerful tool for nuclear structure studies.U 1so 2HrA 3randA(r) (m + Ug + E - U„ -116Fig 11. Volume per nucleon of the real central Schrodinger equation optical potential for p + 40Ca. The dots are obtained from Dirac optical model fits to data. The KMT-IA and RIA predictions are shown by the dash­ed and solid curves, respectively.F ig .  12. Same as F ig .  11 , except f o r  th e  im ag inary  c e n t r a l  p o t e n t i a l .117Tl (MeV)Fig. 13. Same as Fig. 11, except for the real part of the spin- orbit potential.100 200 300 400 600 800Tl (MeV)Fig. 14. Same as Fig. 11, except for the imaginary spin-orbit poten­tial .Estimates of the neutron-proton rms radius difference for 40Ca deduced fromthe RIA calculations yield preliminary values of -0.2 and -0.1 fm at 500 and800 MeV, respectively. These preliminary results are already closer to theexpected value (-0.05 fm, Ref. 33) and less energy dependent than that17 23obtained in second order KMT-IA analyses ’ (see Fig. 15).Calculations at 500 MeV have been made to explore the sensitivity ofthe computed observables to various ingredients in the RIA model. The Breitframe kinematic energy shift was not included in order that the importanceof NN amplitude contributions from energies greater than TL be determined.The result for 40Ca is shown in Fig. 16 where little effect is noted. Onepossibly significant difference between the RIA and KMT-IA models is thatdouble spin flip NN c. m. amplitudes (B, D, and E in Eq. (1)) contribute1—3directly to the scalar and vector Dirac optical potentials whereas these terms contribute less importantly to the first order KMT—IA potential. RIA calculations were therefore made in which B = D = E = 0. The results in Fig. 17 indicate that in fact the NN c. m. double spin flip amplitudes do not contribute significantly to the RIA predictions.The importance of the lower components of the Dirac nuclear wave function (i.e. vector - scalar density difference) has been examined for p + 40Ca at 500 MeV (see Fig. 18) where noticeable improvement in the description of the Ay data results when realistic (Ref. 13) lower componentnuclear wave functions are used. While the scalar density effects arenoticeable at 500 MeV, their effects in this case are not sufficientlyunique or dramatic for quantitative information about the lower component nuclear wave functions to be able to be deduced from RIA analysis of data. Sensitivity of the RIA model to the scalar - vector density difference is currently being investigated at other energies and for different targets.Finally the importance of the tensor component of the RIA optical potential has been examined for several targets and energies in elastic scattering. These preliminary calculations use an approximate form for the tensor density (Eq. (14c)) derived by Wallace.14 It is given by,PT(r) a§[PsM  * PVM ]  , (19)2 B ( r )where118B (r )  = 2m -  e B -  U ^ 6-1 ( r )  + U g ^ C r )  (20)119O0 </> s co >O 0)00 «srOOU>OoTJ0O3T3CDT3XcaO•HP><0Soo00T)GcaoOLOPca< i—iQd0£Xpcac<  -H i—i i—iad i>•H pwo ca P u"OGO hW D OIPcaH003LO G O 2 </)i-H O tp +->P 00 rH• P  0 G 3GO 3  U •H </>•H 0  G 0CP G 0 3 Ucap<PO • P00G•Hco•Hpop•H T) . .0  0  Nh  h  X  oa Ph<p ca0 <  c3  h  a p cdca ,- <p 0 u  ca o x o  papo c +0  *P cJP ( i -Htp p pHW  <P >  w •h a) x S t )  w  G  o  ca . oJ LO p• p 0M 0 p 5 •H G  O  O  Uh 0  tp PhcDm )120Fig. 17. Effect of double-spin- flip NN c. m. amplitudes in the RIA predictions for 500 MeV p + ■^Ca analyzing power and Q.Fig. 18. Sensitivity of the RIA prediction for 500 MeV p + ^Ca Ay and Q to the lower components of the target nuclear wave function. The solid curve corresponds to Ps /  pv  while ps  = pv is assumed in the dashed curves.121and eB > 0 is the average target nucleon binding energy while andare the vector and scalar target nucleon binding potentials. Typically ^(0) = 423 MeV and Ug^8^(0) = —502 MeV (Ref. 34). Both zero range (i.e. Frp(q) = F^,(q=0)) and finite range calculations have been made. The results, shown in Fig. 19 for p + 40Ca at 500 MeV, indicate a negligible effect. Other cases will be investigated in the future.As stated in the introduction the principal difference in physics between the RIA calculation and the KMT-IA approach is inclusion of virtual negative energy states in the former. Such processes are described and contrasted with non-relativistic models in Ref. 6. All possible intermediate scatterings in the NN system are incorporated in the NN amplitudes and hence contribute both to KMT and RIA models. The virtual negative energv channels being considered here correspond to propagation of negative energy states between successive interactions of the incident proton with the one-body nuclear density via the first order optical potential. Roughly speaking this effect is embodied in the non-linear terms in the SchrOdinger equivalent optical potential in Eqs. (17) and (18). These terms have been identified as being primarily responsible for the improved description of pA data provided by the RIA compared to<5 /non-relativistic calculations. » The apparent importance of negative energy states in intermediate energy pA scattering undermines one's confidence in the ultimate ability of non-relativistic theories to describe spin related data, and to a lesser extent, differential cross section data at intermediate energies.In the above discussion the RIA and KMT-IA predictions have been compared to each other and to many examples of proton elastic scattering data. In the next section practical reasons are given for continued, although limited, use and development of NR multiple scattering calculations.III. Non-Relativistic ModelsThe status of the author's non-relativistic multiple scattering work (KMT) has not changed since the IUCF-1982 workshop last fall.17 Herein a discussion is given of the impact which the RIA results have on KMT!r) (NEUTRONS/fm3)* 101220.040.020- 0.02Fig. 19. Effect of the tensor term in the RIA optical potential for p + 40Ca at 500 MeV. Curves correspond to differences between calcu­lations with and without the tensor term. The solid and dashed curvesindicate the effect for spin rotation and A , respectively. These differ­ences are smaller than the errors in the corresponding data (see Fig. 4). Differential cross sections are neg­ligibly altered. The arrow indicates the first minimum in Ay.Fig. 20. Typical result for iso­topic neutron density difference obtained from second order KMT analysis. This example corresponds to pn (154Sm) - Pn(14 Sm).I 2 3 4 5 6 7 8 9  10 r(fm)123analyses. Some practical reasons for continued development and limited use of NR models will also be mentioned.With the success of the RIA it appears that the severe disagreementbetween KMT-IA predictions and spin observable data at 500 - 800 MeV has23been explained. At the time of the IUCF workshop last fall it was generally believed that the bulk of the discrepancy with KMT-IA predictions at 500 MeV at forward angles was attributable to medium modifications of the IA value for the NN effective interaction.1  ^Such conclusions were based on empirical studies of the 500 MeV NN effective interaction33 and medium effect calculations at slightly lower energies (see Figs. 17 and 18 in Ref. 17). With relativistic and medium effects supposedly modifying the predicted observables by similar amounts, calculations with both processes included should be quite interesting and need to be carried out as quickly as possible. Medium modifications might destroy the apparent success of the RIA or detailed calculations might show them to in fact be negligible above 500 MeV. At any rate medium effects must be examined before a final assessment of the relativistic versus non-relativistic question can be given.However, as things stand at the present time use of NR models to interpret intermediate energy spin observables or reactions which are strongly affected by the spin-dependent parts of the NN interaction is ill-advised. It should be stressed, however, that KMT-IA descriptions ofdifferential cross section data, particularly at the higher energies, isquite good. Therefore the nuclear structure information deduced in KMT analyses of > 800 MeV differential cross section data (neutron densities)remains valid.17»18»25>36»37 Since many theoretical refinements exist in current KMT calculations and in light of the tests38 to which these modelshave been subjected and have successfully endured, it is quite reasonable to continue using KMT models at > 800 MeV for nuclear structure studies, at least until theoretically sound relativistic formulations and calculational models have been developed. A recent example, the empirically deduced neutron isotopic density difference between 144Sm and 154Sm, is shown in Fig. 20 (Ref. 37). Application of KMT models to < 600 MeV elastic scattering differential cross section data is questionable since the spin-orbit potential contributes significantly to this observable.23124Likewise, > 800 MeV proton induced inelastic scattering transitions which are not strongly dominated by the spin dependent interactions can also continue to be examined with KMT-IA models. For instance the208Pb(p,p')(3-,2.6 MeV) strong collective inelastic excitation has recentlyO Qbeen successfully analyzed with the KMT model. A great deal of inelastic transition data exists at 800 MeV involving strong collective, approximately spin independent excitations which can be considered suitable for KMT analyses.Further (limited) development of the non-relativistic KMT model is not unwarranted since theoretical refinements to the first order KMT-IA are precisely specified by the formalism and considerable computational machinery can be readily invoked to examine remaining physical effects. For instance, the importance of target nucleon correlations as a function of energy and target size has already been examined in great detail using KMT models and will guide in the development of second order Dirac optical potentials.18,40 Figures 21 and 22 demonstrate the importance of target nucleon correlations in Ay predictions at 500 and 800 MeV, respectively.16The importance of the electromagnetic spin-orbit (EMS0) potentialwas first demonstrated using NR models.16,41,42 From Figs. 23 and 24 it isobserved that the EMSO correction is inconsequential at 500 MeV. However at800 MeV it is quite significant. Comparison of Figs. 25 and 26 with Figs.6 and 9 suggests that EMSO effects will greatly improve the RIA Aypredictions at 800 and 1040 MeV. Other Coulomb corrections remain to be43 44examined; all of which are specified by the KMT formalism. » Coulomb-nuclear cross terms, second order Coulomb potentials, and NN Coulomb rescattering effects can all be readily examined in the KMT model.At energies above the pion production threshold NN interaction models must account explicitly for NN inelastic processes. Such interaction models are crucial in determining medium45 and off-shell effects46 in pA scattering. Non-relativistic NN interaction models exist for energies varying from 0 to 1000 MeV (Ref. 47) and calculational tools are available or are being developed for examination of off—shell and medium modification effects over the full intermediate energy range. Such studies will provide important information regarding hitherto unexamined physical processes and will have great impact on the development of relativistic models.125c^m(deg)Fig. 21. Correlation effects in KMT calculations for 500 MeV p + Ca analyzing power.sc.m.(deg>Fig. 22. Correlation effects in KMT calculations for 800 MeV p + 208pb analyzing power.126Fig. 23. Electromagnetic spin- orbit effect from KMT calculations for 500 MeV p + 40Ca.Fig. 24. Electromagnetic spin- orbit effect from KMT calculations for 500 MeV p + 08Pb.Ay(0)Fig. 25. Electromagnetic spin- orbit effect from KMT calculations for 800 MeV p + 40Ca.Fig. 26. Electromagnetic spin- orbit effect from KMT calculations for 800 MeV p + 208Pb.128The developments needed in the relativistic approach which are of immediate concern are:(1) a relativistic formalism based on multiple scatterings of an incident Dirac plane wave from many independent potentials. ’(2) application of the RIA for elastic scattering for a broader range of targets and energies; comparison with new elastic spin rotation data at 500 and 800 MeV.(3) search for reactions which are sensitive to the lower components of nuclear wave functions.(4) application to inelastic scattering, particularly excitations which are sensitive to the NN spin-dependent amplitudes.(5) examination of nuclear structure information obtained via the RIA model; neutron densities, isotopic matter density differences, transition densities, etc.(6) application to reactions; (p,n), (p,d), (p,7i) with specialattention being given to spin observables.48(7) analogous RIA models for pion and kaon nucleus scattering.Concerning the non-relativistic approach, some immediate goals areto:(1) establish the importance of medium effects and off-shell NN amplitude sensitivity for TLAB > 200 MeV.(2) examine correlation effects which are dependent on the Coulomb and spin-dependent NN interaction.With respect to new experiments it is fairly obvious that pA spin observables and differential cross sections for reactions which are strongly affected by the spin-dependent NN interaction will be sensitive to RIA versus KMT-IA differences in the energy region 200 - 600 MeV. Specifically it would be useful to have high quality pA elastic scattering data in the 200 - 600 MeV region as well as cross section and Ay data for non-naturalparity excitations of single particle levels.IV. Future DirectionsV. Conclusions129Given the tone of this and the previous talks it is apparent thatthe theoretical point of view from which intermediate energy pA reactionsare studied is presently undergoing a metamorphic transformation. It would therefore be unwise to draw conclusions with an air of finality. However, some tentative conclusions are offered:(1) Non-relativistic approaches for analyzing intermediate energy pA reactions can no longer be considered reliable, except under certain limited conditions as noted above.(2) The relativistic approach is very promising, however a rigorous theoretical basis for these calculations is lacking, and many important physical phenomena remain unaccounted for in the RIA results (i.e. medium effects and correlations).(3) In general it appears that the keyword in determining whererelativistic effects will be important in pA physics is "spin".Acknowledgements:The author would like to thank the other members of the Texas - Stanford - OSU - IBM collaboration for their invaluable contributions to the work presented here. These include; Dr. B. C. Clark, S. Hama, Prof. G. W. Hoffmann, Dr. R. L. Mercer, and Dr. B. D. Serot. I am also very grateful to Prof. D. A. Hutcheon for permission to show preliminary TRIUMF data prior to publication and to Prof. S. J. Wallace for pointing out thecontribution of the tensor term to the RIA optical potential. This workwas supported in part by the U.S.D.O.E. and the Robert A. Welch Foundation.References1. J. A. McNeil, L. Ray, and S. J. Wallace, Phys. Rev. C27, 2123(1983).2. J. A. McNeil, J. Shepard, and S. J. Wallace, Phys. Rev. Lett. 50,1439 (1983).3. J. Shepard, J. A. McNeil, and S. J. Wallace, Phys. Rev. Lett. 50,1443 (1983).4. B. C. Clark, S. Hama, R. L. Mercer, L. Ray, and B. D. Serot, Phys.Rev. Lett. 50, 1644 (1983).1305. B. C. Clark, S. Hama, R. L. Mercer, L. Ray, G. W. Hoffmann, and B. D. Serot, Phys. Rev. C (to be published).6. M. R. Anastasio, L. S. Celenza, and C. M. Shakin, Phys. Rev. C23, 2606 (1981).7. A. K. Kerman, H. McManus, and R. M. Thaler, Ann. Phys. (N. Y.) 8^, 551 (1959).8. R. A. Arndt, R. H. Hackman, and L. D. Roper, Phys. Rev. C9, 555(1974); C15, 1002 (1977); and R. A. Arndt, VPI & SU, ScatteringAnalysis Interactive Dialin nucleon-nucleon program.9. W. G. Love and M. A. Franey, Phys. Rev. C24, 1073 (1981).10. J. A. McNeil, University of Alberta/ TRIUMF Workshop on Studying Nuclei with Intermediate Energy Protons, (see previous talk).11. S. J. Wallace, in Advances in Nucl. Phys., edited by J. W. Negele and E. Vogt (Plenum, New York, 1981) Vol. 12^ , 135 (1981).12. J. D. Bjorken and S. D. Drell, Relativistic Quantum Mechanics, (McGraw- Hill, New York, 1964).13. C. J. Horowitz and B. D. Serot, Nucl. Phys. A368, 503 (1981), and B. D. Serot, private communication.14. S. J. Wallace, private communication.15. L. D. Miller, Phys. Rev. C14, 706 (1976).16. G. W. Hoffmann et al., Phys. Rev. C24, 541 (1981).17. L. Ray, AIP Conf. Proc. No. 97: The Interaction Between Medium Energy Nucleons in Nuclei - 1982, edited by H. 0. Meyer (A.I.P. Press, New York, 1983), p. 121.18. L. Ray, Phys. Rev. C19, 1855 (1979).19. J. Decharg6 and D. Gogny, Phys. Rev. C21, 1568 (1980).20. B. C. Clark et al., unpublished.21. L. G. Arnold, B. C. Clark, R. L. Mercer, and P. Schwandt, Phys. Rev. C23, 1949 (1981).22. D. Hutcheon et a_l. , private communication.23. G. W. Hoffmann et al., Phys. Rev. Lett. 47, 1436 (1981).24. T. Bauer et al., unpublished. See G. Bruge, Saclay preprint DPh-N/ME/78-1 (1978).25. L. Ray et_ al., Phys. Rev. C23, 828 (1981).26. G. Alkhazov et al., Nucl. Phys. A274, 443 (1976).13127. D. A. Hutcheon et al., Phys. Rev. Lett. 47, 315 (1981).28. A. Rahbar et al., Phys. Rev. Lett. 47, 1811 (1981).29. B. Aas et al., Bull. Am. Phys. Soc. 26, 1081 (1981) and B. Aas, private communication.30. R. Fergerson et al., private communication.31. B. C. Clark, S. Hama, and R. L. Mercer, AIP Conf. Proc. No. 97: TheInteraction Between Medium Energy Nucleons in Nuclei - 1982, edited byH. 0. Meyer (A.I.P. Press, New York, 1983), p. 260.32. L. Ray, Phys. Rev. C20, 1857 (1979).33. J. W. Negele and D. Vautherin, Phys. Rev. C5, 1472 (1972).34. B. C. Clark, private communication.35. M. L. Barlett et al., to be published.36. G. Pauletta et al., Phys. Lett. 106B, 470 (1981).37. L. Ray and M. M. Gazzaly, Phys. Lett. 124B, 309 (1983).38. L. Ray and G. W. Hoffmann, Phys. Rev. C27, 2143 (1983).39. L. Ray and G. W. Hoffmann, Phys. Rev. C^7, 2133 (1983).40. A. Chaumeaux, V. Layly, and R. Schaeffer, Ann. Phys. (N247 (1978).41. P. Osland and R. J. Glauber, Nucl. Phys. A326, 255 (1979).42. G. Faldt and A. Ingemarsson, Uppsala preprint No. GWI-PH 5/81 (1981),unpublished.43. L. Ray, G. W. Hoffmann, and R. M. Thaler, Phys. Rev. C22, 1454 (1980).44. L. Ray, unpublished.45. H. V. von Geramb, AIP Conf. Proc. No. 97: The Interaction Between Medium Energy Nucleons in Nuclei - 1982, edited by H. 0. Meyer (A.I.P. Press, New York, 1983), p. 44.46. D. H. Wolfe, M. V. Hynes, A. Picklesimer, P. C. Tandy, and R. M.Thaler, AIP Conf. Proc. No. 97: The Interaction Between Medium Energy Nucleons in Nuclei - 1982, edited by H. 0. Meyer (A.I.P. Press, New York, 1983), p. 149.47. E. L. Lomon, Phys. Rev. D26, 576 (1982).48. B. C. Clark and S. Hama, private communication.Impulse Approximation Dirac Optical Potential133J. A. McNeil Villanova UniversityVillanova, Pennsylvania 19085andUniversity of Pennsylvania Philadelphia, Pennsylvania 19042AbstractA derivation of the Dirac optical potential based on the impulse-*• 40approximation is presented. Parameter free calculation of500 MeV p- Ca elastic scattering observables gives excellent agreement with data.Simplified model calculations are also presented which show how thissuccess arises through the density differences that arise naturally in theDirac approach.134One of the more dramatic results to follow the Indiana Workshop last fall has been the first successful microscopic parameter-free calculations of intermediate energy p-nucleus elastic s c a t t e r i n g ^ T h e  key difference with previous calculations was the use of the Dirac equation with the Dirac optical potentials constrained using a relativistic version of the impulse approximation3*4. For the past several years impressive phenomenological fits to a large body of p-nucleus scattering data has been obtained using the Dirac approach5. The optical potentials obtained by these fits for energies above 200 MeV are largely explained by the impulse approximation. The success of the Dirac approach, and particularly its superiority over input-equivalent Schrodinger based calculations has spawned an intensive investigation into the Dirac approach for several classes of nuclear reactions* The purpose of this talk is to present the fundamental basis for the Dirac impulse approximation optical potentials and suggest a simple explanation for its success.The following section derives the Dirac impulse approximation opticalpotential following ref 3 and 4, showing how the optical potential is constrained by the nucleon-nucleon phase shifts. There follows in Section•* 40III a presentation of a calculation of 500 MeV p— Ca elastic scattering observables which is dramatically successful. In Section IV this success is explained by considering an equal density toy model. Our conclusions are given in the last section.I. Introduction135II theoryConsider the elastic scattering of an intermediate energy proton from a spin zero nucleus. The initial and final projectile momentum are k and k' respectively. We shall describe the scattering process using the fixed energy Dirac equationwhere Uoo is the elastic proton-nucleus relativistic optical potential which at this point has arbitrary Dirac structure. The goal of this section is to use the impulse approximation, suitably generalized to the DiVac equation, to constrain Uoo.The scattered wave obeys the following integral equation:O )< r \C l )asymptotically as r+“ , the Green's function becomesAwhere k'*kr. The Dirac projection operator can be rewritten in terms ofsplnors as follows:136which gives' ^ * kf X h  -- e u/Pj » Fs .,(k;i) cr;I?, J ^where Fa »s is the scattering amplitude£ / * ; «  ' 7  v ‘ v  / A ' e  <rfM ( t >The T-matrix by definition is given byA)Jj ’r # 1 It) ti,A) = ^ * 0  \ \ s ) (7)which implies the following integral equation for TooT .. = U.. -  U -  — 1—  X .  . (1)The impulse approximation consists of equating the optical potential,Uoo, with the sum of free two-body scatterings between the projectile and target nucleus averaged over the nuclear ground state:t l L t y  -  <  v  I L C  l b ?  <o| L  < £ '  1 i .  I k >  |o> a )The multiple scattering effects are incorporated via Eq. (8>l Note that in the corresponding nonrelativistic Schrodinger treatment the leading term, Uoo, would be identically constrained by contruction so the only difference between the Schrodinger and Dirac approach, in this optical potentialtreatment of the multiple scattering, Is In the Intermediate propagation.The Schrodinger case has no spin-dependence in contrast to the Dirac case.In order to obtain the Lorentz structure of the optical potential it is necessary to find a suitable manifestly Lorentz invariant representation of the nucleon-nucleon t-matvU or scattering amplitude. If one assumes rotation, parity, and time reversal invariance, one such representation, suitable for identical particles, isFq's> -Fj * r„ y; / y* fr f t V i . %  0 *r v ** v /* /*¥ 1where &  1 spans the Dirac matrix space.The five complex amplitudes 'r, ^  ^  J are a representation of thenucleon-nucleon scattering amplitude equivalent to the more familiarWolfenstein center of mass form£  - A*- Bf.-K ♦ ij + *- £  (\y)where is the Pauli operator for particle i,The (2ik)-  ^ factor renders the amplitudes Lorentz invariant. Given enough nucleon-nucleon data these amplitudes are fully determined via phase shift analysis.The transformation between representations is obtained by calculating the matrix elements of (10) between free Dirac spinors, that istb  f  X<» = 5,A> u,fii f  Cu)137138whereu,‘W l f  I *, ( > * >The resulting transformation can be conveniently represented by aA5 x 5  matrix, 0  .( 1 + )The 5 x 5  matrix 0 Is given in ref. 3. Inverting 0 gives the manifestly Lorentz Invariant amplitudes, F(q,s), in terms of the (presumably) known Vfolfenstein amplitudes fcm. In the lab frame the relativistic t-matrix is then given bya »^ k ' U ;  I fe > = ! ‘/>y\ 0 0 r )where k^ is the projectile lab momentum.The next step is to write the nuclear ground state wave function in Dirac form:_ f/t)|0> -- 11 ^ t r t )C-/139where 4 summarizes the quantum numbers.with- tr-r X mt:nJJ/%  - z  C  :■ ^  x<7 i//I * )where C is a Clebsch-Gordon coefficient.Using the invariant form of the nucleon-nucleon t-matrix (10), theimpulse approximation optical potential, (9), is given by:*• >- < c| I ;  e < / ’ 1 c " )The sum over u for a spin saturated nucleus implies a trace over a (nuclear); the terms surviving the trace yieldu I C k h -  '  ' “ f y / w ](21 )where, f j ’r  e7  £  ( L j  7V ( D  1A  7/ I  A  r ‘ Z  C * * )>u/rJ140The vector density is well determined by electron scattering. Note that Zf>v since nuclear lower components are generally small, also note that p r is proportional to nuclear lower components and hence will be small compared to or . In addition the tensor amplitude is small compared to either the vector or scalar further reducing its importance.Fourier transforming, one can write the IA optical potential as-- +■ y *■ Y  i-Y let-') fjv)where the Y-matrices act only on the projectile splnors, and where-  V r i k  Cj \ ' ‘I  ‘- - ? L 5 .  epir)v 4* J {zV)"*>T n  -• f 4 ,  e  (2?)^  (Z71J• A •where p>r is (23) without the v ‘ factor. The nuclear form factors,P % much faster than the nucleon-nucleon amplitudes so(24) may be reasonably approximated by the forward scattering amplitude» i 'times the densityj >-«■• y 3 ■llj*) ~  ft*** f Y*p r )The vector and scalar optical potential strengths for central nuclear density given by (28) are compared to phenomenologically obtained strengths in Fig. 1.141Figure 1In (a) the isospin averaged impulse approximation vector and scalar optical potential central strengths (lines) are compared with phenomenological strengths (dots). In (b) the energy dependence of the ratio of real vector to real scalar strengths for the impulse approximation optical potential (line) are compared with the phenomenological ratios (dots). The dashed curve is the factor m/E^ which arises naturally in relativistic amplitudes when only the dominant Wolfenstein C term is retained.142One can see that the Impulse approximation optical potential strengths agree quite well with the phenomenological strengths down to around 200 MeV below which energy the impulse approximation is suspect. Note in particular the large mangitude and oppositely signed feature of the potentials. These magnitudes are significant fractions of the rest energy of the nucleon which suggests that a relativistic treatment be used even at low energies.Ill Calculations- 9  u. 0As an example we now turn to calculating p- Ca elastic scattering at 500 MeV where extensive data haKe been measured and where the nn amplitudes are well determined. The relativistic invariant amplitudes are calculated via the inverse of Eq. (14) using the Arndt Sp83 phase shift solution to get the VJblfenstein amplitudes. The nuclear ground state wave functions were fit to electron scattering and empirical separation energies. There are no remaining free parameters. The optical potential is entirely constrained by independent empirical data. In figure 2 we show the resulting cross section, analyzing power, and spin rotation parameter for this case. The agreement is excellent suggesting that the impulse approximation is getting most of the physics right in this kinematic regime so long as one treats the scattering relativlstically. As stated previously the tensor part of the optical potential is small producing an imperceptible contribution to da/d£2 and Ay but it does yield a detectable shift in Q (see Fig. 2). L Ray will present more impulse approximation based calculations in the following talk.(do7dft)cm.(fm'/sr)1431.00.0fiUdeg)11y/\ tft fy> 1,//f tA  1Jft •  // / l  f ' \  /  \  / '  ' '  i  V '  i yf  “ / l y r  • ‘1/1/L if. ___  Olr»<. “'/• ^- _ _ —  Dl»».----i_ _l  - -11 iUi 1 1W 1 1Jl II If •» >1 J1 j1 -• ■... .Il .._____10 20flUWeg)30 40Figure 2Parameter-free calculations of 500 MeV p—^Ca elastic scattering (lines) based on the impulse approximation optical potential are compared with data (dots). The dashed curve is an "equivalent" non-relativistic calculation. The figure was taken from ref. 1 and the data shown is from ref. 6.144IV DiscussionThe success of the Dirac-based Impulse approximation optical potential needs to be understood. Due to historic and pedagogic reasons our intuition seems to function best in, and take its language from, the Schrodinger equation. Most of us have seen enough Schrodinger calculations to know how the typical non-relativistic central and spin-orbit optical potentials influence the cross-section and analyzing power. We have learned that to fit polarization data at intermediate energies some rather unrealistic assumptions about the shapes of these non-relativistic potentials seems required suggesting a breakdown of the impulse approximation7. We now can say that the source of these "anamolous” shapes is the structure of the Dirac equation. The empirical Dirac optical potential shapes closely resemble the nuclear density which is expected considering the short range of the probe. We can illustrate the appearance of "anamolous” shapes by calculating the scattering example considered previously in both the Schrodinger and Dirac methods where the role of the geometries is emphasized by considering a toy model where all densities are equal and no folding over the finite nn range is carried out. The results of this model calculation using the eikonal m e t h o d  8*9 are presented in Figure 3.(mb/sr)145Fig. 3Equal density toy model calculations of 500 MeV p—^ C a  elastic scattering using the Dirac (-) and Schrodinger (....) approaches are compared. The solid curve is a Dirac—eikonal calculation, the dashed curve is the full partial wave calculation, the dotted curve is the Schrodinger—eikonal calculation. The vector and scalar strengths are taken from the relativistic impulse approximation optical potential. The figure was taken from ref. 8 with the data shown taken from ref. 6.146We see that the Schrodinger calculated spin observables display little structure in sharp contrast to the (input equivalent) Dirac calcuated spin observables which show dramatic structure and, although based on a toy model density, closely resemble the data. The structure in the spin observables arises from differences in the (non-relativistic) central and spin orbit densities. By construction these were set to zero in the Schrodinger calculation shown in Fig. 3. We can see how the Dirac approach develops non-trivial effective central and spin orbit density differences by expressing the Dirac equation in Schrodinger form. This is done by eliminating the lower compaonent to give the following Schrodinger-like equation for the upper componentf 1C _ P? _ Vc- Ko ( r - L -  lLe£ = a (L Z** Z'** J Jwhere the central and spin-orbit potentials are given in terms of the scalar and vector potentials:One can see that even if S(r) and V(r) have identical densities the effective (Schrodinger-language) central and spin-orbit densities will not have the same shapes. The difference arises from the sturcture of the147Dirac equation and is the principal source of its success in describing proton-nucleus spin observables at intermediate energies. To get the more detailed agreement shown in Fig. 2 a  more careful treatment of the densities is required.ConclusionWe have shown how to constrain the Dirac optical potential using the impulse approximation suitably generalized to the relativistic case. The vector and scalar optical potential strengths obtained in this way agree well with those obtained phenomenologically. By using electron scattering data and separation energies the optical potentials may be fully constrained allowing for parameter-free calculations. The first such calculations for 500 MeV protons elastically scattered from 40ca give excellent agreement with experiment especially for the spin observables.We believe the principal source for this success, stated in Schrodinger-language, is due to the density differences between effective central and spin-orbit optical potentials which arise in a natural way using the Dirac approach.Acknowledgements This work was done in collabortation with R. D. Amado,J. Piekarewicz, E. Rost, J. R. Shepard, D. A. Sparrow and S. J. Wallace.The section on the tensor contribution to the optical potential leaned heavily on notes by S. J. Wallace. The p-^Ca calculations including the tensor contribution were carried out by J. R. Shepard and E. Rost. The hospitality of the Nuclear Physics Laboratory of the University of Colorado where this paper was written and typed is gratefully acknowledged.148REFERENCES1. J.R.Shepard,J.A.McNeil, and S.J.Wallace, Phys.Rev.Lett. _50,1443 (1983).2. B.C.Clark,S.Hama,R.L.Mercer,L.Ray, and B.Serot, Phys.Rev.Lett. _50, 1644 (1983).3. J. A. McNeil,L.Ray, and S. J.Wallace', Phys. Rev. C27, 2123 (1983).4. J.A.McNeil, J.R.Shepard, and S.J.Wallace, Phys. Rev. Lett. _50, 1439 (1983).5. L.G.Arnold, et.al., Phys. Rev. C25, 936 (1982) and references therein.6. A.Rahbar, et. al., Phys. Rev. Lett. 47, 1811 (1981).7. G.W.Hoffman, et. al. , Phys. Rev. Lett. 4_7, 1436 (1981).8. R.D.Amado,J.Piekarewicz,D.A.Sparrow,and J.A.McNeil, submitted to Phys. Rev. C.9. R.D.Amado,J.A.McNeil,J.Piekarewicz, and D.A.Sparrow, submitted to Phys. Rev. C.149EXPERIMENTAL OBSERVATIONS ON THE QUENCHING OF THE GT STRENGTH *J. Rapaport Ohio University, Athens, Ohio 45701 USAABSTRACTObserved beta-decay rates associated with Gamow-Teller (GT) transitions are significantly below those expected from calculations. This has been interpreted as a renormalization or quenching of the axial coupling constant, and has been a subject actively studies in the last ten years. Recent intermediate energy (p,n) data have become available which may be used to study the complete distribution of GT strength in the final nucleus. This GT strength function in nuclei throughout the periodic table is presented.The sum of the total observed GT strength is compared to a model independent sum rule to obtain an A dependence of the quenching. The fact that less GT strength is observed than is expected may be associated with internal nucleon degrees of freedom.1. INTRODUCTIONUntil a few years ago, the study of the guenchina of the Gamow-Teller (GT) strength was only associated with individual fast beta decay transitions in light nuclei (1-6). The observed rates are significantly below those expected from the use of shell model wave functions together with the value of gA , the axial coupling constant as derived from free neutron decay. Conservation of the vector current assures us that g^, the vector coupling* Supported in Part by the National Science Foundation.constant associated with Fermi beta-decay transitions has the same value for a free nucleon than for nucleons in a complex system such as nuclei.A free neutron transforms to a free proton, an electron and anti- neutrinos with a half-life t = 642.0 ± 7.2 [sec] (7). For this decaygV + 3gA = Ttwhere f is the phase-space factor determined by the total decay energy release. For fy and f^ values see ref. 7. The constant K ‘ is usually written K' = Kg^ with K = 6163.4 ± 3.8 [sec] (8) and g^ is obtained from analyses of super-allowed 0+ ■+• 0+ beta decay (Fermi type) transitions.The fast nuclear beta decay involve transitions without momentum transfer (leptons carry off little momentum) and in this limit we may writeB(F) g§ + B (GT) gj = ^150where[B(F)]1/2 = 1 n  <f||Et*||i:(2J.+1) K *and[B(GT)]1/2 = ---  i m  <f|| Zo„t*||1>(2Jf+l) K K Kare the reduced transition probabilities for Fermi and GT transitions as defined for instance in Bohr and Mottelson (9).The quantity (gA/gv ), ratio of axial to vector coupling constant, has a value (10) (g^/gy) = 1.250 ± 0.009 for the free neutron decay. Calculated beta decay rates may be made to agree with observed rates if a renormalized g^ value is used. A summary of the quenching observed in beta decay transi­tions is shown in Fig. 1. This set of values have been reported by Goodman and Bloom (11). A recent B(GT) analysis of mirror pairs of sd-shell nucleiusinq mixed-confiquration shell-model wave functions presented by Brown and Wildenthal (12) indicates a similar quenchinq, Fiq. 2. Buck and Perez (13) in a recent letter reanalyzed magnetic moments and beta decays of mirror nuclei obtained a value (gA/qv ) = 1.00 ± 0.02 for nucleons in a nucleus, thus quenched by 80% compared to the value for the free neutrondecay.The quenching of in nuclei has been attributed mainly to two sources: a) core-polarization and configuration-mixinq effects and b)non-nucleonic effects (14). A very complete discussion has been presented recently by Towner and Khanna (15). The quantitative separation of these two effects is complicated by the importance of the tensor component of the nucleon-nucleon force as pointed out by Arima (16). The presentations by Rho (17) and Weise (18) at the International Conference on Nuclear Structure (Amsterdam, 1982) discuss this point at length and contain relevant references.In the last few years the study of the (p,n) reaction at intermediate energies and low momentum transfer (0° spectra) has shown that L = 0 transi­tions may be used to obtain B(GT) values. The obvious advantages of the (p,n) reaction is that it is not limited by the energeticsof beta decay and thus it is possible to study the complete distribution of GT strengths in the final nucleus, from the ground state to hiqh eneraies of excitation.The observed GT strength in the (p,n) reaction has been absolutely normalized to the beta-decay strength for several isolated transitions (19) and total B(GT) values have been obtained. These values are compared to model inde­pendent sum rules to obtain the B(GT) quenchinq. This method does not need the knowledge of the final state wave function as it is in the case of beta decay. The magnitude of the observed quenching and its A dependence is in agreement with theoretical considerations involving the coupling of151nucleon particle-hole with A-isobar, N-hole states (17). The A states involved in spin-isospin degrees of freedom effectively remove much of the strength to higher energies.The quenching effect should also apply to all transitions involving the a • x operator, particularly magnetic dipole. These Ml transitions are more complicated by the additional orbital contribution as well as the spin moments.2. EXPERIMENTAL PROCEDURE AND RESULTSAll the intermediate energy (p,n) data discussed here have been obtained using the beam-swinger facility at Indiana University, described in detail in ref. 20. A floor plan and a magnet layout for the beam swinger are shownin Fig. 3. In general two or three detector stations are used. One alongthe 0° line with respect to an undeflected proton beam is usually located at a distance of 100 m. The other stations are positioned 24° apart (fig. 3)thus allowing an angular range 0° - 76°.Time compensated large-volume neutron detectors (21) are used with which subnanosecond time resolution is achieved. The main cyclotron oscil­lator r.f. is pulse selected (1:5) and proton pulses every 150 nsec (approxi­mately) with a width of 300 - 500 psec are used in the (p,n) experiments(fig. 4). The neutron resolution that may be obtained at 100m flight path forseveral time of flight (tof) resolutions is shown in fiq. 5 .In general a typical 0° (p,n) spectrum at intermediate proton energies is dominated by L = 0 transitions. This is shown for the not so typical 1 **C in fig. 6 . The visible peaks are all characterized with AL = 0, AS = 1(AJ17 = 1+ ) or AL = 0, AS = 0 (AJ77 = 0+ ). As may be seen in fig. 7 , ltfNhas many excited states, but the (p,n) reaction at 0° selects mainly those with AL = 0. The same reaction has been studied at 60, 120, 160 and 200 MeV152with the results shown in fig. 8; the yield to the 1+ state at 3.95 MeV has been arbitrarily normalized to show the decrease with energy of the cross section to the analog 0+ state at 2.31 MeV. The ratio of these cross sections is related to the ratio of the spin isospin transfer strength JaT and isospin transfer strength J , of the nucleon-nucleon interaction. This strong energy dependence may be used to selectively excite GT type transi­tions. Similar evidence exists for heavier targets. In fig. 9 the 0° cross section of the 90Zr(p,n)90Nb reaction is shown at 35 and 45 MeV (22) while in fig. 10 and fig. 11 at 120 and 200 MeV. The dominance of the Fermi transi­tion (IA) at 35 MeV disappears with increasing energy and at 200 MeV the giant GT resonances are the main visible peaks in the spectra.A similar type of information is presented in fig. 12 where the ratioarT(0°)/B(GT)R2 = “opTcPT/BTFyis presented versus incident energy. This ratio was obtained for several transitions with known B(GT) values. The value R is approximately equal to the ratio J0T/JT which is shown in fig. 13 compared to some theoretical predictions (23).In brief, the 0° (p,n) spectra and the energy dependence of JaT/JTTTallows a unique determination of transitions characterized by a AJ = 1  transfer.In the following figures (figs. 14-16) a set of (p,n) spectra displaysresults obtained from several targets ranging from 7Li to 208Pb. The aimnow is to obtain in each case the energy distribution of 1+ transitionsand to deduce GT strengths.From the measured cross sections, B(GT) values may be obtained from the relation1530exp<°°) ' KGT <EP >Not Jot B<GT>which is valid (24) for L = 0 (p,n) reactions at low momentum transfer.A similar expression is valid for Fermi type transitions. We have selected cases with known B(GT) values obtained from beta-decay and measured the 0°(p,n) cross section. Other quantities such as KGJ(E ), kinematic factor,D ^and Nqt> distortion factor, may be easily calculated. Thus the (p,n)measurement gives an empirical determination of J . In fiq. 17 some of theOTvalues obtained at 160 MeV are presented. The average value J = 151 ± 5 meV-fm3 is in good agreement with the value obtained by Love and Franey (25).A similar estimation for at 160 MeV is presented in fig. 18.It should be pointed out that B (GT) values obtained from (p,n) reactions by this procedure are absolute values normalized to beta-decay B(GT) values and do not depend on absolute cross section measurements.To obtain the total B(GT) strength, all the L = 0 transfer has to be located. For light nuclei it seems to be concentrated in single peaks (fig. 14). But for medium and heavy nuclei the GT strength is concentrated on giant resonances with isospin T = TQ - 1 (TQ is the target isospin). These are broad bumps (fig. 16) on top of a continuum. To estimate the L = 0 con­tribution one could estimate the location and strength of GT transitions from shell model calculations. In some cases, simple models reproduce quite well the observed spectra as is shown for the 5ItFe(p,n)51*Co reaction in figs. 19 and 20. A more realistic estimation may be done by using the measured angular distributions. The measured energy spectra is divided into 1 or 2 MeV wide regions at all measured angles. The observed angular distri­bution at each energy interval is then fitted with a summation of DW micro­scopic calculations with different L transfers. A sample of this analysis154is presented in fig. 21 for the 58Ni(p,n)58Cu case. This procedure gives non L = 0 contributions at 0° which may be substracted from the observed spectra to obtain just the L = 0 strength. This is shown in fig. 22 for the above case.Before I continue let me single out two interesting cases, a) the 39K(p,n)39Ca reaction. In this case the 6T strength is concentrated in states with (^3/2’d3/2_1 ^ Partic^e_*10le configuration (ground state transi­tion) and (^3/2,c*5/2_^^ con^19urat'’ons (excited states). The observed neutron groups characterized by L = 0 are indicated by an arrow in fig. 23 A preliminary analysis of the GT strength is shown in fig. 24 compared with the I  = 2 strength observed in the neutron pick-up from ‘*°Ca. The d,.^ sub-shell is fragmented in many states but it seems that both location and strength agree remarkably well in both reactions.b) In a simple shell model. shell nuclei should haveno GT strength. However, both in the 160(p,n)16F reaction (26) shown in fig. 25 and in the lt0Ca(p,n)‘t0Sc reaction shown in fig. 26, L = 0 transi­tions are observed. In both cases 1+ assignments are given, indicating at least 2p - 2h configurations in the gs wave functions of these double closed shell nuclei. See also ref. 27 for a detailed discussion.3. SUM RULES AND DISCUSSIONHaving obtained empirical observation of the total GT strength in several nuclei, it is possible to use a sum rule to estimate how much it is observed. A model independent sum rule may be established directly from commutators of the one-body operators t1 and the assumption that and t1 are one-body operators that can only change the direction of spin and isospin of nucleons. This assumption treats the nucleon as an entity with only spin and isospin degrees of freedom. Using closure one gets the sum rule (28)155V  • V  = 3 ( N - z )in units such that the free neutron decay has B (GT) = 3. This sum rule depends only on the neutron excess of the target nucleus and is independent of the assumed structure of the ground state. represents the total B(GT) in B" decay (or (p,n) reaction) while Sox is the total GT strength observed in B+ decay (or (n,p) reactions). In many cases, especially in heavy nuclei, the B+ decay is practically blocked by the Pauli principle and sg+ may be assumed to be zero. In other cases S^+ may be estimated from shell model calculations. In any case S0 > 3(N-Z) is a lower limit forp -  —the total (p,n) GT strength. A comparison of the measured total B(GT) tothe sum rule limit is presented in fig. 27 which gives a quenching ofabout 60 ± 10%. It should be recognized that this ratio depends on details like background subtractions and rw observation of L = 0 strength beyond ^ 20 MeV excitation energy in the cases studied.p f fThis quenching indicates (g^ /g^) ^ 0.8 in good agreement with obser­vations from beta decay (5,12) and magnetic moments (13).A different sum rule results if internal nucleon degrees of freedom are invoked, especially coupling to the A-isobars (M = 1232 MeV, T = Tz = 3/2). Several authors have discussed the effects of A-degrees of freedom in thestrength of the GT resonances (see ref. 17 and 18 for a complete ref. list).In all these studies the A-resonance coupled with a nucleon-hole (A-h) transfer part of the ax strength to an excitation energy region approximately 300 MeV above the observed low-lying GT resonance.To observe directly the GT strength in this high excitation energy region Gaarde et al. (29) have performed 2 GeV (3He,t) reactions; the 12C(3He,t) spectrum is shown in fig. 28. Similarly King et al. (30) have156done 0.8 GeV (p,n) reactions on several targets. The analysis of thedata is forthcoming; one of the difficulties is to extract GT strengthvalues, i.e. to extrapolate down to zero momentum transfer.Finally, as mentioned in section 1, the quenching applies to alltransitions involving the o • t operator. Ml transitions have been observedin (e,e‘) experiments (31) and recently in (p ,p ') experiments at 200 MeV (32). (figs. 29-31)The next three slides/illustrate a comparison of (e,e') (p,p‘) and (p,n) data. Certainly a study like that and a comparison of the observed B(GT) and B(M1) strengths is promising and may help in the understanding of no Ml excitation in (e,e‘) experiments such as the 51V(e,e') (33).The results presented here correspond to a collaborative effort by a group of the following people: C.C. Foster, C. Gaarde, C.D. Goodman,C.A. Goulding, D.J. Horen, J.S. Larsen, T.G. Masterson, E. Sugarbaker,T.N. Taddeucci and T.P. Welch.157158REFERENCES1. D.H. Wilkinson, Phys. Rev. C7 (1973) 930.2. D.H. Wilkinson, Nucl. Phys. A209 (1973) 470.3. D.H. Wilkinson, Nucl. Phys. A225 (1974) 365.4. B.A. Brown, W. Chung and B.H. Wildenthal, Phys. Rev. Lett. 40 (1978) 1631.5. F.C. Khanna, I.S. Towner and H.C. Lee, Nucl. Phys. A305 (1978) 349.6. E. Oset and M. Rho, Phys. Rev. Lett. 42^  (1979) 47.7. S. Ramau, C.A. Houser, T.A. Walkiewicz and I.S. Towner, Atomic Data and Nucl. Data Tables 21_ (1978) 567.8 . J.C. Hardy and I.S. Towner, Nucl. Phys. A254 (1975) 224.9. A. Bohr and B. Mottelson, Nucl. Struct. (Benjamin, NY, 1969), Vol. 1,pp. 345, 349, 411.10. A. Kropf and H. Paul, Z. Phys. 267 (1974) 129;D.H. Wilkinson, Prog. Part. Nucl. Phys. 6 ^ (1981) 129.11. C.D. Goodman and S.D. Bloom, Spin excitations in nuclei, edited byF. Petrovich (Plenum, New York, 1983) to be published.12. B.A. Brown and B.H. Wildenthal, to be published, MSUCL-413, May 1983.13. B. Buck and S.M. Perez, Phys. Rev. Lett. 50 (1983) 1975.14. M. Ericson, A. Figureau and C. Thevenet, Phys. Lett. 458 (1973) 19;M. Rho, Nucl. Phys. A231 (1974) 493.15. I.S. Towner and F.C. Khanna, Nucl. Phys. A399 (1983) 334.16. A. Arima and H. Hyuga in Mesons in Nuclei, edited by M. Rho andD. Wilkinson (North-Holland, Amsterdam, 1979), p. 683.17. M. Rho, Nucl. Phys. A396 (1983) 361c;M. Rho, AIP Conference No. 97, The interaction between medium energy nucleons in nuclei--1982, edited by H.O. Meyer (1983), p. 350.18. W. Weise, Nucl. Phys. A396 (1983) 373c.19. C.D. Goodman, et al., Phys. Rev. Lett. 44 (1980) 1755.20. C.D. Goodman, et al., IEEE NS-26 (1979) 2248.21. C.D. Goodman, et al., IEEE NS-25 (1979) 577.22. R. Doering et al.,Phys. Rev. Lett. 35 (1975) 1961.23. T.N. Taddeucci et al., Phys. Rev. C25 (1981) 1094.24. F. Petrovich, W. Love, R.J. McCarthy, Phys. Rev. C21 (1980) 1718.25. G. Love and M. Franey, Phys. Rev. C24 (1981) 1073.26. A. Fazely et al., Phys. Rev. C25 (1982) 1760.27. K.A. Snover et al., Phys. Rev. C27 (1983) 1837.28. C. Gaarde et al., Nucl. Phys. A369 (1981) 258.29. C. Gaarde et al., Phys. Rev. Lett. 50 (1983) 1745.30. N. King et al., Private Communication.31. A. Richter, Proc. 9 ICOHEPANS, Nucl. Phys. A374 (1982) 177c32. C. Djalali et al.,Nucl. Phys. A388 (1982) 1.33. D. Bender et al., Nucl. Phys. A398 (1983) 408.159160Fig. 1B ( G T )  quenching observed in £-decay80-40-Free  neutron-i 1---r 1---- 1-1-----1-1-----1-1-- r->10 20 30 40 50AM SU X-83-167Fig. 2161IUCF BEAM -SW INGER FA CILITYFig. 3MAINRFw v7YYVTTDISC.PULSESELECTOR1:5Fig. 4STOPTACSTARTNEUT DISC.DETEC vTO ADC162Fig. 5En (MeV)Fig. 6Fig. 7Fig. 8■«crl'f7joy164- If**/n o .  1. Hautroa tlma-of-fllfht spactram at f  «0 * for HZr(#.«>*Nb at E, O ft MaV. Expaotad EAS poaltftooa i r i  labalad with tha aacltatloo M trg lM  of tho pa root aaalog atataa ia **Zr.FIG. t .  Dtffaraotlal eroas aaotioa yaraua aautroo m r  •rfjr for ,lZ r (^ i )MHb at E, - 4 i  MaV aad Thaatralfht lina rapraaaata a backfrouad fit to ra«tooa adjacaot to tha broad paak aad lAft.Fig. 9165Fig. 10166CHANNEL run 6017-4Fig. 11167Ep (MeV)Fig. 13Coaparlaoa of tho oxporlaoatallydotoralaod ratio Co oovoral prodlctlooo boaod oa froo IMI latoractloo otudloo.Fig. 14Fig. 15ACl*mC IIJIO ■10* _ KLXTIIE Tlfl* •(«Fig. 16171Fig. 17Fig. 184 -txio4to m b200 <oE>0153 ' 173< ^ >  = 151+52 - 141Gamow-Teller ( 160 MeV )I-- 1006. . I2_Li C 26.. 42_ 51.. 70_Mg Ca V Zn "4Cd '44Sm1.0 2.0 3.01/34.0 5.0( N - Z )172Fig. 19e(p,n)5£<Co Ep = 160 MeVI| 2 O. i r 1  , 1-13  0 . '  14 0.) 1 5 0 . '  1 6 0 ; JNeutron Energy (MeV)Fig. 20— r~I 2  0 .JK 1 + states In 5l4CoShell-Model calculations Including 600KeV exp. width.C.Gaarde N.Phy. A3^6(80) U97i1 --------------- r130. 14 ou 1 isa.i 16010Neutron Energy (Mev)Fig. 22174Fig. 23Fig. 2410t*5•4 , : i i j | j irf- UO - -  * *  !ft:r*S C —  /• 2.1- f si+-•+••1- »  - *  ■ ■trrr'—  -r ! i i8(zr)\' T.tfl4 ~l,f-I : j ! i l li T ! TTrrTxrfTi't ; ■ T-r r -j; l:_  :  . } . . .  . . j - R RIT |I!. .. j—j .4- '*■* ■f* ■\ : U ±—  I. ;..• h : |• i  i 1  >• Jv .-.t v  : * •.. ..... j  . ,  ■ j  ■. . .  •.!•v  : . ■;  -  i- - 1  . . ,I.. . . . .:• t-1 1  ■!..... —  ...fLl—*. ••. • ' .. ;■ I -.• -r-*~.j...: ! •"‘IF i ,  jI—..... I <? •} ; ! -1 •:i • # '■ ti*rI j| 4..  +•ITTM• it • I l i ¥■ I .4U3(M6.)2X>n- W $i— i— r _0.t .!m4hI1~5. . ..:t - ?-*?-+•i*:L.i i175" 0 < p . n f 6F1 3 5 - 2  M « VFig. 25a6t>zooat1 0  5  0E X C I T A T I O N  E N E R G Y .  EX<M »V)F IO . S. Excitation energy spectra for the reaction at 13S.2 MeV. Spin and panty assignments for must of the states identified in this work are shown.a .  f a z e l y ei ml. PHYS.REV 25C(1982) 1760Fig. 26= 5-).* Am VV I ' 1  < 4 1176Fig. 27Fig. 28Fraction of GT-Sum Rule Observed in (p,n)EXCITATION ENERGY (MeV)C. t* c l ? * I S 0E 62060177I0I01 r-»-l—1 ) 8  6" F e f e . e ’J*4 F e ( p , p ' )e L - 4 *E,* l 6 0 M e t / *4 F e ( p , n )e - o *Fig. 29••toso.178o) Stole* seco(T«2), , I.H11? , T -MNi(T-l) n osk ' 12 ' k ' tEx(MeV) in “ CuMNi (e.e’)T---1--- 1 i— “i-- 1 re 12 6 0Ex(MeV) in MCuFig. 30179Fig. 31Giant Resonances —  Why Protons?Fred E. Bertrand*Oak Ridge National Laboratory*, Oak Ridge, Tennessee 37830Since the topic of this conference deals with the interaction of protons with nuclei it seems appropriate to ask what do we gain by the use of the protons for studies of giant resonances. We know protons excite giant resonances, indeed the systematic establishment of theexistence of the first non-dipole giant resonance, the giant quadrupole2resonance (GQR) came from the use of inelastic proton scattering. The question I will address, however, is how does the proton "stack up" for such studies when compared to the use of other hadronic probes? What can we uniquely learn about giant multipole resonances using proton scatteri ng.Specifically, I will compare results from (p,p'), (a,a1) and (160,160') reactions as regards excitation of giant multipole resonances and I will try to detail some of the advantages and disadvantages to theuse of each probe. I hope to leave the impression that it is in thedetermination of resonance multipolarity by comparison of measured and calculated angular distributions that the proton is a winner. I will show what we are learning about high-L (L > 3) giant resonances using the (p,p ') angular distribution. This discussion will generally belimited to isoscalar electric (i.e., T=0, S=0) giant resonances. Ofcourse, the proton provides the best hadronic probe for excitation of spin and isospin states, but these resonances are discussed elsewhere in the conference.If----------------Operated by Union Carbide Corporation under contract W-7405-eng-26 with the U.S. Department of Energy.B y acceptance of this article , the publisher or recipient acknowledges the U .S . G o ve rn m e n t's  rig h t to  retain a nonexclusive , ro ya lty -fre e  license in and to  an y c o p y rig h t covering the article.181182I will begin my discussion by describing a few things that ine­lastic proton excitation of giant resonances does not do very well,i) This field of study is not unique to proton scattering. Indeed,as will be discussed in more detail below, a great deal has beenlearned about giant multipole resonances from comparison of spectra from excitation by several different probes,ii) The use of inelastic proton scattering is not selective in excita­tion of any particular class of resonances as is the case for(p,n) reactions discussed earlier in this conference. Reference to Table 1 indicates this situation. We deal with four classes of possible giant resonance excitations, as denoted on the table by isospin (T) and spin (S) signatures, e.g., S=0, T=0 denotes non spin-flip and non-isospin flip. Familiar types of excitations of the various classes are also shown on the table. Since the proton is a particle with non-zero spin and isospin, it is clear that all four classes of excitations are excited in proton inelastic scat­tering. [Note, however, that proton excitation of T=0, S=0 states is several times stronger than that for the other classes of exci­tation. The excitation strength ratio between T=0, S=0 states and3states of the other classes is energy dependent, a fact that quite likely will be used to good effect to differentiate between a weak T=S=0 excitation and excitation of a different class of state.] For alpha particles, the lack of spin and isospin provides for essentially only T=S=0 excitation. On the other hand the (p,n) reaction only excites T=1 classes of states. These simple183considerations show why comparison of results from different reactions may help classify the nature of giant resonance excita­tions. Please note that the implications of Table 1 do not con­sider the Coulomb excitation by the incident particle. For example, although 160 has zero spin and isospin, the T=l, giant dipole4resonance is apparently strongly excited via the Coulomb field.TABLE 1voo(rij) + v, n(r. .)t.•x• + 10 ij i jvni(r. .) a. • o. 01 ij i J + v, i (r. .) a. • a- t. • Ti11 ij i j l JT=0 T=1 T=0 T=1S=0 S=0 S=1 S=1GQR GDR spin-flip Ml1st 2 ,3“ 2”,3+ Gamow-Tel lerIAS(P»P') (P,P') (P»P') (P»P')(a, a1 )(d,d1 )(p,n),(3He,t) (p,n),(3He,t)(6Li,6He)iii) Giant resonance excitations are not found as clearly separated narrow states as is generally the case in studies of low-lying states. This occurs both because resonance states having dif­ferent multipolarity can (and do) occur at the same excitation184energy, and, more importantly, because the giant resonance states are unbound and thus broad (2-10 MeV in general).Figure 1 provides a representation of transitions that might comprise various electric modes. The figure schematically repre­sents single-particle transitions between shell-model states of a hypothetical nucleus. Collective transitions result from coherent superpositions of many such single-particle transitions. Major shells are denoted as N, N+l, etc. and are separated by ~ lfioi or ~ 41 A-1/3 MeV. Giant resonances may be considered to result from transitions of nucleons from one major shell to another, under the influence of an interaction that orders these transitions into a coherent motion. The interaction for inelastic scattering can excite a nucleon by at most LRu, or, to state it differently, the nucleon can be promoted by at most L major shells. The number of shells is either odd or even according to the parity.Thus, the isovector giant dipole resonance (GDR) is built upof El transitions spanning lfim. The GDR might then be expected to-1/3be located at an excitation energy of ~ 41 A MeV; however, it-1/3is located at ~ 77 A MeV. This difference arises from the fact that the spin and isospin dependence of the nucleon-nucleon interaction ensures that the S=T=0 collective states move down in energy, and that S=1 or T=1 states move up from the expected energy.For E2 excitations two different classes of transitions are allowed. The first of these, with lowest energy, is comprised of185transitions within a major shell, the so-called Ohio transitions.A second set is comprised of transitions between shells N and N+2, the 2hu) transitions. These transitions would be pushed up or down in energy from 2fio) for isovector or isoscalar modes respectively. While the Ofio), E2, excitations are identified with the familiar low-lying 2+ levels, the 2(io) class carry most of the EWSR and are associated with the GQR. By similar arguments E3 excitations of lfiw and and E4 excitations of Oftu), 2ftu> and are expected.For each class of transitions (El, E2, etc.) the sum rule should be exhausted by the sum of the strength in all the tran­sitions. For example, for E2 transitions the sum rule should be exhausted by the sum of the strength in the Offu> and 2hoo tran­sitions.Clearly, this situation leads to the potential for giant resonance states of different multipolarity to overlap in the nuclear continuum. The possible confusion is further heightened when the spectra of giant resonance states are calculated with damping widths and estimates of their strengths.Figure 2 shows such a calculation for 208Pb by Serr,Bortignon and Broglia. These predicted results show in a more graphic way what was anticipated from figure 1 —  the even multi­polarity (and odd multipolarity), isoscalar giant resonances overlap in excitation energy. The calculations predict sum rule deple­tions of: L=2, 72%; L=3, 35%; L=4, 18%; L=5, 12%; and L=6, 12%.From these predictions we see that it is indeed a challenge to find a way to separate the different multipolarity giant resonances.Giant resonances excited by inelastic scattering are not amenable to precise cross section measurement. The root of this difficulty again lies in the lack of selectivity in the (p ,p') reaction -  the proton excites all types of states. This non-selectivity forggiant resonance excitation is illustrated in the data shown on figure 3. The spectrum shown is a complete proton spectrum obtained from bombardment of 51+Fe by 62-MeV protons. The spectrum is complete in the sense that all emitted protons are detected except for ~ 1 MeV of the spectrum at the very lowest end of the spectrum. The region of this spectrum above an excitation energy of » 10 MeV, contains only ~ 5% of the integrated inelastic cross section. At the highest excitation energy end of the spectrum (lowest emitted proton energy) a large peak is observed which is produced by the nuclear evaporation process. The rather flat region between the evaporation peak and the neutron separation energy is the nuclear continuum which is often described as arising from a pre-equilibrium particle emission process. Where is the giant resonance peak? It is the small bump located at ~ 16 MeV of excitation energy. While this particular spectrum was not selected to emphasize the resonance peak, the spectrum serves to illustrate why one does not make very precise giant resonance measurements -  the giant resonance cross section is only a part (often a small part) of the total. Figure 4 shows partial proton spectra7 plotted to emphasize the giant resonances for the 200 MeV (p,p‘) reaction on 208pb. The giant resonances have been fittedwith Gaussian peaks and the estimated shape and magnitude of the underlying continuum is shown as a smooth solid curve. Here we see that the "background" not only dominates the total cross sec­tion in the resonance region, but the "background" is not flat and changes with angle. It is assumed that the giant resonance cross section does not mix with the underlying continuum and the reso­nance peak is "stripped off" of the continuum (e.g., above the solid line in figure 4). Such an inexact procedure leads to uncertainties in the absolute giant resonance cross sections of at least 15-20%.v) Finally, it is not easy to measure the giant resonance spectra cleanly. We have often found that a clean spectrum in the discrete state region simply means that the background problems have been pushed into the continuum. Since the giant resonances appear as broad peaks in the high excitation energy inelastic spectrum, it is easy to mistake as giant resonances, peaks from scattering from such "nuclei" as the target frame, faraday cup, and beam pipe as all of these peaks appear as broad energy loss distributions in the continuum.So that one is not led by these previous gloomy comments to believe that all is lost there is an important advantage for giant resonance studies. Giant resonances are general properties of all nuclei and because of this the resonance features generally follow a smooth depen­dence on nuclear mass. Figure 5 shows an example of the variation of giant resonance parameters with nuclear mass for the isoscalar giant187188quadrupole resonance. Of particular interest is the predictable energy of the 6QR peak across a large part of the periodic table. This predic­table variation of resonance energy with target mass provides an excellent means to determine whether a peak in the spectrum arises from giant resonance excitation or happens to come from background. For this reason, the strongest arguments for the existence of new isoscalar giant resonances has come from measurements on several different mass targets.gFigure 6 shows inelastic spectra from five targets spanning a widenuclear mass range, bombarded by 152-MeV alpha particles. In eachspectrum a broad peak is observed at an excitation energy that variessmoothly with target mass. Prior to approximately three years ago the2entire peak in each nucleus was attributed to excitation of the GQR. (For the (a, a1) reaction the GDR is not excited to an observable extent.) However, as will be discussed below, we now know that (at least for nuclei heavier than about A=50) the peak contains monopole, hexadecapole (at least for Pb), and quadrupole resonances. The iden­tification of the resonance, i.e., the portion marked E2, as an L=2 excitation is provided by comparison of the measured angular distribu­tions with those calculated using the Distorted Wave Born Approximation (DWBA).Figure 7 shows a comparison between the (a, a1) and (p,p ') giant resonance spectra for 208Pb. The spectra have been normalized to the same number of counts in the continuum near channel 885. The spectra from the two probes are nearly identical. However, the (p,p‘) results show less low-lying structure since the resolution is ~ 1 MeV (FWHM)189compared to ~ 140 keV for the ( a , a 1) measurements. Nevertheless, for the two probes there is little to choose from as regards resonance enhancement over the underlying continuum. Figure 8 shows a comparison between the same (a,  a ' )  data and 400 MeV ( 160 ,  160 ' )  data^ on 208Pb.Again, the data have been normalized in the high lying continuum. The solid line under the peaks is drawn only to indicate the general extent of the underlying continuum. It is immediately clear that the heavy iondata provides a much larger peak to continuum ratio -  almost a factor oftwo larger than for the alpha results. A disadvantage to the ( 160 ,  160 ' )  spectra is the strong excitation of states in the 160 projectile which are seen (off scale) near 8 MeV of excitation energy. However, based on just these spectra one is certainly led to ask "Why protons?" Why not useonly heavy-ions for giant resonance studies?Part of that answer is shown on figure 9 which shows inelastic scattering spectra from 208Pb for 350 MeV and 400 MeV 150 projectiles.The GQR peak ( 1 0 . 9  MeV) and the peak from dipole and monopole resonance excitation ( 1 3 . 6  MeV) are found in the same position in the spectra for both incident energies. This is, of course, what would be expected if the peaks arise from excitation of states in 208Pb. However, at higher excitation energies, considerable structure is observed which moves in excitation energy as a function of incident beam energy! This signifies that the high excitation energy structure does not arise from excitation of states in 208Pb. Instead, the structure arises from the pick up reactions 160 + n + 170 *  -► 160 + n and 160 + p -► 17F* ■+ 160 + p. An analogous problem has been known to plague alpha-particle inelastic190scattering —  the a + n > 5He* > a + n reaction. These reactions, as isobvious from figure 9, can obscure giant resonance structure located inthe high excitation energy region and, worse, can produce peaks which can easily be misidentified as giant resonances. No similar problem exists for the case of proton inelastic scattering, making the proton high excitation continuum cleaner.However, the most serious problem for heavy-ion excitation of giant resonances is in the angular distributions. As shown in figure 10 the angular distributions for L=2, 3 and 4 are for all practical pur­poses, identical, and thus, useless for multipolarity determination. As an example, one might access the usefulness of the angular distributions for the case of detecting the presence of 10% of the T=0, L=4 EWSR located in the same peak with 100% of the T=0, 6QR EWSR. This case issimilar to that predicted on figure 2 for 208Pb. For heavy ions it isobvious from figure 10 that 10% L=4 plus 100% L=2 is completelyindistinguishable from anything else.Figure 11 shows the angular distributions for inelastic alpha par­ticle excitation of L=2 and L=4 states at 10.9 MeV in 208Pb. Beyond ~ 10 degrees, the shapes of the angular distributions for the two multipo­larities are nearly identical. Indeed, as indicated by the curve for 100% L=2 + 10% L=4 it is hard to distinguish that case from the pure L=2 curve. Inside of 10 degrees however, the first maximum of the L=4calculation occurs at the location of the first minimum of the L=2curve. Thus, over an approximately three degree wide region the prediction for 100% L=2 + 10% L=4 is considerably different from that191for L=2 alone. It is to be noted however, that this measurable dif­ference occurs at very small angles, where the measurement of clean giant resonance spectra is the most difficult.Angular distributions for 200 MeV inelastic scattering on 208Pb are shown on figure 12. In this case the angular distribution shapes for L=2, 4 and 6 are very different. (Odd L's, peak between the neighboring even L's.) Figure 13 shows our not completely hypothetical test case of 100% L=2 + 10% L=4. The difference between the sum curve and the pure L=2 curve occurs, as in the alpha-particle case, at the first maximum for the L=4 curve which is coincident with a deep minimum in the L=2 curve. However, in the proton case this difference occurs at fairly large angles where clean measurement of giant resonance spectra is con­siderably easier than at 3-5 degrees. Furthermore, the difference between the L=2+4 and L=2 angular distributions extends for several degrees.Figure 14 shows angular distributions for the L=l, GDR (isovector), L=0, GMR and, L=2, GQR. The fact that the GDR is excited in proton scattering provides both a problem and an opportunity. The problem lies in the fact that the GDR overlaps the GMR (and possibly other resonances) and prevents clear observation of the monopole. The oppor­tunity presented is to cleanly measure the inelastic cross section for the GDR at small angles. This opportunity arises because at small angles the GDR is very strongly Coulomb excited by medium energy protons whereas other multipolarities are affected to a much smaller degree by Coulomb excitation. From the angular distributions on figure 14 one would expect the giant resonance spectrum to be dominated by the GDR at very small angles.192gFigure 15 shows spectra (in the giant resonance region of excita­tion energy) from 200 MeV proton inelastic scattering on 90Zr and 120Sn. Data are shown at angles which should provide maximum cross sections for excitation of L=l, L=2, and L=3 states. At 4°, a large peak is observed which is located at the excitation energy of the GDR. The solid curve shown on the 4° data is the GDR shape and energy from (y,n) measure­ments,^ with magnitude fitted to the data. The GDR accounts for virtually the entire observed peak at 4°. The GMR is located at nearly the same energy as the GDR but the DWBA calculations (e.g., fig. 14) indicate that the GMR cross section is at least an order of magnitude smaller than that of the GDR at 4°. Since the El cross section drops rapidly with increasing angle, the EO cross section becomes increasingly more important compared to the El at larger angles. The 8° and 10° spectra were obtained at a maximum for the L=2 angular distribution for 90Zr and 120Sn, respectively. The solid curve, taken from the shape andglocation of the GQR as determined from (a, a') measurements, provides excellent agreement with the present data. The cross section for the GDR at the larger angles is greatly reduced from that observed at 4°.It can be assumed that at these angles, the cross section in the excita­tion energy region where GDR is located is comprised of GDR and GMR com­ponents in unestablished proportions. In the 12° spectra broad peaks, seen somewhat less clearly at 8° and 10°, are observed at 25 ± 1 and 27 ± 1 MeV in 120Sn and 90Zr, respectively. As we discuss below, these peaks are from excitation of the 3ftuj giant octupole resonance.193The spectra of figure 15 and the angular distributions of figures 12 and 13 demonstrate the ability of medium energy inelastic proton scattering to provide multipole selectivity for giant resonances that has not been achieved through the use of other direct reaction probes. However, before considering some examples of the use of this virtue of proton inelastic scattering we must consider another aspect of inelastic scattering of giant resonances, namely, whether the strength of the resonance excitation can be correctly deduced from the results. Fordirect reactions using hadrons the transition rate [B(EL)] for excita­tion of a state having multipolarity, L, is deduced by comparison of measured angular distributions with those calculated by use of the Distorted Wave Born Approximation (DWBA). This procedure has been established over many years by excitation of low-lying states.Comparison of the calculated cross section with that measured yields the so called deformation parameter, B|_, as:„? _ da(L) measured , da (L) calculated t  ‘ da ' daIf 3|_ is proportional to the mass multipole moment for a uniform distri­bution thenFor excitation of giant resonances it is appropriate to describe thestrength in terms of the energy weighted sum rule which can be 2written in terms of s,2 as:1942 = 2nK2 L(2L+1) I  ^  60L(2L+1)^  “ 3m AR2 E a 5/3 Eif R = 1.2 A 1/3fm and e = excitation energy in MeV.The important question is whether inelastic proton scattering providesthe correct B(EL) via the deduced e2. This has been often demonstratedfor proton energies below ~ 100 MeV. However, for energies in the 200MeV range it was predicted that use of the collective model DWBA mightover predict inelastic cross sections by at least a factor of two.There are now reports9,11 that such is the case although no systematic12experimental study has been made. We have recently measured inelastic scattering on 208Pb at 333 MeV using the LAMPF, HRS facility with - 7 0  keV (FWHM) energy resolution. Preliminary results for ine­lastic excitation of the 2.615 MeV, 3", state indicate an approximately factor of two difference between the data and a collective model DWBA calculation using e2 deduced from the B(E3) measured by Coulomb excita­tion. Similar results were obtained from poorer resolution measurements on 208Pb using 200 MeV inelastic proton scattering. Thus, we conclude that the use of the collective model DWBA to extract cross sections from medium energy (200-500 MeV) inelastic proton scattering may be unreliable. For this reason the EWSR results discussed below from 200 (p,p 1) measurements have been obtained by normalizing the calculations to the cross sections for low-lying states.Proton scattering has been responsible for the systematic obser­vation of several of the so-called "new" or "multipole" giant resonances. The first of these resonances, the GQR was initially systematically observed13 through 62-MeV inelastic proton scattering in 1971. In fact,the GQR was actually observed1^ in 185-MeV (p,p ‘) measurements made nearly 15 years before this. However, the broad peaks observed were incorrectly identified as arising from excitation of the giant dipole resonance and the studies were dropped. Figure 16 shows a comparison for the resonance peak in iron nuclei between the 1956, 185-MeV measurements and the 1971, 62 MeV proton inelastic scattering data. Clearly the peak is identical in shape in both measurements and not located at the GDR location (marked in figure) which we know so well today from photonuclear reactions.Another giant resonance first observed via inelastic proton scat­tering is the 3hu) giant octupole resonance (GOR). Figure 17 shows spectra15 from the 800 MeV (p,p 1) reaction on 208Pb, 116Sn and 40ca.The data show strong excitation of the GQR for each nucleus and exci­tation of a broad peak located higher in excitation energy, labeled HEOR. The angular distributions for the high excitation energy peaks are shown in figure 18 compared with DWBA calculations for L=2, 3 and 4.In each case, the data are very well reproduced by the L=3 calculation,but not matched at all by the L=2 or 4 shape.9Angular distributions from the high excitation energy peak (labeled E3 in figure 15) excited in 90Zr and 120Sn by 200 MeV inelastic proton scattering are shown on figure 19. The data agree very well with the shape of the calculated angular distribution for L=3 but not at all with the L=4 curve. From the 800-MeV and 200-MeV (p,p ') measurements and 172 MeV (a, a1) measurements,15 the peak has been interpreted as arising from excitation of the 3haj giant octupole resonance. Figure 20 shows195196the properties of the 60R obtained from the different experiments. Asis expected for a giant resonance, the excitation energy of the GOR1/3follows a smooth mass dependence, Ex ~ 120 A MeV. The dashed curves for the excitation energy and width are from the calculations^ of Nix and Sierk.As the angular distributions (figs. 18, 19) show, the GOR peak does not seem to contain L=2 or L=4 strength. However, reference to figures 1 and 2 shows that one would not expect to find mixture of L=4 strength in the 3lTu, L=3 resonance since the L=4, 2fico strength is expected to lie at lower excitation energies than the 3Kco, L=3 state and the L=4, 4(ico would be expected to lie at higher energies. A more likely possibility according to the calculations is to find L=5 (3tfw) strength at the same energy as the GOR. Figure 21 shows angular distributions measured in 200 MeV inelastic scattering for the giant octupole resonance peak for five nuclei. For each nucleus, the curves show DWBA calculations for L=3 alone normalized to the data at forward angles, an L=5 calculation for an EWSR depletion taken from or assumed to be similar to that suggested in reference 5, and the sum of the L=3 and L=5 curves. The calculations show that L=5 strengths should be observable by the distinct difference between the L=3+5 calculation and the pure L=3 curve. This difference, as is the case for L=2 and L=2+4, arises from the fact that the L=3 and 5 angular distributions peak several degrees apart. For 60Ni, 90Zr, and 120Sn the data are well described by the pure L=3 curve, yielding no evidence for L=5 excitation. On the other hand, the data for the heavier nuclei, 208Pb and 238U, are better described by a sum of L=3+5 than the pure L=3 calculation. Thisapparent disparity between the light and heavy nuclei could possibly beexplained by the fact that an L=5, 3hu> resonance would be much narrowerin heavy nuclei than in light nuclei. Such is certainly the case forthe low-L giant resonances where the resonance width very closely 1 17 -2/3follows * an A" dependence. Thus, in light nuclei the strength might be too spread out to provide any significant angular distribution differences from the dominate L=3 shape. At best one might say that there is some evidence in heavier nuclei for the presence of L=5 strength at 3pfu). However, the results do not provide a definitive answer, only suggestions.I now return to the question of the possible admixture of 2Ka), L=4 and L=6 strength in the peak at 63 x A“1/3 MeV, the peak which is cer­tainly predominately the L=2, GQR. Figures 22 and 23 show cross sec­tions for excitation of the GQR peak (labeled E2 on figure 15) for 200 MeV inelastic proton scattering on 60Ni, 90zr> I20sn, 208pb and 238u.On figure 22, the curves are from DWBA calculations for L=2 (normalized to the data in first maximum and yielding the EWSR depletion indicated) and (dashed curve) the L=2 calculation with 10% of the L=4, EWSR added. For the 12osn, 208pb and 238u results, the data are better fitted by the dashed curve than the solid curve. For 90Zr the data would be well described10 by the sum of 60% L=2 and 5% L=5. Although the 60Ni are better described with 10% L=4 added to the L=2 curve, it should be noted that the angular distribution for the low-lying, 1.33 MeV, 2+, state in 60Ni also describes the giant resonance angular distribution shape extremely well. Thus the agreement with the 10% L=4 may be fortuitous.197198The same data are shown on figure 23, and the the solid curves show L=2 calculations as in figure 22 but now L=4 and L=6 calculations are shown with EWSR depletions suggested by the calculations of reference 5. Of course, as expected from figure 22, the addition of some L=4 strength to the L=2 calculation improves the fit for the heavy nuclei. However, the addition of L=6 strength, at least in the amounts indicated, seems to be unsupported by the data. For each nucleus, the resonance cross section drops in the angular region where any L=6 contribution would be present to "pull" the experimental angular distribution up, and away from the pure L=2 or L=2+4 curves. This result should not be taken to imply a complete lack of L=6 strength in this excitation energy region. Rather, the results imply that any L=6 strength is very spread out so that the "E2" peak would contain only a fraction of the L=6 EWSR, a fraction that might be too small to make an observable change in the experimental angular distributions.Heretofore the evidence for the existence of 2Ku>, L=4 strength from inelastic proton scattering, and for that matter also from inelastic alpha particle scattering, has come only from comparison of calculated "pure" L=2 angular distributions and L=2+4 angular distributions with the data. No direct observation of a peak from excitation of a giant hexa-decapole resonance (GHR) had been made. The data on figure 24 show what18we believe to be evidence for observation of such a peak. The figure shows giant resonance spectra from 200 MeV proton inelastic scattering on 208pb and 206Pb. The eight degree spectra (peak of the L=2 angular distribution) show very strong excitation of the GQR (E2 peak) with199another peak at 13.6 MeV from excitation of the GMR and GDR (E0+E1).The data at larger angles on both nuclei show a distinct shift of theresonance peak to higher excitation energy. Attempts to fit the largerangle spectra with only the E2 and E0+E1 peaks (with position and widthfrom the eight degree fit) result in a very poor match to the data. Agood fit to the large angle spectra is achieved only by including, forboth nuclei, a third peak located at 12.0 MeV having a width of 2.7 MeV.The same result was obtained, as shown on figure 25, for excitation of12giant resonances in 208Pb by 333 MeV protons. These measurements were made using the LAMPF, HRS facility with 70 keV (FWHM) energy resolution. Again, the larger angle data are qualitatively different from that taken at smaller angles. At the small angle one observes two rather distinct peaks from excitation of the GQR and GMR+GOR, while at the large angle only a single broad peak is observed with a centroid that is between the two peaks. The shapes of the GQR and GMR+GDR peaks from the 5.25 degree data are shown on the 10.25 degree results and those peaks alone cannot explain the data. As was the case at 200 MeV, a third peak located at 12.0 MeV, 2.7 MeV wide, is needed to adequately fit the spectra.Figure 26 shows the angular distribution for the 12.0 MeV peak from the 200 MeV measurements along with the forward angle cross sections for the GQR peak (larger angle cross sections were deleted for clarity). The 12.0 MeV peak cross sections are very well described by a shape of the L=4 DWBA calculation, but not by neighboring multipolarities. The results yield an EWSR depletion of 10% ± 3 if the calculations are nor­malized to 75% EWSR depletion for the GQR in 208Pb. From these results200on two different nuclei, two different beam energies, and using two dif­ferent accelerator facilities, we believe the change in spectral shapein figures 24 and 25 arises from the excitation of the 2lfu>, GHR. Theposition, width and EWSR depletion are in reasonable agreement with the predictions of Serr et_ a K  (ref. 5).To summarize, I hope I have shown that while proton excitation is not the only way to excite giant multipole resonances, and in some cases it may not be the best way, nevertheless there are distinct advantagesto be gained from medium energy protons.201References1. Many of the results presented in this talk were obtained in colla­boration with: E. E. Gross, D. J. Horen and T. P. Sjoreen, Oak Ridge National Laboratory; J. Lisantti, J. R. Tinsley and D. K. McDaniels, University of Oregon; L. W. Swenson, Oregon StateUni versity.2. Fred E. Bertrand, Annual Review of Nuclear Science ^ 6, 457 (1976). "Giant Multipole Resonances," Proceedings of the Giant Multipole Resonance Topical Conference, Oak Ridge, Tennessee, October 1979, ed. Fred E. Bertrand (Harwood Academic Publishers, New York,1980). Fred E. Bertrand, Nucl. Phys. A354, 129c (1981).3. W. G. Love and M. A. Franey, Phys. Rev. C 2A_, 1073 (1981).4. T. P. Sjoreen, F. E. Bertrand, R. L. Auble, E. E. Gross, D. J.Horen and D. Shapira, submitted for publication.5. F. E. Serr, P. F. Bortignon, and R. A. Broglia, Nucl. Phys. A393, 109 (1983).6. F. E. Bertrand and R. W. Peelle, Phys. Rev. C 8 ,^ 1045 (1973).7. D. K. McDaniels, J. R. Tinsley, J. Lisantti, D. M. Drake, I.Bergqvist, L. W. Swenson, F. E. Bertrand, E. E. Gross, D. J. Horen,T. Sjoreen, R. Liljestrand and H. Wilson, to be published, Phys.Rev. C.8. F. E. Bertrand, G. R. Satchler, D. J. Horen, J. R. Wu, A. D.Bacher, G. T. Emery, W. P. Jones, D. W. Miller and A. van derWoude, to Phys. Rev. C 22^ , 1832 (1980).2029. F. E. Bertrand, E. E. Gross, D. J. Horen, J. R. Wu, J. T. Tinsley,D. K. McDaniels, L. W. Swenson and R. Liljestrand, Phys. Lett.103B, 326 (1981).10. B. L. Berman and S. C. Fultz, Rev. Mod. Phys. 47, 713 (1975).11. C. Djalali, N. Marty, M. Morlet and A. Willis, Nucl. Phys. A380, 42 (1982).12. Preliminary results: F. E. Bertrand, D. J. Horen, T. P. Sjoreen,D. K. McDaniels, J. Lisantti, L. W. Swenson, J. R. Tinsley, T. A. Carey, K. Jones, J. B. McClelland and S. Seestrom-Morris.13. M. B. Lewis and F. E. Bertrand, Nucl. Phys. A196, 337 (1972).14. H. Tyren and Th. A. J. Maris, Nucl. Phys. 4_, 637 (1957); 6^, 446(1958); _7, 24 (1958).15. T. A. Carey, W. D. Cornelius, N. J. DiGiacomo, J. M. Moss, G. S.Adams, J. B. McClelland, G. Pauletta, C. Whitten, M. Gozzaly, N.Hintz and C. Glashausser, Phys. Rev. Lett. 45, 239 (1980).16. H. P. Morsch, M. Rogge, P. Turek and C. Mayer-Borieke, Phys. Rev. Lett. 45, 337 (1980).17. J. Rayford Nix and Arnold J. Sierk, Phys. Rev. C 2\_, 396 (1980).18. J. R. Tinsley, D. K. McDaniels, J. Lisantti, L. W. Swenson, R.Liljestrand, D. M. Drake, F. E. Bertrand, E. E. Gross, D. J. Horen and T. P. Sjoreen, to be published in Phys. Rev. C.FIG. 1. Schematic representation of electric multipole transitionsbetween shell-model states of a hypothetical nucleus. Major shells are denoted as N, N+l, N+2, etc. and lie ~ IKToj or ~ 41 x A ~ ^  MeV apart.FIG. 2. Giant resonance spectra calculated for 208Pb from reference 5.FIG. 3. Proton spectrum at 27° from 62 MeV protons in 59Fe. Theenergy of the outgoing proton is plotted at the bottom of the figure, while the approximate excitation energy is plotted at the top. Data have been plotted in ~ 1 MeV-wide bins up to ~ 49 MeV, then plotted in 50 keV-wide bins. Protons below ~ 1.5 MeV were not detected in the experiment. The small, broad peak near Ex ~ 16 MeV is identified as arising from excitation of the giant quadrupole and dipole resonances.FIG. 4. Giant resonance spectra at 8, 12, 16, and 20 degrees from 200MeV proton inelastic scattering from 208Pb. Fits to the various reso­nance peaks are shown along with the assumed shape of the continuum underlying the resonances.FIG. 5. Systematics for the excitation energy, width and sum ruledepletion of the isoscalar giant quadrupole resonance.FIG. 6. Spectra from inelastic scattering of 152-MeV alpha-particleson 208Pb, 120Sn, 90Zr, 58Ni and 96Ti. The giant resonance structure-1 /3located near the excitation energy 63 x A ' MeV has been decomposed into contributions from the giant quadrupole and giant monopole resonances. The peak located at higher excitation energy in the 208Pb and 120Sn spectra are due to hydrogen contamination of the target.203F i g u r e  C apt io ns204FIG. 7. Comparison between giant resonance spectra from 208Pb asexcited by the (p,p 1) and (a, a1) reactions at 200 MeV and 152 MeVrespectively. The data are normalized in the continuum.FIG. 8. Comparison between giant resonance spectra from 208Pb asexcited by the (a,a1) and (160,180') reaction at 152 MeV and 400 MeV,respectively. The data are normalized in the continuum.FIG. 9. High excitation energy inelastic scattering spectra from 208Pb for 400 MeV and 350 MeV 160 projectiles. The results show that the structure observed above 220 MeV of excitation energy does not arise from excitation of states in 208Pb.FIG. 10. DWBA calculated angular distributions for the reaction (ISO,i50') at 400 MeV in 288Pb.FIG. 11. DWBA calculated angular distributions for L=2, L=4 and L=2+4excitations in 208Pb via the (a,a1) reaction at 152 MeV.FIG. 12. DWBA calculated angular distributions for L=2,4 and 6 exci­tations in 208Pb via the (p,p‘) reaction at 200 MeV.FIG. 13. Calculated angular distributions for 200 MeV proton inelastic excitation of a state at 10.6 MeV exhausting 100% of the L=2, EWSR, and exhausting 100% of the L=2 and 10% of the L=4 EWSR's.FIG. 14. DWBA calculated angular distributions for excitation of L=0,L=1 (T=l), and L=2 states in 208Pb via the 200 MeV (p,p 1) reaction.FIG. 15. Spectra from inelastic scattering of 200-MeV protons from 90Zr and 120Sn. The multipolarities shown for the resonances are discussed in the text. The dashed line shows the shape and magnitude assumed for the nuclear continuum underlying the rsonance peaks.FIG. 16. Comparison of the giant resonance peak observed in iron nuclei using inelastic scattering of 185 MeV protons (ref. 14, 1957) and 62-MeV protons (ref. 13, 1972).FIG. 17. Inelastic spectra from 800 MeV protons on 208Pb, 116Sn and 40Ca. The peak labeled HEOR (high energy octupole resonance) is interpreted as arising from excitation of the isoscalar giant octupole resonance (3fia>).FIG. 18. Angular distributions for the giant octupole resonance as excited by 800-MeV protons.FIG. 19. Angular distributions for the GOR in 90Zr and 120Sn excited by 200 MeV protons compared with DWBA calculations (solid and dashed curves).FIG. 20. Systematics of the excitation energy, width, and sum rule depletion for the isoscalar octupole resonance.FIG. 21. Cross section for the "octupole" resonance peak (labeled E3 on figure 15) in five nuclei excited by 200 MeV protons compared with DWBA calculations for L=3 and L=5 excitation.FIG. 22. Cross sections for the "quadrupole" resonance peak (labeled E2 on figure 15) in five nuclei excited by 200 MeV protons compared with DWBA calculations for L=2 and L=2+4 excitations.FIG. 23. Cross sections for the "quadrupole" resonance peak (labeled E2 on figure 15) in five nuclei excited by 200 MeV protons compared with DWBA calculations for L=2, L=4, L=6 and sums of those excitations.FIG. 24. Giant resonance spectra from inelastic scattering of 200 MeV protons from 208Pb and 206Pb. The multipolarities shown for the reso­nance peaks are discussed in the text. The solid curve under the205206resonance peaks shows the shape and magnitude assumed for the nuclear continuum underlying the resonances. The shapes of the individual reso­nance peaks and the sum of the assumed continuum and peak shapes are shown.FIG. 25. Giant resonance spectra from inelastic scattering of 333 MeV protons on 208Pb. The smooth solid curve under the resonance peaks show the shape and magnitude assumed for the nuclear continuum underlying the resonances. The shapes of the individual resonance peaks and the sum of the assumed continuum and peak shapes are shown.FIG. 26. Experimental angular distributions for the 12.0 MeV peak and the GQR peak (forward angles only) compared with L=4, 3 and 2 DWBA calculations which are denoted by the solid, long-dash and short-dash curves, respectively. The EWSR depletions shown were obtained by nor­malizing the L=2 calculation to the GQR cross section as discussed in the text.ORNL-DWG 80-1576920730=sJ"3CO30=o3ro33»#=00Ll I3OroLl ICOLl I3 —>J= LU208CNIC3( A 9 m  ( 3 ) di-209ininoOJin>  00 o5O  x roLl Ininrooinomi i i i | i i i i | i i i i | i i i i | i i i i | i i i i ; i i i i | i r ti i i | i i'i i inCDIDtroLlI CP -'>« S <UQ. n  S  CD LJ ^Z  CM ^g  0, 0O J l. ..UJJ—1—L l I l l l l 1 I I I I 1 I I I 1 1 1 I I I 1 l l I l 1 I I I I 1 I I I I 1>  in a> cn 5LlIZLlIinCMoCMin□in• • • • • • o □ O Oo CD CD zr CM O • • • •CM f * *—* *—* CO CD 3* CMA 3 W / d S / G Wcr\CDCOUNTS/CHANNEL210EXCITATION E N E R G Y  ( M e V )FIG. hT=0, E2 EWSR RESONANCE WIDTH K/ DEPLETION (%) (FWHM) (MeV) ExA3(MeV)211O R N L -D W G  8 0 - 1 5 7 7 0  I S O S C A L A R  Q U A D R U P O L E  R E S O N A N C E8642S t \  w i d t h  * S v  o ..-2/3i.1i i*i i V $ - i — INUCLEAR M A S SFIG .  5212ORNL-DWG 80-40201EXCITATION ENERGY (MW )FIG. 6ORNL-DWG 83-15562213O000)O100)Oo>ooo<T>OO<T>O0000O  O  OO  Q  OO  O  O00 N- toO  O  Oo  o  oO  O  oif) ro13N N V H D /S lN n0DO  O  OO  OO  Ooj —CHANNELCOUNTS214O RN L-D W G  8 2 -1 8 2 5 64 0 0 03 5 0 0  —3 0 0 02 5 0 020001 5 0 0  —10005 0 0  —16 14 12 10 8E X C I T A T I O N  E N E R G Y  ( M e V )FIG. 0COUNTS215O R N L - D W G  8 3 - 1 0 8 9 4EXCITATION ENERGY (MeV)FIG.  9FIG. 9(js/quu) UP/-°P216ORNL-DWG 83-14678ec.m.(de9 )FIG.  10217ORNL-DWG 83-146790 10 15 20 2 5 3 0 3 50c.mJdeg }FIG.  11dcr/dXl (mb/sr)2180  5  10 15 2 0  2 5  3 0  3 5®c.m.(de9)F IG .  12(js/quu) UP/-°P219ORNL-DWG 83-146810  5  10 15 2 0  2 5  3 00c.m.(de<3>F I G .  13220ORNL-DWG 83-14683< W de9 )FIG. ]k3502501505004003002001000*800600coH8 2402001601208011009007005001100900700221ORNL-DWG 84-5587EXCITATION ENERGYFIG.  15(mb/sr • MeV)2223.23.02.82.62.42.22.01.81.6ORNL-DWG 72-4460I i  i i i► K 0,Fe ( ' 0 . 2 ° )  f p = l 8 5  MeV ►^5 6 Fe ip.tp) o-norm{ 2 0 ° )  f p  =  6 l  MeV□  Dl aPOLE ( £ 0 ) FOR =  5 6  SYSTEMATI5 8 Ni (M!  CS (REFEASURED6)) OR'Tf t°l ' ‘ I—►1! *LE-1- j4h- M b - £ f-4 - r ^ r  t1 - r.. m L .11 13 15 17 19 21EXCITATION ENERGY (MeV)2 3 2 5FIG.  16COUNTSORNL-DWG 80-15703E x (MeV)FIG.  17(js/quu) up/xip224ORNL-DWG 80-15707F I G .  18dcr/d U (mb/sr)225O R N L - D W G  82-11414^ c . m .  ( d e g )F IG .  19T=0, E3 EWSR RESONANCE WIDTHDEPLETION (%) (FWHM) (MeV) Ex A (MeV)226ORNL-DW G 8 0 -1 5 7 7 4  ISOSCALAR O C T U P O L E  R E S O N A N C E  ( 3 f i w )1 4 01208 04 00r  •  ( 3 He,  3 H e / ) 1 1 0 - 1 4 0  M eV100%tS U M  R U L E2Y20 6 0  1 0 0  1 4 0N U C L E A R  M A S S1 8 0 220FIG.  20227FIG. 21228ec.m.l<,e9>FIG.  22229ORNL-DWG 83-14686®c.m.<deg>FIG. 23ORNL-DWG 83-9849230s i N n o oEXCITATION ENERGY (MeV) EXCITATION ENERGY (MeV)231— T I------------ 1----------- r------------1-----------:.= 131 4 7 9  > < Y= 0 1 2 0 0 0 )D L IN  £ 5 1 3 8 4 2  CTS 1 1 'S . Z S  J e j* ° ' r b  e t ? ' )? 3 3  t u . *FIG. 25102521015210°521CT152ORNL-DWG 8 3 - 9 8 5 0208 P b (  p, p')E p =  2 0 0  M e VE x =  1 2 . 0  M e V  T  =  2 . 7  M e Vh/  i \G Q R ;  E xr 1 0 . 6  M e V  2 . 4  M e V\ L =  2  7 5 %  E W S RI\10 15® c . m . < d e 9 )2 0 2 5F I G .  2 6III. QUASI-FREE SCATTERING AND REACTIONSQUASIFREE SCATTERING AND KNOCKOUT233N. S. ChantDepartment of Physics and Astronomy University of Maryland, College Park, Maryland 207429 July 1983IntroductionWith the new TRIUMF spectrometers and with the new IUCF spectrometers it should be possible to take data for reactions of the type A(a,cd)B lead­ing to three-body final states which have much better energy resolution and statistics than has been possible in the past. If we select detection angles and energies close to the values for the free a+b->c+d reaction we can expect the mechanism suggested by the diagram shown in Fig. 1 to dominate the reaction. We refer to this process as quasifree knockout.From the PWIA expression it is clear that we can, at least in principle, obtain information both on the spectroscopic factor and momentum wave func­tion for particle b in the target and on the two-body a+b cross section responsible for its removal.At the IUCF workshop I discussed some of the considerations relevant to studying the upper vertex, specifi­cally the nucleon-nucleon interaction in (p,2p) and (p,pn) experiments.^Clearly there is a great deal of phys­ics in the lower vertex as well, namely the spectroscopic factor distribution, or spectral function, and the individ­ual momentum distributions. In addi­tion, other reactions such as (p,pd) or (p,pa) can provide information onclustering and on nucleon-cluster in-2teractions in nuclei.Firstly, I should like to provide some background on current distort­ed wave impulse approximation calculations for quasifree knockout. Second­ly, I will summarize points made earlier concerning measurements of theA(i.c4)l•«kK -  klaoootlc factor -  opoctroscoplc factor ♦ (-P g ) -  H  M M B tio  oovc t a c t io no-k 2-kody cross •action V k  for o*k«c*4F i g .  l234nucleon-nucleon interaction in the nuclear medium. With this out of the way I will turn to some of the other aspects of (p,2p) reactions. Finally, I should like to discuss some possibilities for other reaction studies including cluster knockout processes.2. Theoretical BackgroundAlthough distorted wave impulse approximation calculations have been3 4published for (p,2p) reactions using a local pseudo-potential, ’ most current analyses of experimental data employ a factorized calculation ’ as outlined in Fig. 2, in which the two-body t-matrix is evaluated for the asymptotic kinematics. This, of course, is a half-shell t-matrix since the struck nucleon is bound. Frequently, experimentalists make the addi­tional approximation of replacing the half-shell t-matrix by a nearby on- shell value chosen according to some prescription such as equating the initial or final relative scattering energies. Nevertheless, according to the factorized DWIA it is the half-shell nucleon-nucleon cross section which is accessible to (p,2p) experiments.A(s,cd)BPKIAc o ct - kinematic factor- spectroscopic factor A**B^b t(-Pg) - b-B aonentua wave functiondo - half-shell a-b 2-body cross sectiondfi‘a^b for a^b**c*dOKI A!♦!* - IIt'oLA |whereDWIA with Spin-Orbit Distortions Optical potentials:V 4 i w  ■» v ♦ i  n  ♦ v  !•»SODistorted wives:x(1) -  x(l5* *po P.O ■ t'THence:Tn U  -  t°iLAW e ”c“d“d* , • *. incident/emitted distorted wives- bound state wave function for b calculated LA - -end (for p,2p) dSodfi dfi.dE, c a c • ' • S IS°c°aI ( L A * P b |J>0baocin hoods-Saxon well ,1/jV(r)l t d  4 t oLAl°iec°c“d“dl*ex *♦ V.so Coulomb<||> - p.p 4-shell t-mitrixI Notice: fictorixition of amplitudes, not cross section.Fig. 2Q(8)mb/sr235(a). Factorization TestNotes:1) For an L=0 transition take data at various 6c>6d such that Pg = 0.2) Compute,3 EXPT ft , . 2/ K l ' T  1c  d  c  '  A6* - two-body c.m. scattering angle.{} - varies slowly (a K in PWIA)3) No spin-orbit DWIA predicts Q(0*) =a+b*— 1 --W “ 148.2i A .. ♦.IT T ----- * ........ 101.3, — *- f4 ------j -T--------►..ri------A:-----A------4=----V---454 f )  3 Q  *(b). Ca(p,2p) K (2.52 MeV)L=0 factorization test at E = 45,76.1, 101.3, and 148.2 MeV.P  DWIA (no spin orbit)i.e., do/dn (pp)  DWIA (spin orbit distortionsincluded).toe. (deg)TABLE I40C a (p ,2 p )39K (2 .5 2  MeV 2S1/2)  L=0EPMeVSpectroscopicFactorRatioDKIA/PWIAIUCF 148.2 0.98 ±0.04 0.22MD 101.3 0.88 ± 0.04 0.10MD 76.1 1.09 + 0.07 0.03MANITOBA 45.0 1.18+ 7 0.01Fig. 3In Fig. 2 we see that, while the half-shell a-b cross section appears as a multiplicative factor in the DWIA expression provided spin-orbit terms are not included in the optical potentials, when these terms are includ­ed a more complicated expression results involving a sum over products of spin dependent amplitudes. I shall discuss examples of the influence of spin-orbit terms in the distorting potentials later.At the IUCF workshop I discussed in some detail methods of improving the current factorized calculations. This is, I believe, essential. The improvements in experiental techniques must be matched by correponding advances in the reaction theory if we are to take maximum advantage of a potentially rich field of study. Improvements aimed at eliminating or alleviating the factorization approximation have been suggested by a num­ber of authors:- Calculations using a simple local spin independent pseudo-poten-3tials for (p,2p) have been described by Lim and McCarthy, and, more recen- 4tly, by Koshel who used a momentum representation which would be well suited for more complicated potentials. Unfortunately, no additional work seems to be in progress.- Approximate methods using LEA approaches have been described7 8by Daphne Jackson and by Austern.A first order Taylor's series approach has been suggested by9Redish which may be useful provided corrections are not too large.In what follows I will attempt to point out some of the results whichindicate the importance of eliminating the factorization approximation both in (p,2p) and in cluster knockout reactions.3. Studies of the Nucleon-Nucleon InteractionIf one assumes the validity of the no-spin-orbit factorized DWIA ex­pression for the three-body cross section, it is clear that one can deter­mine the half-shell p-p cross section by dividing measured (p,2p) crosssections by the calculated DWIA terms and appropriate kinematic factors.40 39Results of this type are shown in Fig. 3 for Ca(p,2p) K (2.52 MeV) ata number of incident energies. This is a 2 s L = 0  transition. For theexperts these are simply zero recoil momentum factorization tests. The data shown, from Manitoba, Maryland, and IUCF, are plotted as a function of effective p-p scattering angle and have been arbitrarily normalized236to optimize agreement with on-shell p-p cross sections which are shown as continuous lines. However, the corresponding spectroscopic factors are consistent with each other to within about 10% despite quite large changes in distortion effects with energy. (The ratio of DWIA/PWIA cross sections vary from about 1/100 at 45 MeV to about 1/4.5 at 150 MeV.) It is clear that, for the very modest statistical accuracy shown, the off-shell cross sections are consistent with the on-shell data. Notice also that correc­tions for spin dependence in the distorting potentials are small. Clearly, in order to draw quantitative conclusions concerning the effective p-p interaction much improved statistical accuracy is desirable. With the dou­ble spectrometer systems being constructed both at TRIUMF and at IUCF much greater data rates and hence smaller errors will be possible.If we consider these data more closely the good agreement betweenoff-shell and on-shell cross sections is not too surprising. Firstly, forthe kinematics chosen, such that the residual nucleus is left at rest,we are not far off-shell. For example, for the 150 MeV data, the valueof P rrlP is only about 1.08 for which significant off-shel1/on-she11 off ondifferences are not expected. In addition, modifications due to the nu­clear medium should not be important. This is clear from Fig. 4 in which contributions to the DWIA cross section for the 150 MeV data are compared with the nuclear density distribution. Very roughly, the reaction takes place in a surface region having a density of order 10% of central density or less.237Fig. 4. Radial contributions to DWIA cross section for 1+0Ca(pJ2p) 39K (2.52 MeV,L=0) at 150 MeV. The detected angles are ±41°. The detected energies are equal. The broken curve is the U0Ca density distribution.2384. Studies of Momentum Wave FunctionsIn addition to studying the nucleon-nucleon interaction in the nu­clear medium one can also obtain information on the struck nucleon momen­tum wave function or, more properly, in the DWIA model used here, the pro­jection of the target wave function on the residual nuclear state. Restricting attention for the moment to the valence orbitals, extensive studies of spectroscopic factors are probably not needed in view of the vast body of information available from transfer reaction studies. However, some limited further investigation may be needed in order to confirm thevalidity of the existing transfer reaction data and resolve a few dis-40crepancies. An example of an existing problem is the case of the Ca (p,2p) and (p,pn) reactions at 150 MeV. For the first excited mirror L=0 transitions the neutron removal spectroscopic factor^ is approximately1.9, whereas the corresponding proton removal transition^ yields a value of roughly 1.0, i.e., about one-half of the (p,pn) value which is in reasonable agreement with pickup reactions and with structure calculations. Since similar values are obtained in 75, 100, and 200 MeV (p,2p) experi­ments it appears that the discrepancy is real and needs to be resolved.In order to obtain information on the struck particle momentum dis­tribution it is obviously desirable that distortion effects be fairly smallso that uncertainties in the DWIA analysis do not play a major role. In40 39Fig. 6 we show calculations for Ca(p,2p) K (L=0, 2.52 MeV) at 400 MeV.Shown is the predicted experimental measurement in comparison with theactual momentum distribution assumed, which is taken from the analysis12of electron scattering by Elton and Swift. Clearly, distortion effects are important and must be reliably calculated. However, the qualitative features of the momentum distribution are not obscured and useful infor­mation can be expected. In Fig. 7 contributions to the DWIA cross section as a function of radius are shown for the zero and 169 MeV/c points. As expected the interior region becomes progressively more important as the momentum increases. Thus, the elimination of the factorization approxi­mation and proper treatment of modifications of the interaction in the nuclear medium can be expected to be important. Also shown in Fig. 6 is the predicted result of a 500 MeV (e,ep) measurement. Since there is now only one proton to deal with distortion effects are, as expected, less but must still be calculated.239In order to examine systematically larger values of the ratio P a variety of strategies are possible. These were discussed atthe IUCF workshop. Possibilities include measuring coplanar symmetric angular distributions, which reflect principally variations in off-shell effects folded with the struck particle momentum wave function, and dis­tributions in the residual nucleus recoil angle for fixed recoil momentum, in which off-shell effects are modulated mostly by variations in distortioneffects. In either case the largest off-shell effects are expected for40 39small opening angles between the detected particles. For the Ca(p,2p) Kreaction at 150 MeV discussed earlier at equal 20° detection angles theratio P ,,/P is about 1.5. In Fig. 5 contributions to the DWIA cross off onsection for this angle pair are shown. It can be seen that, in addition to a surface contribution similar to the 41° case shown in Fig. 4, there is roughly a 407, contribution from radii below 2.5 fm where the density is essentially central density. Thus, one can expect to measure a mixture of half-shell and fully off-shell terms in the p-p interaction. Clearly, use of a factorized calculation to analyze data of this type must be highly suspect and one can anticipate various possible medium corrections to the interaction. These studies should complement similar studies in inelastic scattering since they presumably involve very different Pauli blocking correct ions.Fig. 5. Radial contributions to DWIA cross section for 1+0Ca(p,2p) 39K (2.52 MeV,L=0) at 150 MeV. The detected angles are ±20°. The detected energies are equal. The broken curve is the l+0Ca density distribution.0 2 4 6 8Rodius (fm )240Fig. 6. Comparison of pre­dicted experimental measure­ment (DWIA) and actual 1°momentum distribution (PWIA) for 1+0Ca(pJ2p) 39K (L=0, 2.52 MeV) at 400 MeV. The broken ^  curve is the predicted 500 T T  ,MeV (e,ep) result.T 1---1---1-- 5-- ' 1O hW|<_-"i®® -?.®® » t®6 *»® *®®( n * V / c . )Fig. 7. Radial contributions to DWIA cross section for 1+0Ca(p,2p) 39K (2.52 MeV,L=0) at 400 MeV. The detected angles are ±41.5° and ±27.5°, respec­tively. The detected energies are equal.As an example of an attempt to use the (p,2p) reaction to study thestruck nucleon momentum wave function, 500 MeV data from the measurement 4 3of the He(p,2p) H reaction carried out at TRIUMF by Epstein, van Oers 13and others is shown in Fig. 8. Notice that the data extend to momentaof about 500 MeV/c. These data show rather nicely the sort of problemsone must face in trying to obtain momentum distribution information. Thesingle particle wave functions used were obtained from fits to electron- 4He scattering data. The dot-dash curve uses a conventional analysis by Lim in terms of a simple Eckart parametrization. For the continuous curve the electron scattering data were first corrected for meson exchange con­tributions which, as we see, leads to a wave function with reduced high momentum components. The broken curve uses the meson exchange corrected wave function but with the spin-orbit terms in the distorting potentials set to zero. We see that, though negligible below about 250 MeV/c, the spin-orbit terms do improve agreement with experiment at the largest momen­ta and are at least as important as getting the wave function right. Thus, even for this very light target the proper treatment of distortion effects is quite important to the analysis.241q (MeV/c)Coplanar symmetric meson exchangeFig. 8, data; - corrected, DWIA with spin- orbit terms; same with no spin-orbit terms; Lim Eckart wave function.242In order to place this sort of measurement in context, in Fig. 9 we14show the results of calculations by Zabolitzky and Ey of momentum dis-4 16tributions for nucleons in He and 0. The calculations use a generalized Breuckner-Hartree-Fock approximation in which two-body correlations are summed to all orders. In the diagram an uncorrelated calculation (which is essentially the same for all potentials studied) is compared with cor­related calculations for a variety of potentials. The uncorrelated single­particle contribution decreases rapidly for higher momentum, so that the correlation contribution dominates for momenta beyond 2 fm AccordingFig. 9. Momentum distributions for ^He, JH: Hamada-Johnston potential, RSC: Reid soft core potential, SSCB: de Tourreil-Sprung super soft core potential B, UNC: uncorrelated, for the RSC potential. The other uncor­related distributions do not differ appreciably for q>2 fm-1.to Zabolitzky and Ey the main contributions in the region of momenta be­tween 2 fm  ^ and 4 fm  ^ comes from terms in the wave function generated by the tensor force in the nucleon-nucleon interaction. For higher momen­ta, two-body multiple scattering processes from the scalar part of the interaction dominate. No trace is seen of short-range correlations induced243by the "repulsive core" of the interaction. At all momenta shown the medi­um range processes are of dominant important.Clearly, in the context of predictions such as these it is momenta greater than 2 fm *, or 400 MeV/c, which are of importance. In Fig. 10 we indicate the angles of interest in a 500 MeV (p,2p) experiment for a coplanar symmetric equal energy geometry. We see that the angles of inter­est range from about 61° to 111°. Whether the simple knockout reactionFig. 10mechanism will persist in this somewhat unfamiliar region of phase spaceremains to be seen. However, if one can understand the reaction mechanismin this angular region, it appears from the Zabolitzky and Ey calculationsthat a dynamic range of at least 5 orders of magnitude will be desirablein the detection equipment. It should be noted that Epstein, van Oers andco-workers achieved a dynamic range of about 4 orders of magnitude in their 4 3He(p,2p) H experiment at 500 MeV with detector telescopes so that I am optimistic that there will be no problems in this regard with the new spectrometers.244With regard to measurements of the lower momentum region (less than 2 fm )^, while we do not expect any surprises, this is probably also aworthwhile project since very little data exists. In Fig. 11 we show (e,ep)15 16and (Y,p) data for the momentum distribution of a p-shell proton in 0.Fig. 11. 160 p-shell momentum distribution.The solid curve is the ls ^ 2  momentum distribution calculated from the Elton-Swift potential. The dashed curve was obtained from the density- dependent Hartree-Fock calculations of Negele^ and the dotted curve repre­sents Jastrow model calculations by Ciofi degli Atti.^ Again, we see that it is the region beyond about 400 MeV/c that is most interesting. However, at the lower momenta there are significant deviations between the (e,ep) results and calculation which need to be resolved.5. Spin Dependent EffectsIn the approximation that spin-orbit terms in the optical potentials can be neglected the nucleon-nucleon cross section appearing in the factor­ized DWIA may be writtenf i < V  W - 1 * W „ n >  'where PQ is the incident beam polarization, is an effective polariza­tion for the struck nucleon calcuable in DWIA and A and C are the (half-nnshell) nucleon-nucleon analyzing power and spin correlation coefficient,18respectively. This expression holds for polarization normal to the plane in a coplanar experiment. For L=0 transitions P^  is zero. For L > 0 there is a simple relationship between the values of P^ for J = L±^ members of a spin-orbit doublet, which is exact in the limit of degenerate states. Thus, at least in principle, cross section and analyzing power measure­ments can be combined in order to extract half-shell values of A and Cnnin a relatively unambiguous way. Presumably, even in the non-factorized calculations I have been advocating much the same sensitivity will per­sist. With the spectrometers proposed it should be possible to take data using a focal plane polarimeter and thus, at least for the strongest trans­itions, measure other spin variables such as the Wolfenstein D-parameter and thus further unravel spin specific off-shell and medium effects on the interaction.There are some indications from work at TRIUMF that the value of Ais reduced in the nuclear interior. This is also confirmed in both (p,2p)and (p,pn) studies^ at IUCF. At present the origin of the effect is un-18clear. Miller has suggested that the effect merely arises from refrac­tion leading to an effective scattering angle near 90° where A is zero. Again, we see the need for calculations in which the factorization approxi­mation is not made and, thus, do not restrict the p-p kinematics to their asymptotic values.Not only will the simple expression given above be modified in a non­factorized calculation, but also if spin-orbit terms are included in the optical potentials a much more complicated expression results as shown in Fig. 2. Calculations including the effects of spin-orbit distortionshave been carried out for a number of cases.^ In some cases, effects are40fairly small. An example is shown in Fig. 12, again for Ca(p,2p) at 150245246MeV. Both the cross section and polarization analyzing power are reduced in the spin-orbit calculation. It is interesting to note that, at leastFig. 12. Calculations for a quasifree angular distribution for ^Cafp^p) 39K (2.52 MeV) at an incident energy of 150 MeV as a function of the effective p + p scattering angle. The kinematics is chosen such that the residual nucleus is at rest. (a) Polarization analyz­ing powers; (b) differential cross sections.for the analyzing power, it is the incident particle spin-orbit potentialthat is responsible for the effect. Presumably this is simply because wesum over emitted particle spin states. In Fig. 13 we show calculations 40for Ca(p,pn) in a non-coplanar geometry. Shown are I d a n d  trans­itions. Here quite large changes arise from the spin-orbit terms over the entire angular range and at the larger angles there are rather large dif­ferences for the two J values. Even more spectacular results are obtainedfor L=0 transitions in a non-coplanar geometry. In Fig. 14 are shown re-40suits for both (p,pn) and (p,2p) L=0 reactions on Ca. For the (p,pn) analyzing powers, in strong contrast to the relatively featureless no-spin-247Fig. 13. Calculations for ^Cafpjpn) 39Ca (g.s.) at an in­cident energy of 150 MeV in a noncoplanar geometry, where0 p  =  3 0 6 n =  - 4 8 . 7 ' Tp = 90.38MeV, and 8 represents the neutron angle with respect to the scat­tering plane. Both Id3/2 and Id5/2 transitions are snown.(a) Polarization analyzing powers; (b) differential cross section.orbit predictions, the spin-orbit calculations exhibit a rapid swing be­tween positive and negative values at non-coplanarity angles of around 20° to 30°. In part (b) of the figure we see that similar behavior is ex­hibited by the analyzing powers for the analog (p,2p) transition, although the overall magnitudes are smaller due to the differing nucleon-nucleon amplitudes. Referring to part (c) of Fig. 14, in which the cross section is shown for the (p,pn) case, it is clear that the rapid change in analyz­ing power can be correlated with a minimum in the unpolarized cross sec­tion which arises from a node in the struck nucleon momentum wave function at about 120 MeV/c. This is similar to behavior found in many other re­actions where small differences in partial cross sections for spin up and spin down can, near a minimum, yield very large analyzing powers. Frequent-248Fig. 14. Calculations for L=0 nucleon knockout from l+0Ca at an incident energy of 150 MeV using a noncoplanar geometry, where 0p = 3O°, 8n = 48.7°, Tp= 90.38 MeV, and 3 represents the neutron angle with respect to the scat­tering plane. (a) Polarization analyzing power for lt0Ca(p,pn) 39Ca (2.47 MeV); (b) polarization analyzing power for 1+0Ca(p,2p) 39K (2.52 MeV); (c) differential cross section for ^°Ca(p,pn)39Ca (2.47 MeV)• The curve labeled PW is the square of the struck neutron momentum wave function in arbitrary units plotted as a function of Pg, the recoil momentum of the residual nucleus.249ly these are essentially diffraction minima so that the data serve to con­strain some sort of strong interaction radius. However, in the present case the effect may well provide a valuable constraint on the location of the node in the nucleon wave function. Since I am uncertain whetheryou will be able to rotate one of your spectrometers 60° out of plane I208show in Fig. 15 results for the (p,2p) reaction on Pb in a coplanar geometry. For the 3 s L = 0  ground state transition at 45.12° detection angles the no-spin-orbit analyzing power is approximately zero since the effective scattering angle is close to 90°. However, the spin-orbit cal­culation of the analyzing power is again large near the minimum in the cross section. This minimum, which is also due to a node in the struck proton momentum wave function, becomes somewhat shallower and is slightlyFig. 15. Calculations of the L=0 (3S2/2) energy sharing dis­tribution for 208Pb(p,2p)287T1 (g.s.) at an incident energy of 150 MeV, 6C = 6d = 45.12°.(a) Differential cross section;(b) polarization analyzing power.250shifted in position as a result of introducing spin-orbit distortions.In any case, we see that the occurrence of large analyzing power excursions in the vicinity of nodes in the momentum wave function is not restricted to non-coplanar geometries.6. Cluster Knockout ReactionsIn addition to studying nucleon knockout we can also measure clusterknockout. In Fig. 16 are shown studies of the factorization approxima-19tion for (p,pa) at 100 MeV. It is clear that, as in (p,2p), one needs to eliminate this restriction. Nevertheless, spectroscopic factors fromFig. 16. Factorization test for (p,poi) at 100MeV;  free p+a crosssection; data points Q(0)(p,pa) reactions seem to be consistent with existing (d, Li) data as can20be seen from Fig. 17 in which results for a number of medium mass nuclei are compared. Typical counter telescope (p,pa) data are shown in Fig. 18 for various targets at 100 MeV. It may be worthwhile to emphasize the ob­vious point that momentum distribution information can, at least in princi­ple, be obtained from the knockout reaction study whereas the transfer reaction suffers much more severe distortion effects which are almost cer­tainly impossible to unfold. Since even the low momentum portions of alpha cluster wave functions are not accessible to transfer reactions and are251Fig. 17. Extracted spectroscopicfactors for gound state transitions asa function of target mass. The lines merely guidethe eye. The left scale indicates the relative value (normalized to unity at A=20) and the right scale the absolute value extracted in (p,pa) .not well established, momentum distribution studies would be useful. In20Fig. 19 are shown results from a 100 MeV experiment which show some sensitivity to the assumed radius parameter in a (p,pa) analysis using a Woods-Saxon description for the cluster wave function. With betterE p (MeV) Ep(MeV) Ep(M eV)Fig. 19. Energy sharing distributions for (p,pot) ground state transitions. Curves are normalized DWIA calculations for different alpha particle bound state radius parameters rp (0.7,----; 1.3,  ; 1.9, 2.5,statistics and higher energy data rather better discrimination can be ex­pected. In Fig. 20 we show calculations for the ^Ca (p,pa)^Ar (g.s.)reaction in which the predicted experimental distorted momentum distribu­tion is compared with the plane wave result. Despite a reduction of about252Fig. 20. Comparison of the assumed momentum distribution with the predicted experimental measurement for ^CaCpjpa) 36Ar(g.s.) at 150 MeV.30 in overall magnitude the experiment can be expected to follow roughly the envelope of the actual momentum distribution and there does appear to be useful sensitivity to the assumed distribution. In fact, even a fairly crude measurement would be quite useful since wave functions needed to reproduce both transfer reaction and (a,2a) absolute cross sections have unphysically large rms radii.Experiments using polarized beams may also be of interest, both for reaction mechanism studies and possibly as a useful additonal constraint on the cluster momentum wave function. As in the case of (p,2p), the in­clusion of spin-orbit terms in the nucleon optical potentials leads to significant changes in the (p,pa) analyzing powers. For the cases consider­ed so far the analyzing power is generally large and is rapidly varying close to nodes in the assumed momentum wave functions for some angle pairs. However, the structure is somewhat different from that predicted for (p,2p) reactions and may, or may not, provide useful constraints on the assumed wave function and on the treatment of distortion effects.%  o  <*o fco fie iso \*Lo7. Deep Hole StatesRecently, at IUCF (p,2p) and (p,pn) experiments were carried out at 150 MeV using polarized protons in an attempt to locate deep-lying proton and neutron hole states. The idea was to take advantage of the j-depen- dence of the polarization analyzing power in order to differentiate be­tween j = 1± % hole strength. Earlier studies at TRIUMF were also partially motivated by similar ideas. The IUCF studies were generally unsuccessful. Not only were concentrations of hole strength difficult to identify cleanly, but also the j-dependence of the DWIA predictions were sometimes ambiguous.21As pointed out by Maris and others one problem of this type of studyis the proper treatment of multiple scattering. In addition to "elasticmultiple scattering" which, hopefully, is largely taken into account byrefractive effects of the optical potentials in DWIA one must consider"inelastic multiple scattering". These latter effects are included in somesense via the absorptive part of the optical potentials for transitionsto low-lying discrete states. However, studies of the four-body continuumregion in search of deep hole states is subject to contamination by eventsin which quasifree knockouts from valence orbitals are followed by inelas-58tic scattering. For the 200 MeV Ni(p,2p) reaction to the four-body con-2 otmuum region, Ciangaru has calculated the inelastic multiple scattering assuming an initial quasifree transition to and 2sl/2 hole statesfollowed by inelastic scattering. The procedure used was to fold empirical inelastic scattering data with a DWIA calculation of the initial "doorway" transition. Typical results are shown in Fig. 21. We see that agreement with experiment in shape and absolute magnitude are quite encouraging from the point of view of the calculation or discouraging if one is interested in deep hole states. At least for the kinematics considered here one can expect any spectroscopic study of the four-body continuum region to be swamped by inelastic multiple scattered events. At higher energies some­what cleaner spectra can be expected. For example, in the old Liverpool23experiment of Arthur James and collaborators, it was necessary to sub­tract backgrounds of 1570 to 20% from the data at an excitation energy of 48.5 MeV. Clearly, it would be of interest to extend Giangaru's calcula­tion of two-step processes to higher energies and to repeat some of the earlier studies using polarized incident protons. However, it does appear that this type of study is much better suited to TRIUMF than to IUCF.253254200E2(MeV)Two-dimensional energy spectrum above the particle evaporation (equi­librium) region. The diagonal line marks approximately the separation between the three-body QF region and the pre-equilibrium (PEQ) continuum region. The inset presents schematically our model of the mechanism of the coincidence continuum.A calculation (full line curves)^  of the continuum spectrum from the2* 75 ^®Ni (p,2p) ^ 7Co reaction at Eq = 198“ MeV. The data correspond to theaverage yield in a slice through the two-dimensional energy spectra, The agreement in magnitude is re­flected by the ratiosN = a /a.,exp theorbTSf<E>OOMPROTON LAB ENERGY E, (MeV)F ig .  21In summary, provided the experimental advances are matched with theo­retical advances there are many interesting possibilities for the future. With regard to the theory, at the very least modern effective interactions should be incorporated into DWIA codes which do not employ a factorization approximation. With this step there should be some interesting comparisons between (p,2p) and (p,p') concerning the N-N interaction and between (p,2p) and (e,ep) with regard to momentum distribution and deep hole state stud­ies. As far as cluster knockout is concerned, any proton-induced studies would be helpful since the corresponding electron induced experiments are not really feasible with present accelerators.References1. N. S. Chant, in Proceedings of the Conference on the Interaction Between Medium Energy Nucleons in Nuclei-1982, IUCF, edited by H.0. Meyer (AIP, New York, 1983), p. 205.2. N. S. Chant, in Proceedings of the 3rd International Conference onClustering Aspects of Nuclear Structure and Nuclear Reactions, Winni­peg, 1978, edited by W. T. H. van Oers, J. P. Svenne, J. S. C. McKee, and W. R. Falk (AIP, New York, 1978), p. 716.3. K. L. Lim and I. E. McCarthy, Nucl. Phys. £58, 433 (1966).4. R. D. Koshel, Nucl. Phys. A260, 401 (1976).5. N. S. Chant and P. G. Roos, Phys. Rev. C U5, 57 (1977).6. N. S. Chant and P. G. Roos, Phys. Rev. C 21_, 1060 (1983).7. D. F. Jackson, Physica Scripta 25_, 514 (1982).8. N. Austern, Phys. Rev. Lett. 41, 1696 (1978).9. E. F. Redish, Phys. Rev. Lett. 617 (1973).10. J. Watson e^t a_l. , preprint.11. L. Rees, Ph.D. thesis, University of Maryland, 1983.12. L. R. B. Elton and A. Swift, Nucl. Phys. A94, 52 (1967).13. M. B. Epstein e_t a_l. , Phys. Rev. Lett. 44, 20 (1980); W. T. H. vanOers e_t a_l. , Phys. Rev. C 25, 390 (1982).14. J. G. Zabolitzky and W. Ey, Phys. Lett. 76B, 527 (1978).15. J. L. Matthews, Momentum Wave Functions-1982, edited by E. Weigold (AIP, New York, 1982), p. 57.16. J. W. Negele, Phys. Rev. C _1, 1260 (1970).17. C. Ciofi degli Atti, Nuovo Cim. Lett. 1_, 590 (1971).18. C. A. Miller, Invited paper presented at the 9th International Con­ference on the Few Body Problem, Eugene, 1980; C. A. Miller, Common Problems in Low- and Medium-Energy Nuclear Physics, edited by B. Eastel, B. Goulard, and F. C. Khanna (Plenum Press, New York, 1979), p. 513.19. P. G. Roos £t a_l. , Phys. Rev. C 1_5, 69 (1977).20. T. A. Carey e_t £l^ . , Phys. Rev. C 2_3, 576 (1981).21. Th. A. Maris, Nuclear and Particle Physics at Intermediate Energies, edited by J. B. Warren (Plenum Press, New York, 1976), p. 425.22. G. Ciangaru et al., Phys. Rev. C 27, 13b0 (1983).2558.  Conelus ions257(p,d)-Reactions at Intermediate EnergiesJ.M. Greben Department of Physics University of AlbertaI- ; ■ ' ' , . i ■' • ■ ; '*Edmonton, Alberta, T6G 2J1, CanadaABSTRACTA brief review is given of the goals of studying (p,d)-reactions at intermediate energies. We then discuss some newly developed methods which extend the description of these direct reactions beyond the usual distorted wave Born approximation. In particular, we discuss results obtained with a Faddeev-like many-body theory for the case 24Mg(p,d)23Mg(j+) at 96 MeV and compare with recent Indiana data. We also present TRIUMF data on 0 and Ca, and compare these with standard DWBA —calculations.Our general conclusion is that (p,d)-reactions at intermediate energies are not (yet) well-understood. Although it is encouraging that several microscopic theories now give practical results, they have to be developed further in order to give reliable quantitative information.I. Why Study (p,d)-reactions at Intermediate EnergiesIn the last ten years we have seen a lot of experimental and 4-8theoretical interest in the intermediate energy (p,d)-reaction. To some extent this represents a natural extension of the traditional nuclear physics interest in this reaction into a new energy realm. However, there are also a number of specific reasons for studying this reaction at inter­mediate energies, which I want to review here:(1°) Sensitivity of this reaction to high-momentum components of the nuclear wave function. This objective has been stated by many authors^’ and provides a good focus on this reaction. High-momentum components are not easily accessible and if they could be studied in this reaction then they might provide valuable information on the short-range interaction and consequently on the quark degrees of freedom in nuclei, which must play a role at short distances. In the last few years it has become clear that it is not at all easy to isolate these short-range, high-momentum effects and one has come to appreciate the necessity of a better understanding of the reaction mechanism.(2°) The rearrangement reaction can also be used to test multiple scattering theory outside the usual context of elastic scattering. This could provide valuable new information on the validity of various approxi­mations in multiple scattering. As in (1°), the study of these aspects requires a more fundamental description than the DWBA. At lower energies three-body models have been examined extensively, however, they would be inappropriate in the present context as they do not account properly for the many-body effects. We also note that in certain multiple scattering theories the Pauli exchange term appears explicilty in the elastic scat­tering amplitude, and can be treated by the same methods as other rearrange­ment problems.2581-3259(3°) At intermediate energies one witnesses the preferential excita- tion of certain states, in particular high spin States. Examples are: the strong excitation of the 3+-state in ^Li; the 2+ and 4+ level in "*^ C; the 5/2 and 7/2 level in ^C; and the 5/2+ and 7/2+ level in "*"^0. The latter two cases are shown in Figure 1 and are taken from Ref. 9. Unfor­tunately, the cross-section for these reactions is rather flat as a function of angle, so that it is difficult to acquire information on the angular momentum.(4°) Excitation of A-degrees of freedom. The A can play an importantrole in the reaction mechanism, even if it is not present as a resonance inthe final state (in which case it is note easy to detect or verify its pre-3sence experimentally). Such a mechanism has been studied for d+d->- He+n by Laget et al.^and is illustrated in Figure 2a. It also has been used by Dillig and co-workers^, although they use a two-nucleon mechanism as indi­cated symbolically in Figure 2b. One can also excite the A "externally", as shown in Figure 2c, although this does not lead to a two-body final state. This A-mechanism has a clear experimental signature and has been used recently by Toki (Ref. 12) to explain a strong enhancement in the background proton production.- Let me now give you a brief review of the theoretical situation regarding the microscopic description of the (p,d)-reaction. As I indicated earlier an elaborate description, going beyond the DWBA, is necessary to attain most of the goals set out for studying transfer reactions at intermediate energies.II. Microscopic Formulations of (p,d)Formally, the rearrangement amplitude for the transfer reaction13can be broken up into a direct and an exchange parti - /s+r udlr - z i“ chi .Most practical descriptions of (p,d)-reactions ignore the second termwhich does not contain the usually dominant neutron exchange diagram. n . _ ~dir .One can write T in various ways, e.g.Tdir = «t> <p lt»|v +V |'f(+)> d C pC pn p= < ^ _) |v +V U  k> d 1 pC pn1 A= <4'^ ")|v |Xi+)m>d 1 pn1= < ^ _)|v +v _ -u .|<t>. xi+)>d 1 pn pC pA1 A kwhere V and V are the interactions of the initial proton with the trans-pn pcferred neutron and the core respectively; <J> , <f) and <p are bound-stateA d  Cwave functions of the initial nucleus, the deuteron and the residual nucleus;and 4^  ^ is an exact wave function originating from (resulting into)d pan ingoing (outgoing) wave in the deuteron (proton) channel. One can eli­minate V by introducing a many-body distorted wave Xi*+^m > an<^  finally pi~* K.one can introduce a simple two-cluster distorted wave X^+  ^ correspondingkto U .. If one neglects (V „ -U .) in the last expression and replaces pA pC pA^> by |x, p-, we obtain the usual distorted wave Born approximationd d, k d C(DWBA). If we want to go beyond this approximation then we have to decidehow to deal with(1) ^ _) ,(2) xj* or alternatively with VOne of the most popular descriptions of (p,d) at lower energies is the adiabatic model^. Although it accounts to some extend for break-up effects,260261which are expected to be important at higher energies, it also has some dis­advantages: it is in essence a three-body model, so that many-body effects are hard to include; also it is not clear how to generalize it to higher energies and,finally the connection to microscopic optical potentials is unclear.More recently Tekou^ has used the Glauber approach to describe the 4(p,d)-reaction on He at 770 MeV. One of the advantages of the eikonal representation is that one does not have to replace the many-body wave function by a two-body cluster wave function before making further approxi­mations. In order to get practical results Tekou had to make rather drastic assumptions, in particular he assumed that the interactions are purely central. His main finding is that the two-nucleon mechanism dominates the reaction. A similar study, though different in detail, was done bygVary and Ludeking . They study the (p,d)-reaction on carbon but do not make any comparisons to experiment. Again, spin effects are neglected.In this talk I will mainly concentrate on an application of exact many-body theories beyond the usual realm of three-body models. The prob­lem with standard few-body models is that one only keeps a few important few-body channels and throws away many-body channels and many-body effects which could be very important at higher energies. To go beyond these standard models one has to use projection techniques and one should at the same time avoid cluster approximations (Q-space=0) by developing an alter­native approximation which exploits the high energy nature of the reaction.It is clear that such an approach will have more in common with multiple scattering theory then with the cluster models like the resonating group structure method (RGM).15In a recent paper I developed such a theory and I would like to briefly review it. Relying on the experience of many decades we want tomodel our theory around the approximate validity of the DWBA. In this theory the distorted waves play a very important role, and it appears that in a suc­cessful theory one first has to address how these waves should be defined optimally. In order to define these distorted waves one has to use the pro­jectors for the asymptotic channels in which these waves "reside". The remaining Q-space is then ideally absorbed in high-order terms of the t-matrix, or in the effective distorting potential which defines the distorted wave.The problem with rearrangement reactions is that the asymptotic channels are not orthogonal, so that the use of projection techniques is not straight­forward. This problem is circumvented in the Faddeev equations which repre­sent the minimal generalization of two-body equations to the three-body level consistent with unitarity.Introducing the channel Hamiltonians and pair interactions in the usual way, one obtains the following three coupled equations:(E - H.)¥. = V. I i * j = 1,2,31 1  1 Jwhere xa=Z'¥.. An important property of is that it carries the asymptotic i 1 1component in channel i, so that we do not have any asymptotic information if we only solve for the projected wave function PjJ^» where is the projector for the asymptotic channel i. The development of a set of coupled equations for these wave functions is now straightforward, with the remainingcomplexity residing in the effective operators. Rather than solving for these wave functions and deriving the relevant transition amplitudes from their asymptotic behaviour we managed to express the transition amplitudes directly into a matrix element of a transition operator sandwiched between generalized distorted waves. These new distorted waves X are the analogons of the Feshbach elastic wave functions X belonging to the Feshbach optical262263F j .potential U for single channel scattering. In the following we give resultsfor the first-term in the transition operator, which is the usual pn-interac- tionTdir = |V +  V I (f) k>d 1 pn pc1 A- < 1  v d v + - M +k  ■’Ineralized distorted wavesge  Contrary to some other theories, these generalized distorted waves x are functions of the relative channel variable only, so that all many-body effects are buried in the transition operator and in the effective potential defining X» The distorted waves can be expressed in terms of the Feshbach elastic wave functions; e.g. for the proton channel we have /w(+) _ (+) _ ,, I t,F r I (+)^^p ,]£ ^,k a ' p oIxp ’where Gq is the Green's function for the three free relevant clusters inthis process (the proton, neutron and core). For large energies G^ isapproaching the two cluster Green's function and the second integral lookslike the scattering term of the Feshbach elastic wave function, so that X^ ?P >kapproaches a plane wave state. For smaller energies the second term is ofshorter range and seems to suppress X ^"*"4 in the interior. The physicalP > kmeaning of the counterterm is harder to explain than its implications.Part of the problem is that the exact expression of the transition amplitude does not have a very intuitive interpretation, with the initial and final wave function playing a very different role (one being a plane wave the other being an exact wave function). We propose the following interpreta­tion: The (Feshbach) optical potentials are made up of many intermediatestate contributions, in particular those corresponding to the three clustersrelevant for our problem. However, since these latter three-body states are the simplest states common to both the intial and final state potential ("the largest common denominator") they play a special role for the (p,d) process. It seems natural to include such a coupling through the common three-body state in the transition operator, and this is exactly what has happened in our formulation. The subtraction term in x then ensures that there is no double counting of this mechanism.We now proceed to discuss practical applications. First of all, the three-body Green's function can accurately be replaced by a renor­malized two cluster propagator G^ at a shifted energy. The calculations can then be done with standard zero-range and finite range codes, requiring only a modest generalization to account for the transformation of the dis­torted waves. Since we will in general not have available the true Feshbachoptical potential, our calculations will be based on a phenomenological optical potential.24 -* 23We have applied this formalism to the reaction Mg(p,d) Mg (|r "*"» 2.36 MeV) , which has recently been studied extensively^ ’ ^  because of the claim of a major failure^ of the DWBA.In the first figure (Fig. 3a) we compare the standard zero and finite range calculations,obtained with the input parameters of Ref. 15, with the data. The finite range effects are practically negligible for this valueof the zero range constant (D^=-100). In Fig. 3b we show various calcu­lations using the new formulation. The curve marked x is obtained with the simplest approximation for % in terms of the Feshbach elastic wave function. The curve "Opt" is obtained by refining our description of the three-body Green's function and the deuteron distorted wave. Although this gives an improvement over the simplest approximation for x> it only gives a slight264improvement in shape over the original standard calculations, while the change in magnitude goes in the wrong direction. In Fig. 4 we show the corresponding analyzing power data and theoretical results. The new results represent a substantial improvement over the standard FR results, in particular if we use the optimal approximation for the distorted wave x^ .- The curves "V^=0" cor­respond to a particular approximation for x^ where the effective potential energy of the deuteron is taken to be zero. This represents an approximation which should do reasonably well at very high energies. From these results we would like to draw the following conclusions concerning the use of the effective Faddeev-like equations for (p,d):(1) Many-body scattering theories can be applied to realistic scattering situations and are not necessarily limited to simple three-body models.(2) Since we did not get agreement with the data it appears necessaryto include higher-order terms in the transition amplitude. The most impor-18tant other diagram is probably the one shown in Fig. 5. In earlier workwe found that this rescattering mechanism is important in the forward andbackward hemisphere. In particular, it gave a reasonable description of4backward (p,d) on He. Other improvements within the context of the present formulation also deserve attention, although we do not expect them to be as important as the rescattering term. For example, we could calculate the exchange amplitude and thereby restore the symmetry required by the Pauli principle. Or we could improve the description of the deuteron optical potential.Since the input to our calculation (bound-state wave functions and optical potentials) is identical to that in Ref. 16 we should say a little bit about recent work that seems to indicate that the"failure" of the DWBA is not as dramatic as was originally believed, and that a more extensive265calculation with improved parameters could give a much better description. Ifthis is true than our failure to get the right magnitude for the cross-sectioncould possibly be contributed to the input. The first improvement of this19kind is by Ichimura et al. , who found that the multistep process through the + 235/2 state in Mg leads to a considerable reduction of the cross-section (bya factor three). Somewhat disturbing is the fact that this result dependscrucially on an unknown sign and that the opposite result (an enhancement by20a factor 2) obtains for the other sign. Just recently, Hatanaka et al. got reasonable agreement with the shape of the cross-section (Fig. 6a) and polarization (Fig. 6b), although the magnitude of the theoretical cross-section is still much too large, as is reflected in the small spectroscopic factor.He uses slightly different optical parameters and standard non-locality para­meters (.85 for the proton and .54 for the deuteron).A final note on this topic is that the Dirac calculations by Shepard21et al. for this process, which also were reported at the Indiana Workshop22in 1982, are now being discarded by the same group , as they feel that one does not understand the relativistic treatment of the deuteron sufficiently well, to make reliable predictions.We will now discuss TRIUMF (p,d) data on ^ 0  and ^ C a  whose theo-23 13retical analysis has just been completed . Some other TRIUMF data on C24were published before . In Figure 7a and 7b we show the cross-section16and analyzing power results for the transition to the ground state in 0.The standard DWBA calculations are most sensitive to the deuteron opticalpotential, which was obtained according to the adiabatic model prescription25of Wales and Johnson . All input parameters are shown in Table I. These results were obtained with R. Abegg. In this, as in the following cases we find that the experimental observables vary faster with angle (or momentum transfer) than their theoretical counterparts. Generally the structure in266the theoretical cross-section is much too pronounced, a feature also observed 13 2 Ain the C-case . The difference between finite range (FR), which include the D-state, and the zero range (ZR) calculations is not large, and only in the Ca-case shown in Figs. 9a and 9b do we see a noticeable improvement.In all cases considered the spectroscopic factors are small compared to thetheoretical shell-model values: for ^0(p ,d) ^ 0 (g. s.) we find .67 rather than16 -* 15 . - 40 -* 39 -2; for 0(p,d) 0(3/2 ) we find 1.68 rather than 4; and for Ca(p,d) Ca(3/2 )•' < • ' ’ \ '!.*■'■ * we find 1.79 rather than 4. This indicates a systematic failure of theDWBA - calculations in this energy range.In summary, we would like to make the following conclusions:- (p,d)-reactions are not (yet) understood at intermediate energies.More theoretical work is needed.- A microscopic description of (p,d), which can exploit the know­ledge of microscopic optical potentials, is available; however it appears likely that the first-order term is not sufficient.- Based on further calculations not shown here we find that thenecessity for the suppression of the interior contributions24 13in (p,d) has only been established for light nuclei ( Mg, C) , but not for larger nuclei (^Ca, ^ ^Pb) .- Experimental (p,d)-work should certainly include analyzing power measurements; however, the present state of the theory does not provide much hope that information on large momentum components of wave functions can be measured in the short term.- Deuteron Elastic Scattering Data are very useful, since the deuteron optical potential is not well-known at intermediate energies and the (p,d) cross-section is very sensitive to this potential.267Ackn owle d gemen tsThis work was supported in part by the Natural Sciences and Engineering Research Council of Canada. We thank Dr. R. Gourishankar and Craig Land for assistance with numerical work, and Dr. R. Abegg for analyzing the TRIUMF data.References1. S.D. Baker et al., Phys. Lett. 52B, 57 (1974); T.S. Bauer et al., Phys.Lett. 67B, 265 (1977); J. Kallne et al., Phys. Rev. Lett. 41, 1638(1978); T.S. Bauer et al., Phys. Rev. C21, 757 (1980); J. Kallne et al., Phys. Rev. $21, 675 (1980).2. J. Berger et al., Lett. Nuovo Cimento 19^ , 287 (1977); J. Kallne and A.W. Obst, Phys. Rev. C15, 477 (1977); J. Cameron et al., Phys. Lett. 74B,31 (1978); G. Bruge, J. de Physique 4(3, 635 (1979).3. D.W. Miller et al., Phys. Rev. C26, 1793 (1982); ibid C.20, 2008 (1979).4. N.S. Cragie and C. Wilkin, Nucl. Phys. B14, 477 (1969); C. Wilkin, J.Phys. C. : Nucl. Phys. 6^, 69 (1980).5. E. Rost and J.R. Shepard, Phys. Lett. 59B, 413 (1975); E. Rost, J.R.Shepard and D.A. Sparrow, Phys. Rev. C17, 1513 (1978); J.R. Shepard,E. Rost and G.R. Smith, Phys. Lett. 89B, 13 (1979); J.R. Shepard andE. Rost, Phys. Rev. Lett. 46, 1544 (1981); ibid. Phys. Rev. C25, 2660 (1983); A. Boudard et al. , Phys. Rev. Lett. 46^ , 218 (1981).6. A. Boudard et al., Phys. Rev. Lett. 46^ , 218 (1981).7. A. Tekou, Nuovo Cimento 54A, 25 (1979); J. Phys. G. Nucl. Phys. 1_, 1439 (1981).8. L.D. Ludeking and J.P. Vary, Phys. Rev. C27, 1967 (1983).9. G. Smith, Thesis, LASL-report LA-8166-T (1980).10. J.M. Laget, J.F, Lecolley and F. Lefebvres, submitted to Nucl. Phys. A.(1982).11. A. Boudard et al. , Phys. Rev. Lett. 46^ , 218 (1981).26812. H. Toki, Phys. Lett. B125, 442 (1983).13. M.L. Goldberger and K.M. Watson, Collision Theory, John Wiley & Sons (1964) p. 837.14. R.C. Johnson and P.J.R. Soper, Phys. Rev. (TL, 976 (1970).15. J.M. Greben, Phys. Rev. C25, 446 (1982).16. J.R. Shepard et al., Phys. Rev. C25, 1127 (1982).17. G.H. Rawitscher and S.N. Mukherjee, Phys. Lett. H O B , 189 (1982).18. J.M. Greben, Proceedings of the Workshop on Nuclear Structure withIntermediate-Energy Probes, Los Alamos LASL Report LA-8303-C, 1980, p. 402.19. M. Ichimura, in Proceedings of IUCF workshop on "The Interaction Between Medium Energy Nucleons in Nuclei-1982", ed. H.O. Meyer, AIP Conference Proc. 9_7, 192 (1983).20. K. Hanataka et al., presented at the International Symposium on "Light Ion Reaction Mechanisms", Osaka, 1983; I thank E.J. Stephenson for drawing my attention to this work.21. E. Rost, J.R.Shepard and D. Murdock, Phys. Rev. Lett. 49^ , 443 (1982).22. J.R. Shepard, private communication.23. R.P. Liljestrand, J.M. Cameron, P. Kitching, R. Abegg, J.M. Greben,D.A. Hutcheon, J.R. Kraushaar, R.M. Lombard, W.J. McDonald, C.A.Miller, J.G. Rogers, J.R. Shepard, C.E. Stronach and J.R. Tinsley, to be submitted to Nucl. Phys. A.24. R.P. Liljestrand et al., Phys. Lett. 99B, 311 (1981).25. G.L. Wales and R.C. Johnson, Nucl. Phys. A274, 168 (1976).269Optical Potential Parameters - Table270H60M<Dcwao•tHUacd<vcr*<TvOvOCMImCMvO0000oovOcoOCMr-00 r—IovOi—I<rooCMoUOooCMooo\mCT\vOCOrH00vOCMCOvOCOCMvOOOU0COCM!ovOCMOOvCMCM00rHVOuovO<rcoco<rooCMcduCOCMvOOOOvOvOCMOvOU0CM•<rvoi—icocoCMCMCOvOOuoPu cdCJvO oo•H4JcdrOcd•Hnocd* •• C rHrH o cdcd C/Dc 4-J•u rC cu0) o*“ > 4-Ju n o0) TJ C>> C cd0) cd SX r\C/D O• 0) COo rH• cd •sd PH/—>*tH CM c oV-/ V-/ 'w'271Channel NumberF i g . l a Spectra collected at 5.2° (A) and 19°(B) o f  the -800 MeV 12C(p,d)1:LC reaction.2721/2 F i g .1 b273(a)( c )  F i g . 2sec(m b/sr)274THETfl C.M. (deg. )F  i g . 3  aSEC275IX0 . 0 1 0 . 0 2 0 . 0 3 0 . 0 4 0 . 0THETfl C.M.5 0 . 0F i g . 3 bANALYZING PGHER276THETfl C.M.F i g  - 4 aANALYZING POWER277THETfl C.M.F i g . 4  bAF i g . 5d(7/cin(mb/sr)12|>lA1^1 0C”S.--6sv „1 0 'PW3A (adiabatic)—  DWBA (conventional) c ls *  ,\i0.j L i J i L l__20 40 60 800  c .m . ( d e g . )Fi q . 6 a•mil-- l- 1..1. 1.1 Ul! i -■ L LLLLllI I-i.i i I jl «.«,«  1 t-JLUJUiJ 1 i-ULUXL§:lL*'>tOH4--cVs-^A_r/ —o”«4H-12Uj-j>C ~r  i(JS/quu) -joos ‘281T h e l " a c _mF i g . 7 a282T h e t a ( d c a )F i g . 7 b  s_ Se cL (m b/sr)283F i g . 8 a a n 9 l e c .m284c n 9 ' e c . m .F j g . 8 b_ SGci'.(mb/sr)285a n 9 lec .m.F i g .  p a286F i g . Q b287OVERVIEW AND SYSTEMATICS OF THE (N, tt) AND (N, Y) REACTIONSPierre Couvert Physics Department, University of British Columbia,Vancouver, B.C., Canada V6T 2A6 andD.Ph.N/ME, C.E.N. Saclay, 91191 Gif-sur-Yvette-CEDEX, FranceABSTRACTExperimental trends of the pion and photo production reactions are reviewed with respect to our present understanding of their reaction mechanisms. Special attention is given to the implications of the strongly varying kinematics of such high momentum transfer reactions and new systematic features are extracted from a phenomenological analysis of the existing experimental data.INTRODUCTIONGiven the tremendous amount of effort devoted to both experimental and theoretical studies of the various exclusive (N,tt) and (N,y) reac­tions,1*2 it becomes more and more difficult to make a complete overview within the allotted time. Instead, I will present, in the first part of my talk, some of the main features of these reactions with respect to our present understanding of their reaction mechanism. Since it becomes more and more evident that a coherent systematic comparison of not only the numerous existing pion production experimental results but also of the different (N,y) or other one-nucleon-transfer reactions will be very helpful to serve as a guideline for further theoretical or experimental investigation, I will show, in the second part of this presentation, some of the systematic trends we can presently extract from the existing experimental data. Such a comparison could be useful to get more inform­ation about the dynamics of these reactions and, eventually, to finally extract new information about the nuclear structure. With that respect, special attention will be given to the important influence of the kinematics when comparing such high-momentum-transfer reactions.I. THE PRESENT SITUATION OF THE (N,tt) AND (N, Y) REACTIONSFor more than ten years now, an important effort has been made in the experimental investigation of both pion and gamma production reac­tions. > 2 The first transparency (T 1) displays the present experimental situation of these reactions. More or less complete angular distribu­tions of cross sections, and more recently of analyzing powers, have been accumulated for the (p,rc+) and the isospin or time reversal related (Pi*0)* (n »1T_)» (1t+*P) an  ^ reactions on more than 20 differenttarget nuclei from *H up to 208 Pb. Despite its very low cross section, the double-charge-exchange (p,*-) reaction has been extensively invest­igated, especially within the last few years. Angular distributions and analyzing powers are now available for many light nuclei and an impres­sive systematic study of excitation energy spectra on medium and heavy target nuclei has been done recently at IUCF.3 All these (p,i0 reactions have been studied throughout the world within a wide incident proton energy range, from threshold to above 1 GeV, which largely covers the (3,3) resonance region.T lExperimental sihvaWen of exclusive (N#iO 4 C^lf) roocKons( p , i r * )  (p i ir * )  (n ,ir*) o r  ( i r * p ) ( i r - n )•  ^/ilLand/or Ay on  :p,  s Ke He, s ® S'1°B, "& “C, -“C ,"C,MN,M0, “ 0 ..*^ 8, “M4. ”s£> ‘" ‘Co., " T i .  , 90Z r  / ° 'P b( P i T T -),  d<r/i A  and /or Ay . n - . ^ > eA / V V V V ^ >.  5 pec ProB C r ^ l / i / S f ,  ,5y, b * , > ' k „T p  : Hire%V\. —v ! 2 GfiVL a b ; C e fW jtlfp s a l^ O rs a y ^ S q d ^ /rA iu M F ^ a M P F , ,uCF> SitJjtk •n )  o r ( p ^ )On: d-, 3He., * Wc,j6LL} ; 9&e.,* 0  , 2 V  , ^ °Ca.E y  up t o  * /  4 0 0  MeVl a b : Main*, Bonn t ALS Society, Cal Tech t Bahtst Fcasceth', TftiUMF, Sahurt fcae*ay t Or say , e k -288289If the experimental situation of the (Y,p), (Y,n) or (p,Y) reactions is less rich, these difficult low cross section experiments are now undertaken in many different laboratories. Angular distributions have been measured at rather low energies for target nuclei up to A=16 and at photon energies up to ~ 400 MeV for very light nuclei. The energy vari­ation of the cross section of the (Y,p) reaction has also been particu­larly investigated at fixed laboratory angles.Despite these impressive experimental results and the important effort they have incited in theoretical analysis, our understanding of the dynamics of these reactions is still far from being complete. This comes from the fact that the reaction mechanism of these pion or photo production reactions seems to be far more complex than expected. Furthermore, in these high momentum transfer processes, all the complex­ities of the reaction mechanism (production process, but also distortions, off shell behaviour, etc. . . ) are intimately interfering with not only the influence of the nuclear structure of the target and residual nuclei, but also with the important effects of the rapidly varying kinematics of the reaction (T 2).The various theoretical analyses of pion production reactions are usually classified into two types of models according to the number of nucleons involved in the elementary production process: the so-calledOne-Nucleon-Model (ONM), or stripping model, and the Two-Nucleon-Model (TNM). In order to stress the eventual relationships between different one-nucleon-transfer reactions we present (T 3), a schematic represent­ation of these two models for three of the most important ones: the( P * ^ ) .  ( P »  Y) and (d,p) reactions. The "ONM/TNM" terminology may, how­ever, be misleading where the underlying physics is concerned; in the pion production reaction in particular, the distortion of the pion wave function plays such an important role that it can no longer be reasonably considered as a perturbation to the elementary production mechanism.Then, the One-Nucleon-Model, which was originally hoped to be a promising tool to study the high-momentum components of the single particle wave functions, turned out to be a multi-nucleon process involving an im­plicit momentum sharing between the projectile and one or more target nucleons. Nevertheless, in the following we will keep that terminology with the condition to interpret it as the image of the successive terms of the development of the full n-body production operator and not as a prejudice on the underlying physics of the reaction mechanism.I will start my selective review of our present understanding of the pion and photo production processes by the (Y,p) reaction. At low energies (Ey < 100 MeV) and low momentum transfer (qcm < 450 MeV/c) the interpretation of the (Y,p) experimental data in the frame of the ONM was seen as rather promising. As an example, we can see (T 4) that the single-particle momentum density extracted from a modified PWBA analysis4 of the Y,p) 1 s# experimental results 5 is in good agreement withthe one extracted from the quasi-free 12C(e,e'p) 1 ^ g .S. process.5 Both semi-experimental informations agree with the 1 p 3/2 single-particle momentum distribution calculated from an Elton-Swift potential7 whose parameters were determined by fitting electron scattering data.This relative success of the ONM may however be misleading if re­stricted to the analysis of low momentum transfer kinematical regions or of the only (Y,p) reaction. Recent experimental results of neutron photo­production, for example, give evidence of the failure of the ONM even at photon energies as low as 60 MeV. Since the strong interaction is290 T2291T3(**4)'/jr/&( p ^ )7(r h )♦ O N M  * * T N M *292T Ao A*C  £©» e 'p y 'B. ^ C C V , P ) ,JBB y  = f C j B o / o c  MevX  Meu^ey efc ol M . P J l f i  XL. Matthews **■?. * U *  (iW) S IM OM ENTUM  ( M t V /c )l ^ y O O l *  from  Ell-sn 4 Su).9T f c4-et,Vialgffect of to*/. Hpfi atfmixfore.293T 5P W B fld<x/dA(y,p) ^  ( 2  kp * m ’e p +  /“•? k *  ) I W | 2 * r / d A ( T f , » )  ~  0 * i  W»* )  l < t > „ ( q ) | 261m «  VP » k ,  « *  90** <x«,p> 10Expec. ! ,40(rinV*0 O'.*. 4 £®ei**y.r •* o|. ?L WB 0**o) <ll,60(^p)'5Nfr.t ♦ Findlay NP «z*9 Cl»Tr; >65Theory , P.C. 4 Kttllis294supposed to be charge-independent, the only difference between (Y,p) and (Y,n) reactions should come from pure coulomb interaction effects. The momentum of the outgoing proton being much higher than the photon mom­entum, a PWBA prediction should give, except at very forward or backward angles, a much higher cross section for the (Y,p) reaction than for the (Y,n) reaction since the interaction potential of the latter contains only a magnetic term when the interaction potential of the former in­volves both a magnetic and a current term (T 5). However, the measured cross section of the 180(Y,n > 15°g.s. reaction8 happens to be of same magnitude as the 180(Y,p)15Ng.S. reaction9 at 60 MeV photon energy and even much larger at backward angles at 80 MeV. To illustrate this dis­crepancy between the predicted, in the ONM frame, and the experimental ratios of the (Y,n) and (Y,p) cross sections on 180 we give the results of both plane waves and distorted waves calculations10 of these reaction cross sections at 60 and 80 MeV (from charge independence arguments, the same nuclear optical potential is taken for both the outgoing proton and neutron and no attempt has been made to get a "good fit" to either of the experimental data sets) .Another difficulty of the direct stripping model is encountered when the single particle momentum density is investigated at higher momentum transfer (T 6); such a density for 180 up to 900 MeV/c has been ex­tracted11 from an extensive experimental study of the 160( Y,p) 15N'g . S. reaction.9*12 As in the 12C case, we can see here a rather good con­sistency between the experimental density and those calculated from real­istic single-particle wave-functions up to 400 MeV/c. However,at higher momentum, these wave-functions give a much too low contribution of high momentum components, in particular when using an Elton-Swift potential. The choice of a more sophisticated (Hartree-Fock) shell model wave function13 may remove a fair amount of this discrepancy but the resulting momentum density is still one order of magnitude too low compared to the experiment. On the other hand, the momentum density calculated11 from a Jastrow correlation model 19 seems to give a much better agreement up to 900 MeV/c. Despite the highly phenomenological character of this type of calculation, this may indicate an increasing contribution of a Two- Nucleon mechanism to the momentum density at q > 400 MeV/c.More direct evidence of such a TNM may be seen (T 7) in the calcu­lation of Londergan and Nixon15 who analyzed the high energy experimental excitation functions of the 160(Y,p) 15ng.S. reaction. 12 In their model, they consider explicitly the absorption of the incoming photon by a pair of interacting target nucleons through the excitation of an intermediate A(1232) isobar. If the agreement with the experiment is still poor it shows nevertheless a clear improvement of the calculations compared to the results of a DWIA analysis12 considering the direct absorption of the photon by a single target nucleon. However, we must point out here that the role of the (3,3) resonance in the (Y,n) reaction does not seem to be clearly established at that stage of the theoretical interpretation. For example, recent calculations by Gari and Hebach16 using phenomenological non-resonant meson exchange currents give reasonable agreement with both (Y,p) and (Y,n) experimental results. Nevertheless, it is clear that more detailed and systematic theoretical interpretations of the (Y,n) reactions still need to be done.We now turn to the exclusive pion production reactions. Since many review papers exist on both theoretical and experimental aspects of these reactions1*10, I will restrict myself to a few experimental evidences|<t>(<0|’ . x V r a c V e d  f r c w  “ o f W ' N * , .>Fi»»d\ay 4 R.Owc«s P.L.74BCW6) 305E x p  • • 40 MeV ^  loo MeV Findlay eh al.a 45* ") O 9 0 *  > IOO<E2r4 350MeV J. M a H W e w & .  e* al.& 135° J295T6T'he.e'ry : -  £ll-o*\  ^ Siulfh W-F.— — —• Harlree . FocU v/-F. (fJey ic )......... 3«5Vr6U> coxT«\al-it)»\ wedel CCiefi de^ ifiH-i)296M.J. Leitxb Th-X t o n d c r ^ A n  C-.Ki j«on P A  C t* (l9 7 9 t) 9 9 6E y  ( M * V )C x p »  ♦ ?.t-Mci^^he«rS iV< P R L  S 8 C * # 7 7 )  8297T8F. S o o p  t t  olpR.fie. 1 The moment uni trans­fer versus pion momentum at the minimum, in angular dis­tributions from transitions in C, Si and Ca.2O10 t—oLdmmmccru<f— -IC  10'  I2 _  , 12 *C ( p , 7 T  +  ) ctE ,S I N G L E - P A R T I C L E  0  0 0 1/2" AS T A T E S  3 0 9 1 / 2 * ms es 5/2* •gp-IM STATti’ S.66 S/2" A6 6 6 5/2* •9.SO 9/2* ■F.Sogo ei- al. p. a . c u C 't e & i )  5 7 oeg I O04106 o e 1.0 12cm2 5 10 20 SO 40 SO 60 70 CM lw (MeV!f i g - 2  The total cross section versus pion energy for some transitions in the 12c(p,v*)13c reaction.T9298r*00-I20f2 40-w-:<-4-6 M«v19)sie • ',V2+ at 4.64 MeV 19 F :U/£ ^  6 50 McV^Vz+ 40 -J 2 M<vI! 10 9 0Ejct'otior Et’*'?* (M«/)400;S20-19C-tt•0-t*V.J « V B.T-) Sof*c 19 10 9 C Excitation Ene;y 'Me.1'?  n  -4tot: st Ip1 * 0 ( p , « " 5 1 **a asd l * H f 'p ,a ~ ? 2 S . I * 6 • JCi Ifcf and »,U e  • 3:*.Vi a “ B ) ’; ,lc ° ’ i 3- 2' ^ 0 & v 0* ; » c  V »  1A/ll 5 0 f r .s.  'h' ; , A C  O 4 VztAir‘'emf;<y 2299concerning the reaction mechanism. The various theoretical analyses of the existing (p,n) experimental data did not point out, at least up to now, any clear indication of an eventual leading contribution of the one nucleon pion production mechanism. In spite of the encouraging results of the relativistic approach of the ONK by Cooper and Sherif, 1 on some selected experimental data, these calculations are still in their infancy and a more systematic study of the near threshold data must be pursued.On the other hand there are some more or less clear indications of a specific contribution of the absorption, or production, of the pion by a a pair of interacting nucleons. In the (p,ir) experimental data, for ex­ample, some noticeable differences in behaviour have been detected between final states involving strong single particle excitation and those which are known to contain mainly 2 particle - 1 hole configurations. On the first figure of transparency (T 8) are displayed the positions, in momentum transfer qcm, of the first mimimum of the angular distribution versus the outgoing pion momentum, for the (p,n+) reaction leading to specific final states of 13C, 29Si and 91Ca.18 The energy dependence of the position of these minima is linear with the same slope for the three single-particle states (3.85 MeV, 5/2+) of 13C, (2.03 MeV, 5/2+) of 29Si and (G.S., 7/2") of 41Ca. Whereas the 2p - lh configuration (6.86 MeV, 5/2+) final state of 13C follows the same linear variation but with a noticeably different slope. Such non-zero slopes clearly indicate an interference between the reaction mechanism and the influence of the nuclear wave functions since a minimum of the angular distribution due only to the latter should appear, in a plane wave approximation, at constant qcm*A similar distinction between single-particle and 2p - lh configur­ation final states can be seen (Fig. 2 of T 8) on the energy variation of the total cross section for various excitation levels of l8C measured near threshold.19 However, in this case, the 2p - lh (9.5 Mev, 9/2+) state follows a pattern closer to the one shown by single-particle states rather than by states with similar nuclear structure configurations.Then, if the comparison of such unusual experimental observables may bring useful information about the reaction mechanism, the influence of the nuclear structure and their interplay, it is still necessary to pursue these systematic studies.As for the (p,ir-) reaction, there are recent experimental evidences in favour of a two-nucleon reaction mechanism (T 9). Because of the double-charge-exchange involved in this reaction, such a 2 NM selects a unique p + n -► p +  p +  it-  two nucleon elementary process which leads naturally to the excitation of specific 2 proton particle - 1 neutron hole states in the residual nucleus. Such a selectivity of the (p,ir~) reac­tion can be seen in Fig. 1 of (T 9) where most of the excitation strength seems to be monopolized by one or a few high-spin two particle - one hole states. In the 0(p,ir-) 19Ne spectrum,3*^0 for example, the highly excited state at 4.6 MeV corresponds, within the experimental energy resolution, to a known (4.64 MeV, 13/2+) 2p - lh state in the 19Ne nuclear level scheme; two other strongly excited peaks are observed at energies where known 2p - lh states (6.50 MeV, ll/2+) and (10.42 MeV,13/2 ) exist in the 19F mirror nucleus spectrum. Selective excitation of such stretched 2p - lh states by the (p,^-) reaction have been observed for many final nuclei from oxygen up to molybdenum.Another example of the selectivity of the (p, ) reaction is given(Fig. 2, T 9) by the j-dependence observed for this reaction on, or lead­ing to, spin-zero nuclei. Differential cross sections and analyzingT 4 0ya. X G c m 4rK in e m a f tc f t  •-*— — *«oy »  "G e m^ c n ,  -  I &  - P b  I t  . ( E a - E t ) * - ( & - & ) *T a  lo b .\fF = (mQ + Z mflTi°ke r  s ' / s ’ - « n a - m ft M * l  U v £ n .  ine 9*  -  m b -  + Q  fc>»*ol k tn .E n . ocl*cm d V d t(2*o.*<Xa3»«"0 5 K I * & cm301powers of the 13C(p, tt~) 11*0g . s. an<3 11+C(p, *”) 150g .S. reac tions, which both involve a Aj = 1/2 angular momentum transfer, present striking simi­larities.21 On the contrary, the 12C(p, if”) 130q .S. , with Aj = 3/2 angular momentum transfer, leads to a much lower cross section and a negative analyzing power. Assumirig an elementary p + n +  p + p+Tr- two nucleon process and given the fact that pion production on nuclei at energies below the free NN NNtt process requires the Fermi motion of the struck neutron to be directed toward the incident proton, simple angular mom­entum coupling arguments allow a surprisingly clear interpretation of these experimental features.At this point of my presentation it won't be of any help to state, once again, that more experimental data and more theoretical analysis are needed; every new experiment, every further interpretation will point out some interesting or unknown feature of the pion and photo production reactions. However, it seems to me that we have reached a point where a systematic and coherent study of these reactions from both points of view of the theoretical analysis and the phenomenological comparison of the existing data must be done. Concerning the former, much progress should be made in the near future; I already mentioned the development of the relativistic approach of the ONM17 and an important effort is presently being devoted to a coherent analysis of the (p,ir) reaction in the frame of the two-nucleon model with the development of more or less standard­ized and multi-purpose computer codes.10*22 On the other hand, as stated in the introduction, a direct comparison of existing data of various one-nucleon transfer reactions, in particular the (p,ir) and (p,Y) reactions, could lead to a phenomenological understanding of these pro­cesses and then guide further experimental and theoretical investigations. However, the interpretation of such a comparison for a large sample of reactions, target nuclei or incident energies may be difficult, if not impossible, due to the extreme differences of the possible kinematical configurations.II. THE ROLE OF THE KINEMATICSThe two-body relativistic kinematics is obviously not a matter of discussion. However its effects, with respect to the kinetic energy of the projectile or the mass of the target may have unexpected implica­tions in the interpretation of the final result of a theoretical analysis or, even more, when comparing experimental results on different nuclei in different kinematical configurations. Furthermore, the choice itself of particular kinematical observables (T 10) may have a physical meaning or, at least, reflect some preconceived ideas about the underlying physics which can be extracted from experimental data or theoretical analysis.For example, the choice of the momentum transfer qcm, instead of the c.m.ngle, is obviously suggested by our hope to extract as direct as possible informations about the nuclear structure; on the other hand, high energy physics prefer the use of the covariant Mendelstham variable t. Simi­larly, the choice of an energy related observable is not unique. The choice of incident kinetic energy Ta may be misleading in reactions like ( P , tt)  since the threshold varies strongly from very light nuclei to heavier ones; we may prefer the c.m. total energy /s which, however, is directly dependent upon the masses of the particles involved in the reac­tion. To remove that dependence we can subtract these masses in the incoming channel, but a better observable seems to be the total c.m.302 J>(p,Ofct  (G eV/t)*303kinetic energy in the outgoing channel since it also takes into account the Q-value of the reaction.To illustrate the importance of such a choice of the kinematical observables I will take the particualr case of the (p,Tf+) reaction (T 11). In Fig. 1, the (p,ir+) kinematics for D, 12C and ^Ca targets is displayed as the energy variation of the momentum transfer qcm for selected fixed c.m. angles. With such a choice, we note that there is little overlap­ping between the kinematics of these reactions, especially for very high target nuclei; if the threshold kinetic energies is, of course, dependent on the target mass we can see that it is also the case for the minimum momentum transfer qcm involved in each reaction. On the other hand, if the same kinematics are plotted as the variation of the four-momentum tranfer t upon the total kinetic energy in the outgoing channel e£ for fixed c.m. angle, we observe an almost perfect ovelapping of these kine­matics for all nuclei with A > 10. For very light nuclei the remaining deviation is certainly due to the strong effect of the recoil of the re­sidual nucleus. For all these kinematics, the minimum value of is obviously zero but, more noticeable, the threshold in four-momentum transter is exactly the same; it can be shown23 that this minimum value of t is equal to (nip - m^)2. Before proceeding further, we must point out here a particularity of the kinematics of the (p,ir) reaction10; at fixed forward angle we note that the momentum transfer decreases when we increase the kinetic energy from threshold up to ~ 25 MeV; this kine­matical behaviour may have some implications in the interpretation of the rising of the (p,^) cross section from threshold, increase which is stronger than what can be expected from pure phase space considerations.A first example of the influence of the kinematics when comparing different experimental data is given on transparency (T 12); as it was previously noticed 1 the energy variation of the shape of the angular dis­tribution of different (p,^+) reactions is somewhat puzzling. For the **°Ca(p, tt+) 3 s. reaction, we note a shift of the position of the first minimum toward backward c.m. angles with increasing kinetic energy; in the case of the (3.85 MeV, 5/2+) state of 13C we also observe such a shift but in the opposite direction while the position of the first mini­mum remains at fixed c.m. angle for the 28Si(p, ir+) 29Si (2.03 MeV) reaction. In fact, this turns out to be a systematic trend where the kinematics are concerned. When plotted (T 13) on the "universal" (p,ir+) kinematics defined above, the positions in t of these first minima of the angular distribution show a linear dependence on with very similar slopes for different (p,^+) transitions. An additional systematic trend is observed in the fact that, at a given energy, these first minima occur at increasing four-momentum transfers with decreasing mass of the target nucleus (these trends have been previously reported l8» 13 without explicit reference to kinematical effects).Another example of the influence of the choice of a specific kine­matical observable is given by the comparison (T 14) of the analyzing powers of the (p, if+) reaction on %  at 375 MeV24, %  at 277 MeV25 and 12C at 200 MeV.26 The c.m. angular distributions of these analyzing powers show a strong minimum at very similar c.m. angles for both *H and 2K targets, while such a minimum is observed at a much forward angle for 12C. When plotted against momentum transfer qcm, the situation looks quite different since then it is the deuterium and the carbon targets which show a similar behaviour of the analyzing powers. In fact, when welook at these experimental results in terms of the e* and t kinematicalr304B-Hoishad , 10Cr Workshop focr1X4CAngular distributions from the *°Ca (p ,n + ) 4 ^ Ca g. s . reaction.Angular dis­tributions from the ■ ^ i ^ ^ ) 13C«(3.B5 MeV)cC f l L ' l l U I l  -sl 1 r t* H < ( 2 D 3  M »v V 2 *V 2 '■ 3(M»V, (Mr.T *  j' ’ Ie «s 4j =V me* 3 V *  1* • iidjd♦ ♦>I•0 ft• 1. ••♦ *49 1 6  1Ji K  K  iSt Ai'e ™Angular dis­tributions from the 2Bsi(p,7T*)29£i* (2.03 MeV) reaction.T12305T45Poa iH on  of H»o f  \r%Y minimum of ^ / d A• ‘' ° C a C p . « * ) <"C«i &•&• ? / 2 "A >« O  (p.w*) ' * o &•&• ^/2 +■ 16 Si.(PJT ' ) * V 2.03 Me*/ 5/2 +B3 62 MeV 7/2"X 4* c (  p > ^ )  « b 3 6 8  Hcv w4 u 3.36'5/2*O k §>j S-5 W,*/*r, * 1 *AyCe)0 - 0.2.€<1-0.4— -- ----- ----«----- — 4-- -(a)20 60  loo MrO 40o 500 600 700& ir  ,cm Scm (MeV/c)P- W olcl«-n«ka*6 .1 .0 to* oi-ol. prtfrin*'t*V  o^ r p p - » d i r + at 3 ? 5 M tVu c ( £ w T c t t. °t- 2 . 0 0  Me.v e.ftM -  .1 •>«.*,«=.).4 0.5 0.4 )e £  .  40 ?M eV44.5 M tY  47 I  MtVT AS307308observables, we note that they have been obtained at similar values of e£ and that a strong minimum of the analyzing power appears in the same t region for the three targets. Of course, the physical meaning of such a behaviour remains to be understood.I will conclude these remarks on the influence of the kinematics by looking at the role of the phase space factor in the definition of the cross section (T 15). It is well established now that the cross section of the (p,n+) reaction is strongly decreasing with increasing mass of the target nucleus; an example is given in Fig. 1 where the total cross section, estimated from experimental angular distributions of various (p,ir+) transitions, is plotted versus the atomic number of the residual nucleus. 27 Such a behaviour is usually interpreted in terms of increasing pion absorption with increasing amount of nuclear matter involved in the reaction. On the other hand, we can extract, from experimental differ­ential cross sections, a Lorentz invariant matrix element |M| 2 by calcu­lating the relativistic phase space factor 1/F (see transparency T 10):dO 1 I i 9 9 Pa 1  = —  x M 2 with F = 64it2 s —  ---- 7 . (1)dft cm F Pb (he) 2 'The energy variation of the quantity F (Fig. 2 - T 15) is very similar from one target nucleus to another except, of course, that its magnitude increases strongly with increasing mass. When we compare (Fig. 1) the mass dependence of the phase space factor 1/F (at = 60 MeV) and of the total cross section we observe a surprisingly good agreement between the two. This seems to indicate that such an invariant matrix element may be, in first approximation, constant throughout the periodic table. The relationship between such an observation and the usual pion absorption argument is under investigation.III. SOME SYSTEMATIC TRENDS IN (N,it) AND (N,y) REACTIONSThe first to use such a Lorentz invariant matrix element in the com­parison of experimental data seems to be B.M.K. Nefkens in a phenomeno­logical study of the role of the (3,3) resonance in the (Y,p) reaction. 28 The transparency (T 16) shows the experimental results of the 3He(Y,p)d reaction (Fig. 1) at two different lab. angles for a wide range of inci­dent photon energies. 28 The differential cross section of that reaction shows an exponential decrease with increasing Y energy with quite differ­ent absolute normalization and slope for the two angles. However, when we extract the corresponding invariant matrix elements |m| 2, In the way given above, and plot them against the four-momentum t, the two sets of experimental data fall into a unique simple variation of JM| 2 upon t (Fig. 2). This t-dependence of |M| 2 can be fitted by an exponential|M| 2 = A eat (2)with the slope a = 5.6 + 0.5 (GeV/c)-2. This fit is compared on Fig. 3 (solid curve) with recent measurements of the d(p,Y)^He angular distri­bution at 350 and 500 MeV incident proton energies. 30 As we can see, the t-dependence of the invariant matrix element extracted from either the excitation function at fixed angle or the angular distributions at various energies are in excellent agreement. The absence of any clear309energy dependence of the invariant matrix element, at fixed t, is inter­preted by Nefkens as a possible evidence of a small contribution of the A isobar in the 3He(y,p)d reaction at intermediate energies. This conclu­sion may be corroboratd by the completely different situation encountered in the deuteron photo-desintegration (T 17). In this reaction, where the contribution of the A(1232) resonance is much better established,2»3* the t-dependences of the invariant matrix elements extracted from experi­mental excitation functions32 at two fixed lab. angles (Fig. 1) are dif­ferent. Each of them shows up a broad peak centered approximately around the photon energy at which we expect the dominant contribution of the (3,3) resonance (indicated by arrows). These maxima of |M|2 occur, of course, at quite different four-momenta at each angle. It is interesting to note (Fig. 2) the striking similarity between this behaviour of the invariant matrix element of the Y + d -*■ p + n reaction and the one of the elementary Y + p * n + tt+ pion photoproduction reaction. 33 In the latter case the strong dominance of the Ar-contribution doesn't need any further proof.When we turn to heavier nuclei it seems we find again a situation close to the one observed for the d(p,Y)3He reaction. I have already mentioned that the 160(Y,p) 1 ^ g .S. reaction has been extensively studied in a wide range of photon energies and momentum transfer. 12 The excitation functions of the differential cross section of this reaction (T 18) show quite different behaviours, in shape and magnitude, for each detection lab. angle. However, when these cross sections are analyzed in terms of invariant matrix element (T 19) we observe, as in the case of the p + d -*• %e + Y reaction, an almost unique four-momentum dependence of |M|2 for the three measured lab. angles. Here too, we do not observe a clear s-dependence of the invariant matrix element at any fixed t. However, I want to point out that, by definition, the covariant four- momentum t contains an explicit energy dependence. Furthermore, we saw in the first part of this presentation that these experimental data have been analyzed, with some success, in the frame of a two-nucleon model involving the excitation of an intermediate A resonance16 (see transpar­ency T 7). Finally, we must notice the similarity between this t- dependence of the invariant matrix element and the q-dependence of the proton momentum density (see transparency T 6). In the latter case, the shoulder at high momentum transfer may be interpreted as a possible evidence of the absorption of the photon by a pair of interacting target nucleons. All these observations are a clear indication that an eventual contribution of the (3,3) resonance in the (Y,N) reactions on composite nuclei must be investigated in more detail.On the contrary, the (p,ir) reaction seems to show quite different features. For example, when the 10B ( p ,tt+ ) 1 ^ q .s . experiment differential cross sections10*34 are converted into invariant matrix element (T 20), we observe an evident energy dependence of |m|2 at fixed t. Moreover, each set of data shows a slope which is slowly varying with incident energy. This is more easily seen when each of these sets is fitted by an exponential function given by Eq. 2 (T 21). Then, the magnitude A of the matrix element increases strongly from threshold up to about Tp = 320 MeV and then decreases slowly with increasing energy. On the contrary, the slope a decreases strongly in the same range of energy and then increases slowly above Tp = 320 MeV. We must note that this kinetic energy, where the derivative of both parameters A and a upon energy changes sign, seems to correspond exactly to the value e* = - Mn - m^ where the maximum(«/qu) UP/^P310&.M.K. tfe fken * f lry tm e  Conf. M p y 8 3T46&aVfe* *H  t C l f j r f dfis. K.T R I U M Fd (p ,y ) * H ePi3.a.r^onne Conf* M ay  83311£  t u n dO  T o k y o9\c\- 4.T o k yo4<f-10’■PI8c-.s.• ©lab • 4 5 °♦ ▲ 90°- ^ 5 (o♦ ♦m  '«i £d A c n  (nt/irf,4 (fl- ++4ftL  *  ‘ * *  * * f  *  * ♦ * < ! » * !+++4{+I .1 I I * , »400 200 f£-g 300.< .2 O.•B— I I I  1 I  —  t  1 i •  1 ^<6o ( v , p ) ^ e.s.. 45 °v A 00°♦*«\4«S» •& 5 °J, .-.-I.-*' *■" . -*    ■»  ^ ---------------- M.8 -6 •* -2 O- t(G-tV/c)*V20¥♦  f£♦♦tTpa  45* M a V la  4 6 6  J  { l ? C Fo 250 o 291o 32 0  □ 4 10v  465 ▼ 606r  . .v_. '»*•cJqyt•a t  f a t f h YT2A315316Influence of the A-contribution is expected. This trend, which has been unsuccessfully analyzed in the frame of the ONM,35 should be studied more closely within a two-nucleon model involving the excitation of an inter­mediate A. A more extensive and systematic analysis of the existing (p,*) data on nuclei other than 10B is under progress.I will end this presentation by an unexpected phenomenological observation made on different (p,*) experimental data. On transparency (T 22), for example, we present the experimental data of the 9Be(p,n+)8Be reaction at 410 and 605 MeV measured at Saclay. 10* 34 The momentum transfer distributions of the cross section, presented here in terms of |M] 2 versus t, are very similar for both the ground state (0+) and the first excited state at 3.37 MeV (2+). In fact we have a good overlapping, within the experimental incertitudes, between these two states, for both energies, if we renormalize the 2+ state cross section by a factor 1/5.The interesting point is the fact that this factor 5 is precisely the ratio of the number of spin states (2Jp+ 1) in the outgoing channels.If we turn to the 28Si(p, ir+) 28Si reaction near threshold18*36 we note (T 23) a surprising resemblance in shape, and moreover in the energy variation of this shape, between the momentum transfer distribution of the cross section of the (1/2"6) 28Si ground state and the one of the (3/2+, 1.27 MeV) excited state. If we accept a slight shift toward higher momentum transfer for the higher excitation energy, we observe an almost perfect coincidence between these two sets of data when we renorm­alize the (3/2+) state cross section by a factor 1/2, which corresponds, here too, to the ratio of the (2 Jp+1) factors between the (l/2+) ground state and the (3/2+) excited state. The same observation can be made (T 24) when comparing the (5/2+ , 2.03 MeV) and the (7/2", 3.62 MeV) states of 28Si. The momentum transfer distributions of their cross section and their energy variation, are identical, but*different from the previous case. Furthermore, the shift in momentum transfer happens to be in the same direction as in the case above, which could be an effect of the kinematics. Finally, the ratio between the cross sections of these two states is about 0.75 which corresponds, once again, to the ratio 6/8 of the (2 Jp+ 1) factors. This phenomenological rule may be accidenta 1 but we have observed some more or less accurate examples on other (p.ir'*’), and also high energy (d,p),37 experimental data. However, this rule does not hold, for example, for the 6Li(p, tt+) 7Li reaction at 600 MeV which could be due to the complexity of the nuclear structure configuration of the 7Li states. The origin and the degree of validity of this previously unreported observation are under investigation.SUMMARY AND OUTLOOKSI have presented some of the salient features of the pion and photo production reactions at intermediate energies in connection with the present status of our knowledge of their reaction mechanism. In spite of much progress made during the past few years, there is still a kind of confusion regarding these high momentum transfer reactions, in particular when we attempt to analyze them in a systematic and coherent way. We saw, for example, that the (Y,p) reaction seems to require quite differ­ent reaction mechanisms depending on the photon energy. However, this evidence may be questioned where the (Y,n) reaction is concerned. Furthermore, the role of the A(1232) isobar in the (Y,N) process is still unclear when target nuclei heavier than deuterium are involved. On the317T 2 2$ B e  ( p . n ^ B eU +) [ 9 . w |.0 0  t;cvo 605 a 6I30000 - lood[iOOpjL  10O o?tii* \*XI I4.6 A  -2H frcV /c)*clff/cJiXcm nb/frr318 T 2 1 3?' 8 5 i ( p > f r + ) 2 9 S i/ ■(r .5(00totooAO<------------ 4.2?  K.eV 3/a+ • H ▼{*> *Tp(McV)(*i m  U p p s a l a  y.A G>10&  toftHI*!1<•4fi*♦< 6 0  i w c f10*t< 4 9 ^,i»W» ,1 l> ll«^  -• —•f " 0 0  ^CTn 603(W«V/c)UOO V C 3V i  : £  S*p<* 4. o  4: & 3 v « - d  eT2A3192 8  S i (p ,T r+) « s i100*AC£oCl“015tooto100 ^r K x Ttoo102  03 MeV 5/ *3  62 MftV 7/2~ ■ ** TP (H eV )%«| > 1 8 5  U ^ * o \q  * 4 - 6460 IUCF* .•-f tJL.I__ I. -i J4 6 9 I W C FI • ■ • ‘5 0 0 6 o o TOO7 /a ‘  2 T p * l e 8  5/2+ 2 ^ * 4  • *320other hand, a two-nucleon mechanism with the excitation of an inter­mediate (3,3) resonance seems to be the most promising picture for the (N ,t t )  reaction. Some more or less clear "experimental evidences" of such a TNM have been seen in many pion production results in general and in the (p, tt— ) reaction in particular. However, a systematic and coherent phenomenological data analysis of all the (N , t t ) ,  ( y , N ) ,  (d,p)... reac­tions must be pursued. I have presented here some preliminary results of such a study and tried to stress the importance of the kinematics and of the choice of the different observables in this kind of comparison of experimental data. This type of systematics may reveal some unsurmised common features among the existing data and may serve as a guide for further experimental and theoretical investigations of these high momentum transfer reactions.REFERENCES1. For a complete experimental and theoretical review of the (p,it) reaction see H.W. Fearing, in: Progress in Particle and Nuclear Physics, vol. 7_, ed. D. Wilkinson (Pegamon, Oxford, 1981), p. 113;H.W. Fearing, "A bibliography and summary of data for the (p,iO reaction", Internal Report TRI-80-3, TRIUMF, 1980;D.F. Measday and G.A. Miller, Ann. Rev. Nucl. Part. Sci. 29^ , 121 (1979);B. Hoistad, in "Pion production and absorption in nuclei", IUCF Workshop, Bloomington, Oct. 1981, A.I.P. Conf. Proc. 79_, (A.I.P.,New York, 1982), p. 105.2. For a complete experimental and theoretical review of the (N,y) reactions see J.T. Londergan, in "Pion production and absorption in nuclei”, IUCF Workshop, Bloomington, Oct. 1981, A.I.P. Conf. Proc.72, (A.I.P., New York, 1982), p. 339;J.L. Mathews, in "Nuclear Physics with electromagnetic interaction", Mainz Conference, June 1979 , Lecture Notes in Physics, vol. 108, ed. H. Arenhovel and D. Drechsel, (Springer-Verlag, Heidelberg,1979), p. 369.3. For recent (p,*-) results near threshold see "Scientific and Internal Report", Indiana University Cyclotron Facility, 1981 and 1982.4. D.J.S. Findlay and R.O. Owens, Nucl. Phys. A292, 53 (1977).5. J.L. Mathews et al., Nucl. Phys. A267, 51 (1976).6. J. Mougey et al., Nucl. Phys. A262, 461, (1976).7. L.R.B. Elton and A. Swift, Nucl. Phys. A94, 52, (1967).8. H. Schier and B. Schoch, Nucl. Phys. A229, 93 (1974);H. Goringer and B. Schoch, Phys. Lett. 97B, 41 (1980).9. D.J.S. Findlay and R.O. Owens, Nucl. Phys. A279, 385 (1977).10. P. Couvert, These de Doctorat-d'Etat, Universite de Paris-SudOrsay, Note CEA-N-2320, Saclay, 1983.11. D.J.S. Findlay and R.O. Owens, Phys. Rev. Lett. 37_, 674 (1976);D.J.S. Findaly et al., Phys. Lett. 74B, 305 (1978).12. J.L. Matthews et al., Phys. Rev. Lett. 38_, 8 (1977);M.J. Leitch, Ph.D. Thesis, Massachusetts Inst. Tech., 1979.13. J.W. Negele, Phys. Rev. Cl_, 1260 (1970).14. C. Ciofi degli Atti, Lett. Nuovo Cimento 1, 590 (1971).15. J.T. Londergan, G.D. Nixon and G.E. Walker, Phys. Lett. 65B, 427 (1976);J.T. Londergan and G.D. Nixon, Phys. Rev. C19, 998 (1979).32116. H. Hebach, A. Wortberg and M. Gari, Nucl. Phys. A267, 425 (1976); M. Gari and H. Hebach, Phys. Reports 72, 1 (1981).17. E.D. Cooper and H.S. Sherif, Phys. Rev. Lett. 47^ 818 (1981);E.D. Cooper and H.S. Sherif, Phys. Rev. C25, 3024 (1982).18. T.P. Sjoreen et al., Phys. Rev. C24, 2569 (1981).19. F. Soga et al., Phys. Rev. C24, 570 (1981).20. S.E. Vigdor et al., Phys. Rev. Lett. 49^ , 1314 (1982).21. W.W. Jacobs et al., Phys. Rev. Lett. 49, 855 (1982).22. B. Keister and L.S. Kisslinger, in "Pion production and absorptionin nuclei", IUCF Workshop, Oct. 1981, A.I.P. Conf. Proc. 79,(A.I.P., New York, 1982), p. 243 and 265, and to be published;M. Dillig, F. Soga, and J. Conte, ibid, p. 275 and 289 and in preparation;W.R. Gibbs, ibid, p. 297, and in preparation;J. Iqbal, Ph.D. Thesis, University of Indiana;G. Walker and J. Iqbal, in preparation;P. Couvert and M. Dillig, in preparation;M. Hirata et al., Tokyo preprint, 1983, and K. Yazaki, privatecommunication.23. G. Jones, private communication.24. P. Walden et al., Phys. Lett. 81B, 156 (1979).25. G. Lolos et al., submitted to publication.26. E.G. Auld et al., Phys. Rev. Lett. 41, 462 (1978).27. B. Ho'istad, Adv. Nucl. Phys. JJ_, 135 (1979).28. B.M.K. Nefkens, contribution to the symposium on "Delta-Nucleusdynamics", Argonne, May 1983.29. W.J. Briscoe et al., Phys. Rev. Lett. 49, 187 (1982).30. R. Abegg et al., Phys. Lett. 118B, 55 (1982);J. Cameron, private communication.31. J.M. Laget, invited talk at ”7° Session d'Etudes biennale de physique nucleaire", Aussois, mars 1983.32. P. Dougan et al., Z. Phys. A276, 55 (1976) and A280, 341 (1977);K. Baba et at., Phys. Rev. Lett. 48, 729 (1982);K. Baba et al., Phys. Rev. C28, 286 (1983);T. Kawamoto, thesis (unpublished).33. T. Fujii et al., Tokyo preprint (1976).34. M. Dillig et al., Nucl. Phys. A333, 477 (1980).35. W.R. Wharton and B.D. Keister, Phys. Rev. C23, 1141 (1981).36. S. Dahlgren et al., Nucl. Phys. kill, 245 (1974).37. A. Boudard et al., Phys. Rev. Lett. 46, 218 (1981).323A-Isobar Effects in Quasi-Free Scattering M. Dillig+Institute for Theoretical Physics, University Erlangen-NeurnbergErlangen, West GermanyAbstractQuasi-free nucleon knock-out is conventionally treated as a genuine two-nucleon process, incorporating the 'hard' nucleon knock-out in the elementary NN t-matrix, while treating 'soft* multiple scattering cor­rections as initial and final state interactions via optical potentials.A more realistic description of these reactions, especially above the pion threshold, requires the inclusion of mesonic and isobaric degrees of free­dom. In particular at higher energies, the influence of genuine three- nucleon mechanisms, induced by the excitation of the A(1236)-isobar close to its mass shell, is epxected to be rather important.OutlineIo General ConsiderationsII. Calculation of A ContributionIII. Present Status: A Few ResultsIV. Summary/OutlookThe work reported here was done in collaboration with V.E. Herscovitz and M.R. Teodoro from the Universidade Federal do Rio Grande do Sul, Porto Alegre, BrazilWe thank the CNpq-KFA (Brazil - W. Germany) and the Finep (Brazil) for financial support.324I .  G enera l C o n s id e ra t io n s- f c J . S .  Cfraictz j »•»A ' i A - ir^J^ — - S^XsJ-oJOfr^d ' Tdi2o 40., clfc.Z y o  Kai^e_ •<• )i I f i t  . , t -Z-e. "  ^ ( r ) c i r t -------------------I - a ^ Q ^  j e _p L a w c  cccu}^ d n u kI ■ Q - u g s c ' f < ^ - e - |  -  Z ~ h o c U j  m ^ _ c f t c u a s w-  ( A - i )  n te c S jD R SA - iso b ath  ctecjt&iof fizA .cLohn :QjULaik G r .T . bomsUi'oh."•£■-I*lajhi# bCr^r1)( A  ■£■ -n^ahix )fooc^- £ - -t ( K,jr1 Rua? A  — eJ^dbjchloft^t A« •326j\ppycp*ate J< W e s ]6d/*jI * l M/‘IIIGJ_ '  )  j A (w M )•fckl*StJCO»\.ctnunMjf.C a -;*) S fx s J c J o tS_Arlawie.: o3cvo Kxape. O^j ^  ^  ) ~^2L 3T a ( » )±^ A Ma-for\Q.re.4- Q ^ V S— co /a, ~ £ a k j  ~  ^ c t ^ m—  LoufX- tww&*h.nt 4vcun </ey«S’ !T a - * . - * * 8 ^ 6  ♦ *  "T Z r -t£ skfiM-Vf 1 ^327I I . C a lc u la t io n  o f  A -C o n tr ib u t io nWe e s t im a te  the in f lu e n c e  o f  the  A - is o b a r  in  a m ic ro s cop ic  meson- exchange m odel, in c o rp o ra t in g  tt and p exchange to g e th e r w ith  a Landau- M igda l type  p a ra m e tr iz a t io n  o f  the  ( re p u ls iv e )  s h o r t- ra n g e  NA c o r r e la t io n s .  To keep the  e v a lu a t io n  o f  the  t r a n s i t io n  am p litu de  a n a ly t ic a l ,  we employ a few a d d it io n a l a p p ro x im a tio n s , such as to  expand the t r a n s i t io n  p o te n t ia l  in  Gaussian forms and to  use a s im p l i f ie d  WKB re p re s e n ta t io n  fo r  the  d is ­to r te d  waves o f the  p a r t ic le s  in  the con tinuum . N uc lea r s t r u c tu re  e f fe c ts  are  e va lu a ted  in  an harmonic o s c i l l a t o r  b a s is .A excikxKoicik. HM-cXeu.'Snt txhCa s*Cp, *1°)SOCCcta/iok ^m e d i u m  Cvf'ro.oh'ohs: ?■ ~Tjo =  5  co  Jte\T3 C€j\JLuii-?5T>T a . ~  ok*y<L  Gp A  ^  ^ S D  HxJ/fc. A ? ~ 3A ^ O  H-eiYc A P~0S i n a i a -HacU uJk  £$tdrG\ X ■IT*' 4*aH.sLbibk, 11328ETX'fere/nes Jr*Pvee.£ A - C O  A N TG a a ( u )6 ^  \ d  -4=f> X[ ( A A ^ X C M jCT^ . ^JTCZJlz £ a n t  ~A hujh Ik COkftK.U.UM,A Shxks Oi clejXUJCHxfe-C£oS(Ja£_A  -Cl hxxdjcas m tx tL u m  S p k lK tc jp  o £  A  S p t . c h v J ’k  LCu*j<l rvKMluttL Zjf{tcbs<po/ Lzio nxu.U{foolciM.JiLs 0 ^<Ss.a tu^cL (for (A A ) ^  staffs ■.C L d s c - U  s Wr 'JL  IU X .cL.q u S  r• X #  ( a w ) X ' / z ~ ' "U V 3lC>T ~' m329| A -  d o m U a k jJ .  iy n M .^ U i^ n c  grxp^JucLg.^* 4 ------------------  -tA  “^ I ^ A A .  ^ A A  U / >(7TcUC.S0^C>‘C  ^ X)-Kit/vCitsr>=  , ( y ^ - V g  ) S-r  ^ ) ‘ ^Sor/ortx.:-K-f balwLOLg - S  f r T :  « S /o c H .^ » c e _ t 'T c + p■N+ 'T T +-  4 ( q a  ) x T  : VipuXstv*. n a  c o h t M t o *CoadMo/t spate. : ("f-e. ) * T r  k h a M « .3301 'I a 111I+  «-ftce.o -  £ A m  WcIo SU lLZ.s r+  -pr* [ C M ) ) { & A )  | £ 0-,u - ~lAUMUl£|Mf. e 6-,u --«0 GO - £ L ^ik. L^sobcxr CDc>pi'U)ciy JJo^lePZDuX^oka/igr^. '-W -A A . =  +  (* i r # u )  +  T a  +- f -  V a  '  T ^ a C  nucut. /£ d Uf ^ c o  4-f V a  f Cow/jUa/) fa &Sjo*pKirt ci^ cikKQj.s’ /  *  '  i ^ — f  +i  tQasHi-ctaMut J^w _-e M M  A - 6 N l C331III. Present Status: A Few ResultsPreliminary calculations on 12C show an appreciable influence of A-degrees of freedom. At low incident energies (~ 100 MeV) isobar effects are found to be of similar importance as off-shell corrections in the elementary NN t-matrix. At higher energies (> 400 MeV), especially at energy transfers around the AN mass difference and at high momentum trans­fers, they dominate the cross section (details depend sensitively on the inclusion of the isobar via a closure or a medium corrected propagator)0h o b U m :CohtpLexihj >  O z i a t H  lisKaE* C(il0.si - S t u ^ h i  s o  'fxy p ioA iA  :— B— a— i ■ ——— »—  -faxjctLgciKok.— Grcucsclou. q f  A W  U fu a _ c K 'o ic—  G xxxjls sloux c U s b t H o u s~~ hJoodiS '--C a X  C>*. Co. p .  £Xf?(UM dJLd tk  QtUtSjCjOULS4<JnaS ^fi*co£ b  shvdbu o o k o u J  L K ^ ^ c U z h t^  G tn c l a p ^ o x o T t .G L K ‘oK g332c J I omJz \ 3  Loomiyfon. - Ooi'ic<s-fo>f>hjjxoo&UJLcvhxis&j  Guqslfajt,— — GJF -I- A>  too KeV~ :l-gobcuic. /-K*rottic. e/fcote ^  off skxjR coi^H^sfLH. tppAJP*i#(iqr^) -2 S3■Noh e W c  Idhe-M a h ' o ^ :UlozJ W  -&-c& cLsl' cLe;  to J b J r . (Luij-s )—  Gjuaii-fite^—  G F +—  ©F-fKtdAUMno  Eu (H*v)t ?oa/vo2J ° - S /'UGfW>(HiJTOo\t by A~z.ffco.ks; u s k . h \ a U c< <3334i 11 1 ' ........J+Cyl 63. - bt£a<jcoar,acC f>,^) 'c  (g.s.) ,  «T*^ (P ^ ( z o K t yOJJL3ishd'o»e ! T//<3—  Gmas'ofuiA.—  O . ^  -+ £>Cu<ofi a F  +  ^ ( w d ,JiecUuto coiv<ic.t..' 3>tMS\hj ctty?. A-.Se£/.^ f x j u d  A  e $ c c b  a f  k u o e .  G L  3<^rUXjM+tik vK_ CoM cTmsxoi s "S* Ct^ jfoilioMX, • -' I'**31*- ** is^ CC--335Coh*.cKont Dt ,3r C .C p, d p p )( A -3) f .p Skx»i> Ai £f°° teVfc)^-Ba&d Ad<3~<Qd d ^ c i ^ a ^ d E ^ 1A  £art>. aui>.s: )4- TTfa..S'fc ACUoM\/(c)I  tII Tv**- A ""—  A—  T^eje. A-f /oU) vmJKyo^. 'ftcU. abjotpKvu.—  —  v^tJJL dfoJO\,y,ij&K f_2j.—  Cju.c(si <h<x. a^clfy om fy0 .5  -•2XX> -?SO100 Oit :336[ A ~ ^  K S  uA' ok I k  C o o i c C K a U i ^pct c£-Tj/aC -($ . s . )•s*^ )- o - Q —  "Ar-- <•*/_  < ^ AN 1 l-sv^ A  '-^AO-sJ) ~  E L - ^ T / zj a  -  [He/')t ’U r )  ^A  * boiULcl s W t*r  ho ClbSOipf\c>H_-i s  7 —  hxxc^jo,^r ^ h j )A  Ccwe^ fi^ hCtuLji KT"J~A ^  ^pzce-3371. A degrees of freedom expected ata) > m , Q > 3m .TT TT2. Different reactions/kinematics to distinguish-*■ quasifree A propagation-*■ (AN) states (medium corrections)3. Problems:Calculations too crude (distortions; factorize,....) Exp. information not specific enough (except13C(p,dpp))IV .  Summary/Conclusions4. Theory:Develop approximations to include A as effective wave function in standard codes.5. Experiment:Comparative studies of high Q, (jJ£x „ 300 MeVCorrelation of different reactions:(p,2p) - (e,e'p) - (e,e') ....(p,p ) - (n,tt*) - ....In conclusion we find a nonnegligible influence of A-degrees of freedom on quasi-free scattering: for the extraction of subtle effectsat low energies and in general for most kinematics at medium energies, isobar induced three-body contributions have to be included. This trend should be confirmed by more realistic calculations in the same micro­scopic meson-exchange model, which avoids, however, the approximations mentioned above (claculations are in progress). As a guide for such a theoretical program, new experimental data at kinematics appropriate to unravel A-isobar contributions— preferentially at energies far above the pion threshold and at momentum transfers above the Fermi momentum—  are clearly needed.339MEDIUM RESOLUTION SPECTROMETERC.A. MillerUniversity of Alberta/TRIUMF, Vancouver, British ColumbiaThe TRIUMF Medium Resolution Spectrometer (MRS) is a 1.4 GeV/c QD system. It has a solid angle acceptance of 2.5 (1.5) msr at scattering angles above (below) 15° and a momentum acceptance of more than ±5° and a momentum acceptance of more than ±5%. Good scattering angle resolution requires the use of a front end chamber with the concommitant flux limitations. The spectrometer beam line is presently limited to beam currents less than 100 nA although it appears feasible to raise this to 1 pA. Several hundred nanoamperes of polarized beam are typically available from the cyclotron continuously variable in energy from 200 to 500 MeV with 100% macroscopic duty factor.The MRS upgrade program which started over 2 years ago is now in its final stages. The goal is to provide an energy resolution under 100 keV as well as enhanced count rate capability. Dispersion matching is implemented in order to accommodate a beam energy spread of 1 MeV or more.The major elements that have been commissioned during the past year are the six-quadrupole dispersion-plane twister in the beam line and the continuous vacuum target chamber. The twister quadrupoles are installed in the 10 m gap between the intermediate focus at the upstream target location4BT1 and the spectrometer target location 4BT2. The twister rotates the horizontal plane of dispersion of the beam line into the vertical bend plane of the spectrometer. The quadrupoles are mounted on a carriage which can rotate to adjust the twisting angle and accommodate a spin-precession solenoid near 4BT1 as well as translate along the beam line to maximize floor space at either target location. Since the twister acts as a unit section between 4BT1 and T2, its first-order optics are independent of this translation. The beam line can provide momentum dispersion at the target up to 20 cml/% which will match the spectrometer for the (p, tt) reaction at 350 MeV. Reactions producing protons require much less.In order to establish a sufficiently accurate dispersed focus from the stripping foil in the cyclotron to the spectrometer target the optical properties of all beam line elements including the cyclotron extraction port must be measured. Such measurements have occupied a dozen shifts of dedicated cylcotron time delivering a beam with small phase space. The extraction port properties have been measured at two energies (200 and 350 MeV) and the effective lengths of the beam line quadrupoles have been determined at the the 1% level of accuracy. However, since some quadrupoles must be known to better than 0.2%, further work is needed. Using the available information and a small prototype drift chamber at the spectrometer focal plane, a resolution of less than 200 keV at 350 MeV hasbeen measured.The continuous-vacuum target chamber has been in use for some time at scattering angles above 15°. In this range, the chamber rotates with the spectrometer over a range of ±13°. Larger excursions require a spectrometer340port change which is accomplished in a few minutes without venting the chamber or spectrometer. The micro-processor based controller will allow this to be done by users in the counting room. Scattering angles in the range ±15° require the installation of a horn-shaped extension to the chamber which encloses a small beam blocker. It obscures the range ±3° about the beam direction and limits the beam current to a few nanoamps.This equipment is now available but has not yet been used. Its installation or removal is expected to take a few hours.Installation of the remaining major elements of the upgrade program will begin in the December/83 shutdown. All of the existing focal plane instrumentation will be removed and a wedge-shaped vacuum vessel extension will be installed in order to place the exit window close to the focal plane and reduce the effects of its multiple scattering. Then a new detector support frame will be installed and the first of the two 30 cm x 115 cm Vertical Drift Chamers (VDC) will be mounted. Each VDC contains two anode planes, each of which has 176 active wires with single-transistor pre­amplifiers at the ends of the wires. The wires of one plane of each chamberare tilted at 30° to measure the transverse coordinate. All planes of thefirst VDC are now complete and it is expected to arrive at TRIUMF in early December. The planes of the second VDC are ready for winding and it is expected to be available in early January/84. The readout system for the VDC's is the LeCroy 4290 TDC-per-wire system which will maximize the particle flux capability. In tests with the small prototype VDC, this readout performed well. The spatial resolution was measured to beapproximately 200 pm. Rates up to 200 kHz per wire were accommodated.341Above the drift chambers will be mounted an array of plastic scintillator trigger counters, each 6 mm thick by 10 cm wide in the dispersion plane. This will allow convenient selection of momentum bite in the event trigger. Also to be installed in December are some collimating veto plastic scintillators inside the MRS dipole vacuum vessel to reduce in­scattering from the poles and vacuum vessel.During the January-February/84 beam schedule, running of experiments on the MRS has been deferred in favour of commissioning and instrumentation tests with beam. Among the activities expected then are the continuation of beam line calibrations, testing of the focal plane instrumentation, refinement of the spectrometer dipole pole-edge shims and the installation and testing of a new low pressure wire chamber at the spectrometer front end. As the capabilities develop, sample data taking by participating experimenters should be possible.Work has begun on other enhancements of the MRS facility. Design has started for the mobilization of the 8" aperture quadrupole doublet collecting the beam after passage through the target. This will allow the doublet to move on rails along the beam line and approach the target location as the spectrometer vacates this area as it moves to larger scattering angles. Less beam spill will result so that decreasing scattering yields can be compensated by a larger product of beam current and target thickness.Some effort is being devoted toward the development of a focal plane polarimeter. Attention is being restricted to a design involving a carbon analyzer with wire chambers. Some existing 1 m 2 wire chambers are being342studied in order to decide whether repairing and refurbishing them for this application is worthwhile. Also, possible designs for new such chambers are being considered. Although the new focal plane detector support system was designed to accommodate the addition of a polarimeter, it will be necessary to raise the proton hall roof beams by perhaps one or two feet to provide adequate head room.343EXOTIC CONSTITUENTS OF NUCLEINON-NUCLEON DEGREES OF FREEDOM IN NUCLEIF.C. KHANNAAtomic Energy of Canada Limited Chalk. River Nuclear Laboratories Chalk River, Ontario, Canada K0J 1J0High energy probes nave been used to study in greater detail tne structure of tne nucleus. In electron scattering1, transfer of large momentum to the nucleus yields a better understanding of the ground state charge distribution (elastic scattering) and the transition charge density (inelastic scattering). Investigations with high energy protons may be expected to yield similar information about nuclear structure. The outline of tnis talk, is as follows:1. Introduction2. Elastic scattering - a remark3. Inelastic scattering and nuclear response4. Role of nuclear structure - two examples5. Conclusionsi. INTRODUCTIONTne structure of the nucleus in terms of nucleon degrees of2freedom was established after careful experiments like (p,2p) and (e,e'p). Nucleons from deep lying states were knocked out, and the spec­tra displayed a structure that could be interpreted as shell structure ofthe nucleons in the nucleus. The shell model found theoretical justifica­tion in the work of Brueckner which established tnat, despite strong two- body interaction among nucleons, the structure of nuclei may be interpre­ted in terms of nucleons moving freely in a nuclear potential. The Brueckner theory3 explained the ground state properties of nuclear matter and of finite nuclei. Furthermore, it provided a qualitative understand­ing of tne single-particle (i.e. nucleon) excitations in nuclei.346But over the last two decades the Idea of the structure ofa nucleon in terms of quarks has been established . The nucleon is a com­posite structure of 3 quarks. Furthermore, it is easy to understand excited states of a nucleon. Tne lowest excited state is the isobar (A) with spin (S) and isospin (T) equal to 3/2. In transferring energy, (co) and momentum (q) to the nucleus, do tne isobars begin to play a signifi­cant role at large q and m? It may be appropriate to ask the question:Should the Dirac equation be used to describe the dynamics of a composite system like a nucleon?Pions occupy a special place in quark phenomenology.Their structure in terms of the quark-antiquark (q-q) system is suspect. Should pions be considered to be Goldstone Bosons resulting from the spon­taneous breakdown of chiral symmetry?The introduction of meson factories or high intensity medium-energy proton beams has made it possible to take a closer look at pions and isobars. It is possible to study the propagation of isobars and pions in nuclei. In tact, the propagation of pions would involve the pion self energy (1 )^ in the nuclear medium and the relationship of self energy to the optical potential is well known6. The pion self energy in terms of Goldstone diagrams is shown in Fig. 1. The particle-hole excita­tions with the particle being a A provide a large contribution to the pro­pagation of a pion in a nuclear medium. The propagation of isobar parti- cle-nucleon hole (A-h) in nuclear medium (Fig. 1) is the important ingre­dient in the pion optical potential. Tne dynamics of A-h states in nuclei has been a subject under intensive study tor many years347With this background let us look at elastic and inelastic scattering oi medium-energy protons by nuclei.2. ELASTIC SCATTERING - A REMARKIt is usual to analyse the proton elastic scattering data in terms ol an optical potential, which may be either a parameterisen form with several parameters or a torn obtained by a detailed microscopic cal­culation. The latter involves an evaluation ot the proton sell energy in nuclear medium. For finite nuclear systems and for low-energy proton scattering, high energy and low energy (or collective) excitations of nuclei contribute approximately equal amounts to the proton self energy. The contribution of high energy excitations in finite nuclei may be included by a ladder summation ot the iterated interaction between twognucleons, as is the case tor infinite nuclear matter . Low-energy collec­tive excitations are included by an RPA summation ot nucleon particle-hole states: For elastic scattering of high-energy protons it may be appropri­ate to consider the A-n collective excitations in finite nuclei. Diagram- matically the parallel is displayed in Fig. 2. The nucleon p—h state con­tribution to the nucleon self energy in second-order perturbation tneory is shown in Fig. 2a, while the A-h contributions in second order are shown in Fig. 2b, 2c and 2d. It is usual not to include the A-h contribution to the nucleon optical potential. In higher orders the A-h contribution to the nucleon self energy is shown in Fig. 3. It is interesting to note that tne propagation ot A-h state in the nuclear medium (Fig. 4) is common to the nucleon (Fig. 3) and the pion (Fig. 1) optical potential. With the A-h contributions forming a crucial part ot the pion optical potential,348should such contributions be ignored in the proton optical potential in an energy range where excitation of A is possible? This naturally leads to the question: Are there contributions from A-h states to elastic scatter­ing that are being masked by the use ot free parameters in the optical model potentials?It may be useful to calculate tne role of nucleon p-h states and A-h states in a model that treats tne propagation ot p-h and A-h states in a consistent manner. It is not easy, but consistency is crucial tor an understanding of the isobar degrees of freedom in elastic proton scattering from nuclei.3. INELASTIC SCATTERING AND NUCLEAR RESPONSEThe nucleus is a many particle system with a finite size. There is a variety of excitation modes of the system:i) Low-energy rotational and vibrational modes. These excitations arise from the rotation and vibration ot the finite nuclear sys­tem. These states are at low energies and we shall not consider them here since they are not expected to play an important role in scattering ot medium energy protons, ii) Single-particle modes. These are the modes alluded to in theintroduction; the observation of these modes provided a justifi­cation for tne shell model ot the nuclear systems. Excitation ot such states in quasielastic scattering has been discussed by Dr. Chant.iii) Collective states. The nuclear collective states may be classi­fied as follows:349Electric Multipole. E1,E2,...The giant dipole resonance has been studied extensively. The giant resonances ot higher multipolarity have been discussed by Dr. Bertrand. The experimental data may provide us with the fine structure of these resonances. The excitation ot the electric multipole resonances does not exploit the spin ot the proton.Spin Electric Multipole. El: (axY^)1, E2: (oxY2)2,...States ot this type are not excited by electrons or by spinless projectiles. Only projectiles with spin will excite sucn states. Spin electric multipole excitations do play a role 10 in enhancing low-energy electric multipole transitions in odd nuclei. No information about the giant resonances in nuclei is known at this time. Protons may be a suitable probe tor the study of spin elec­tric multipole giant resonances in nuclei.2Magnetic Multipole. Ml: a, M2: (axY ,...Magnetic giant resonances may be studied both by electron and proton scattering. Study of Gamow-Teller resonances isospin rotation ot the giant Ml resonances has been carried out very effectively with medium-energy protons. It is anticipated that other various magnetic multipoles will be investigated with protons. One particular unnatural parity resonance that belongs in this category ot resonances is a 0+ -K)~ transition in a nucleus. This is one of the examples that will be considered in detail, to show that pionic effects are dominant and that a study of such resonances may have important implications for an understanding of Chiral invariance of strong interactions in nuclei.Ttiis discussion indicates tne richness ot collective states in nuciei. For a long time we have restricted ourselves to only the nucleon degrees ot treedom. Addition ot isobar degrees ot treedom will enhance the collective models ot excitation. Ot course the nucleon and tne isobar collective modes will interact and tne distnbuion ot strength at low energies (10-40 FleV) and at high energies (- 300 MeV) will be modi- tied depending on the interaction.It the quark degrees ot treedom are dominant it is interes­ting to enquire about the collective modes ot nuclei. What does the exci­tation spectrum look like?3.1 Nuclear response1. Proton inelastic scattering with an energy transter m and a momentum transter q will involve a nuclear response, k(q,m), which, with spherical symmetry, will depend ontwo variables i.e. R(q,u>). This is to be contrasted with the2elastic scattering, where the response depends only on q . Heun- stically the nuclear rsponse may be expressed as the excitation and propagation ot p-h states in the nucleus. For an interacting p-n system with an interaction V(q), mdependant of w, the nuclear susceptibility may be written as:1 + V(q) xo(q.to)where xcKq*00) ls the susceptibility of a non-interacting p-h. The nuclear response R(q,a>) is simply related to x(q»(»>)• The cross section tor proton inelastic scattering depends on the reaction mechanism, the kinematics and the nuclear response i.e. the nuclear structure. To gain useful information about tne nuclear351response or tne reaction mechanism a consistent calculation is essential. There has been a great deal ot discussion about the reaction mechanism over the last two days. Let us consider the role of nuclear structure.ROLE OF NUCLEAR STRUCTURE - TWO EXAMPLES Gamow-Telier transitionsGamow-Teiler and Ml transition rates in nuclei are strongly quenched compared to single particle strengtns. The quencning effect may be attributed to a combination of tour different effects:i) Core polarisation. This corrects tne simple snell modelassumptions about the structure ot nuclear wave functions. Inclusion of p-h states in second order ot perturbation theory is carried out. ii) Isobar effects. This is an attempt to include the collec­tive modes ot excitation due resulting from tne isobar degrees of freedom. Inclusion of A-h states in second order of peturbation theory is carried out.1 1 1 ) Meson-exchange currents. Tne G-T transition operator is modiried by explicitly including a two-body operator cor­responding to the p-ir diagram. The Ml-operator is changed by meson-exchange currents arising from the pionic current, the pion pair term, the p-meson current, the p-pair term and the tt-(i> current. It is to be noted that the meson- excnange current effects are different for the G-T and Ml-transitions.iv) Relativistic corrections. Tne G-T operator being ot 0(1),2tne relativistic corrections are ot 0(1/M ), M being tne nucleon mass, while tor Ml-operator which Is ot 0(1/M) the3corrections are ot 0(1/M ). Only corrections to the G-T operator are included.In calculating the corrections arising trom p-h and A-h states two separate model interactions are used:l) 6 + tt + p interaction. This model has its basis in Landau theory ot Fermi liquids. The torm ot the interaction is V(r) = t g 1 ai d£ ti•T2 + (In and lp-exchange potentials). Tne A-h interaction is obtained by making appropriate modi­fication to the p-h interaction. The constant g' is assumed to be the same tor ph and A-h states. Tnis univer­sality is based on the assumption that tne nuclear system is complicated enough that tne nucleon and the isobar have the same renormaiisation. Calculations in this model are performed for different values of g'. It is found that tor0.6<g'<0.7 the experimentally deduced quenching of G-T matrix elements can be explained quite well. A large trac­tion of the quenching is caused by A-h states. For details see Ret. 15.ii) V(r) = 1tt + lp + lm + la exchange potential.This one-boson exchange potential (OBEP) is taken as the effective p-h interaction and appropriate scaling is car­ried out to obtain the A-h interaction. The coupling con­stants tor nucleon system are obtained from experiments353wherever possible, and for transformation to the isobarsystem values from the constituent-quark model are used13(For details see Towner and Khanna ).It should be noted that the tensor force in the two bodyinteraction leads to excitations to - 2 0  hm which corresponds to an energyof =300 MeV in 160. Such p-h excitations are comparable in energy to the A-n excitations. This gives a heuristic justification for including the isobar degrees ot freedom.Corrections to the isoscalar magnetic moments are compared with the calculated results in Table I. Isobars do not contribute in this case. Tne renormalisation ot the isoscalar moments depends on core polar­isation and the tensor correlations. Meson-exchange currents play only a minor role. A reasonable agreement between the calculated and the experi­mental results gives confidence in the treatment ot tensor correlations and the effective nucleon-nucleon force.Corrections to the Gamow-Teller matrix elements and the iso­vector Ml-transition matrix elements are shown in Table Ila and librespectively. Again the agreement with the experimental results is reasonable. The transition matrix elements fy/2 *  ^ 5/2 in systemis snown in Table Ila. The tneoretical model predicts a total quenching ot =20% in the matrix element. The tensor correlations and the isobar contributions are equal in magnitude. It the experimental value of the ANu coupling constant is used instead of the quark model value, the isobar contribution will increase from 6.3% to 8.5% but will still be only a third of the total quenching ot the matrix element. There is no experi­mental result tor the G-T quenching in the A=41 system; in the A=48 system354355system the strength is quenched by 40%, which is roughly consistent with the results given in Table Ila. For Gamow-Teller transitions the resultsgiven in Table Ila suggest that no one mechanism is dominant, and it isonly through a combination ot core polarisation, tensor correlations andthe isobars tnat the large observed quenching can be explained.Similar comments may be made about the quenching ot iso­vector magnetic moments and Ml-transitlon matrix elements. Tne calcula­tions agree quite well witn the observed quenching and the overall trend is reproduced. It should be noted that the spin part of tne Ml operatoris quenched more than the orbital part.b. 0 + 0  transitions.Heuristically17 it can be argued that such transitions should be dominated by pionic effects. In Fig. 5a, tor an external vector current (V^) the NNVtt coupling has to be such that the nucleon part hasthe structure 'FYjjT5'F. Tne space (time) part of this current in the non- relativistic limit nas the magnitude 0(1) (0(q/M)). In Fig. 5b, tor an external axial-vector current (A), the nucleon part of the NNAir vertex has tne form The space (time) part ot this current in tne nonrelati—vistic limit has the magnitude 0(q/M) (0(1)). This may be summarised as:Space TimeVector 0(1) 0(q/M)Axial-vector 0(q/M) 0(1)Tnis indicates that pion effects like those shown in Fig. 5 will dominate for the space-part and time-part of the external vector and axial-vector current respectively. Magnetic moments give an example of the space part356ot the vector current and have been discussed in the preceding section.The time-part of the axial-vector current will manifest itself in0+ + 0-transitions in nuclei. An interesting example to consider is:16o (0+ ) + y 1rn (o") + vy y16N (0“) -*• 160 (0+) + e" +Both the muon capture rate and the 3-decay rate are known experimentally. Tne calculations18 were carried out with both the model potentials mentioned in the last section. Core polarisation corrections were inclu­ded to second order ot perturbation theory. The ground state of l60 in-16eludes 2p-2h effects, and tne 0 state ot N, which is lp-lh in first order, includes 3p-3h effects. It is important to include the ground- state correlations in 160. Tne meson exchange currents make a large con­tribution to both y-capture and 3-decay, but the effect is more dramatic in 3-decay. The results of the calculation are shown in Table III.Line 1 in each case used simple shell-model wave functions, while line 2 includes effect ot first order ot perturbation theory. The line labelled total includes all core-polarisation effects. The two columns correspond to the use ot impulse approximation (IA) one-body transition operator and the addition of meson exchange currents (MEG) to the impulse approxima­tion. For y-capture rate the results with OBEP are in reasonable agree­ment with the inclusive y-capture rate. The results can be brought into better agreement by increasing the pseudoscalar coupling constant, Gp, from its PCAC value of 7.0 to about 9.0. The meson exchange currents enhance the capture rate by about 30%. For 3~decay of N the calculatedresults are in excellent agreement with the measurements by Gagliardi et al. The importance ot meson exchange currents tor this 3-decay is apparent.Even thougn the isobar effects are small the pionic effects are very large. This emphasizes the importance of non-nucleon degrees ot freedom in this transition. It will be very interesting to find ways to measure such transitions in proton inelastic scattering.5. CONCLUSIONSTwo examples are given to show that it is important to deal with the nuclear structure very carefully. Furthermore, the experimental data clearly indicate the necessity of including non-nucleon degrees of freedom, whether they are isobaric or pionic. Even in the case of proton elastic scattering there is a need to consider nucleons and isobars as a coupled system in order to gain a better understanding of the physics con­tained in precise experimental data at large momentum transfers. The con­tent of the talk may be summarised as follows:i) Careful consideration of nuclear structure is important,ii) Non-nucleon degrees of treedom i.e. A,ir,etc. are importantingredients in a successful interpretation of the data.For experiments involving large values ot q and m it may be premature to rule out the importance of isobars. The role ot anti-nucleon degrees of freedom is not clear as yet.iii) There is a need for consistent calculations that includesthe nuclear structure and reaction mechanism on an equal footing. Construction of an optical potential cannot be357entirely divorced from nuclear structure. Only consistent calculations can teach us new physics.There is a great deal of experimental work, to be done to establish the roles ot nucleon and non-nucleon components in nuclei. Not only Ml, but also higher multipole spin flip-isospin flip states should be studied. Studying 0 states in nuclei will be very fruitful. There is in addi­tion the question ot spin-electric resonances. In each one of these cases measurements of spin variables should pro­vide valuable additional information. So far only giant dipole and quadrupole resonances have been studied in detail. Baryons nave spin and isospin and these lead to a much richer spectrum ot collective states in nuclei. Pro­tons are an appropriate tool to study the spin and isospin of giant resonances in nuclei. Medium-energy protons should provide a vast amount ot new information about nuclei.The proton is a composite system of 3 quarks. At high momentum transfers it must reveal its structure. At high energies the proton has to be treated relativistically.But is the Dirac equation the correct dynamical equation to describe a composite system? At medium energies, the elas­tic and inelastic scattering of protons from nuclei must reveal deviations from a point nucleon. The question is: how do we recognize such a deviation when we see it?TABLE I ISOSCALAR MAGNETIC MOMENTS AS PERCENTAGE CHANGEIN THE SHELL MODEL VALUEA=15 A=17 A=39 A=41- 1 . , - 1  f  1/2 d 5/2 3/2 7/2C.P. (2ho>) +10.8 -0.4 3.9 -0.4Tensor 12.1 -1.9 7.8 -1.8CorrelationsMEC - 2.3 0.4 - 1.1 0.3TOTAL 20.8 -1.9 10.7 -1.9Experiment 16.7 -1.8 11.1 -1.0C.P. (2fiu>): Core polarisation including p-h states up to 2fiw.360TABLE Ila CHANGES IN GAMOW-TELLER MATRIX ELEMENT AS PERCENTAGEOF THE SHELL MODEL VALUEA=15 A=17 A=39 A=41 A=41P l/ 2 P l/ 2d  , +  d  ,5/2 5/2,— 1 ^-1 d , d / 3/2 3/2 S / 2 * f7/2 £ 7/ 2* t 5/ 2C.P. (2tiw) - 4.4 - 3.5 - 6.3 - 3.9 -5.3TensorCorrelations - 1.8 - 3.0 - 5.6 - 4.4 - 6.3Isobars 7.2 - 1.6 - 1.5 - 3.2 - 6.3MEC - 4.9 - 1.3 - 3.2 - 1.7 - 0.2Relativistic - 4.4 - 2.7 - 3.7 - 3.4 - 1.9TOTAL - 8.2 -12.2 -20.3 -16.6 -20.0Experiment1: -13.2 -13.8 -33.7 -26.7TABLE lib CHANGES IN ISOVECTOR MI MATRIX ELEMENT AS OF THE SHELL MODEL VALUEPERCENTAGESpin 19.7 - 3.1 -17.4 -4.5 -15.1Orbital -10.8 2.6 - 6.5 3.6 - 0.5TOTAL 8.9 - 0.5 -23.9 -0.9 -15.6Experiment2: 11.1 - 1.3 -38.4 -8.91. Ret. 162. Ret. 13361TABLE Ilia Muon qaptqre race on (0+) -*■ 16N (0 ) in units otot 10 s" .MODEL POTENTIAL 6 + tt + pIA IA + MEC1. 2.37 3.742. 2.37 3.54TOTAL 0.38 0.52MODEL POTENTIAL OBEP1. 2.30 3.262. 2.30 3.11TOTAL 1.48 2.00Experiment : 1.56 ± 0.11TABLE Illb 6-DECAY BATE %  (0~) ♦ 160 (0+) IN UNITS s“ XMODEL POTENTIAL 6 + tt + p1. 0.30 1.252. 0.21 0.93TOTAL 0.02 0.08MODEL POTENTIAL OBEP1. 0.29 0.942. 0.18 0.64TOTAL 0.12 0.42Experiment2; (0.40 ± 0.05) s~ 11. Ret. 192. Ret. 20Line 1: with shell model wave functionsLine 2: shell model witn first order core polarizationTotal: shell model and all core polarization corrections.362References1. See tor example: H. Uberall, Electron Scattering trom ComplexNuclei, Academic Press, New York. (1971).2. W.J. McDonald, Nucl. Pnys. A335 (1980) 453 and reterences quoted therein.3. For a thorough treatment see B.H. Brandow, Rev. Mod. Phys. 39^(1967) 771.4. F.E. Close, An Introduction to Quarks and Partons, Academic Press,New York (1979).5. V. Vento, M. Rho, E.M. Nyman, J.H. Jun and G.E. Brown,Nucl. Phys. A345 (1980) 413.6. J.S. Bell and E.J. Squires, Phys. Rev. Lett. _3 (1959) 96.7. K. Klingenbeck in "From Collective States to Quarks in Nuclei",Edited by H. Arenhovel and A.M. Saruis, Springer-Verlag Berlin (1980) and reterences quoted therein.8. Q. Ho Kim and F.C. Khanna, Ann. Physics J36 (1974) 233.J.P. Jeukenne, A. Lejeune and C. Mahaux, Phys. Reports 25C (1976) 83. See also talk by Prof. von Geramb at this workshop.9. The classification is similar to the case ot inelastic electron scattering. For some information see Ref. 1.10. M. Harvey and F.C. Khanna, Proc. Int. Conf. on Nuclear Physics (1973), Munich, Vol. I, p. 277.11. C.D. Goodman, Nucl. Phys. A374 (1982) 241C and the talk by J. Rapaport at this workshop.12. For general question of response function see A.L. Fetter and J.D. Walecka, Quantum Theory of Many-Particle Systems, McGraw-Hill Book Co., New York (1971).13. I.S. Towner and F.C. Khanna, Nucl. Phys. A399 (1983) 334 and references quoted therein.14. J. Spetn, E. Warner and W. Wild, Phys. Report _33 (1977) 127 and references quoted therein.15. E. Oset, H. Toki and W. Weise, Phys. Reports H3 (1982) 281.16. S. Raman, C.A. Houser, T.A. Walkiewicz and I.S. Towner, At. Data Nucl. Data Tables 21 (1978) 567.36317. K. Kubodera, J. Delorme and M. Rho, Phys. Rev. Lett. 40 (1978) 755.18. I.S. Towner and F.C. Khanna, Nucl. Phys. A372 (1981) 331 and references quoted therein.19. P. Guichon, 8. bihoreau, M. Griffon, A. Goncalves, J. Julien,L. Roussel and C. Samour, Phys. Rev. Cl9 (1979) 987.20. L. Paltty, J.P. Deutsch, L. Grenacs, J. Lehmann and M. Steels, Phys.Rev. Lett. 34 (1975) 212.C.A. Gagliardi, G.T. Garvey, J.R. Wrobel and S.J. Freedman, Phys. Rev. Lett. 48 (1982) 914.3640  00  +  ( f  +  J  +FIG. I:.d □>(a) (b) (c)FIG. 2:/o( d )" D. 0 '  +FIG. 3*  +  ( \FIG. 4(a)O '. 0:o+ —0...0 /'I +FIG. 5365FROM QCD TO SHORT RANGE NUCLEAR PHYSICS 'Anthony W. Thomcu CERN, Geneva, SwitzerlandABSTRACTWe briefly review the relationship of phenomenological models of hadron structure to QCD. Particular attention is paid to the chiral bag models and their implications for hadron size. It is shown that deep inelastic scattering already places severe constraints on these models, leading in fact to a bag radius greater than 0.8 fm. As a consequence of this we expect that quark degrees of freedom should play a significant role in nuclear physics. Some hints of this in recent data taken by the EMC collaboration at CERN will be reviewed.1 - INTRODUCTIONIn searching for a sound starting point from which to develop a credible theory of nuclear structure we must consider quantum chromo­dynamics (QCD). Certainly QCD is considered by most theorists to be the theory of the strong interactions. Unfortunately, it is too difficult to solve the QCD equations except in some limits. For example, at high Q2 it is established on the basis of the renormalization group that QCD has the property of "asymptotic freedom". That is to say that if we determine the colour coupling constant at some (arbitrary) momentum scale Q., then it must decrease logarithmically as Q2 increases beyond Q2. Thus at large momentum transfer, or short distance, quarks should behave essentially like free particles. This is the underlying reason behind the success of the naive parton model which we shall review briefly in Section 3. Perhaps the great hope of relativistic heavy-ion physics is to be able to make dense enough systems of quarks and gluons (densities beyond ten times nuclear matter density) that one could study QCD in this asymptotically free regime.A second limit where it is believed (but not proven) that we understand QCD is low-Q2, or large separation. In that region, QCD is supposed to be divergent, leading to confinement. Finally, the fact that the masses of the u- and d-quarks in the QCD Lagrangian are very small on the usual hadronic scale (A- 10 MeV or less) means that the strong interactions are predicted to have an exceptionally good symmetry -- namely chiral symmetry (or invariance under SU(2)  ^ x SU(2)^).366On a time scale of many years it is possible that brute force numerical calculations on a space-time lattice may unambiguously tell us what QCD implies for the structure of the nucleon. In the meantime, QCD is simply too hard and we must deal with phenomenological models which build in the three features already mentioned, namely confinement, asymptotic freedom and chiral symmetry. The choice of phenomenological models which incor­porate two or more of these ideas is rather large, ranging from the non- relativistic constituent quark models (1), through variants of the kind proposed by Shuryak (2), to the relativistic bag models (3,4).A common feature of essentially all phenomenological models proposed by high energy theorists is that the radius of the region within which the quarks are confined is of order 1 fm. This brings us at last to the question of what is meant by "short range nuclear physics". A very natural definition would be that internucleon separation at which it is no longer sufficient to describe nucleon-nucleon scattering in terms of nucleons and pions alone. Within conventional nuclear theory the exchange of the massive td meson leads to a repulsive core at distances of order 0.3 to 0.5 fm. Because of its large mass, the p meson does not contribute much beyond 1 fm. Nevertheless, there is tremendous model dependence in most calcula­tions because of the interplay of short-range correlations and the exchange of p, p-rr, cott, and so on. (These ambiguities are compounded in calculations of electromagnetic processes because of the difficulty of imposing gauge invariance in the presence of ad hoc form-factors at the meson-nucleon vertices.) Within this framework the no-man's-land of uncontrolled short distance corrections is typically 0.3 to 1.0 fm.On the other hand, if one thinks of nucleons as composite bags of quarks with a radius of order 1 fm [as in the Cloudy Bag Model (CBM)], it is clear that short-distance physics begins at 2 fm! Certainly at an inter­nucleon separation of 1 fm nuclear phenomena should deeply involve quark degrees of freedom. Rather than being more complicated than the conven­tional meson exchange picture, because of the property of asymptotic free­dom, there is reason to believe that this approach may be simpler and far less ambiguous.A number of us have become quite excited by this possibility in the last few years, and have begun to examine a variety of nuclear processes from this point of view (4,5). On the other hand, it has been suggested by the Stony Brook group that non-linear effects associated with theimposition of chiral symmetry could compress the size of the confinement region in the nucleon to a few tenths of a fermi. In this way, one would revive the conventional nuclear physics picture of essentially point-like nucleons exchanging heavy mesons. This is the little bag model [LBM] (6).In what follows, we briefly review the ideas of these two chiral bag models, and then show how existing deep inelastic scattering data can distinguish between them (7). Some recent applications of the surviving theory -- the CBM —  will then be reviewed. Finally, we discuss some recent results on deep inelastic scattering on Fe, which reveal large corrections to the effective structure function of a nucleon inside a finite nucleus (8,9).2 - THE CHIRAL BAG MODELSAs we mentioned chiral symmetry is an important property of QCD with u and d quarks. However, because the particles occurring in nature do not come with degenerate, negative parity partners, this symmetry must be realized in the Goldstone mode. There are very good reasons for believing that the pion, with its remarkably low mass, is very close to being a Goldstone boson. Unfortunately, one of the mysteries of QCD is that we do not yet understand the dynamical mechanism whereby this collective qq state appears.Certainly the one gluon exchange is extremely strong in the pion channel -- without it the p and it would be degenerate at ^ 650 MeV in the MIT model, and in first order, one gluon exchange lowers the pion mass to some 280 MeV (10)1 Several groups have been led by this to suggest that iterated gluon exchange could be the mechanism for dynamical symmetry breaking (11). Others have shown that instanton effects can produce a strong attraction in the pion channel (12,13). Whatever the mechanism, all chiral bag models accept the necessity for including the pion field in the quark model Lagrangian (4). Of course, this does not mean that we expect to see pointlike, pseudoscalar objects in deep inelastic 1epton-nucleon scattering! Instead, we are constructing a phenomenological model meant to be applied at momentum transfers low compared with the internal structure of the pion. There are many examples in physics where the introduction of such collective pairing effects are essential in order to describe observed phenomena.367The usual idea in introducing such a field is to couple it in the minimal way to the confined quarks in order to restore the global chiral symmetry that was broken by confinement. To lowest order in the pion field that coupling is unique, and by imposing PCAC, we can eliminate the need for any undetermined additional parameters. In order to guarantee exact chiral symmetry in the limit of a massless pion the pion coupling to quarks in the bag must actually be highly non-linear.The principle difference in philosophy between the Stonybrook approach (6) and ours (4) can be stated quite simply. In the CBM we in­vestigated the possibility that hadron sizes are determined by non- perturbative QCD effects which are not significantly altered by pionic effects. Then it makes sense to calculate pionic corrections as a small perturbation about the MIT bag model solutions. In the LBM, on the other hand, the pionic effects were supposed to be intimitely linked with the process of confinement, compressing the bag to perhaps one tenth the volume of the MIT model. In the absence of reliable solutions of QCD both of these are legitimate phenomenological ideas which deserve to be pursued. Like all phenomenology it is an experiment which must be the arbiter.A second difference between the models, which has recently faded to insignificance was the original insistence in the LBM on excluding the pion from the interior of the bag -- a strict two-phase model. In the CBM, this was not the case; the pion was allowed throughout all space for two reasons. Firstly, the theoretical case for a strict two-phase picture is by no means universally accepted, and secondly the exclusion of the pion field destroys one of the major successes of the MIT bag model, namely the quite accurate prediction for the axial charge of the nucleon. In the CBM this correct prediction is preserved in a very simple and natural way (4).In Section 4 we shall briefly describe some applications of the CBM in nuclear and medium energy physics. However, at this stage we would like to ask whether there is any experimental data which could distinguish between these two models. Surprisingly, it is only in the last few months that is was realized that such data already exists! In order to understand it, we must recall some classical concepts which lie at the heart of the general acceptance of the quark model.3683 - DEEP INELASTIC SCATTERING The phenomenon of Bjorken scaling in deep inelastic scattering of leptons from nucleons was discovered at SLAC in the late 60's. We now understand fairly well why scaling violations must occur if QCD is the theory of the strong interactions, and these violations have been studied systematically. Nevertheless the property of asymptotic freedom also ex­plains why the naive quark-parton model works so well over a large range of Q2. For our purposes it will be sufficient to use this language (14).Very briefly, the quark-parton model can be summarized in the following way. The nucleon contains a number of point-like, massless, spin-J con­stituents whose couplings to electromagnetic and weak interactions are those expected of the quarks. (That is, the charges are ±V3, ±2/3; the weak interaction is [V-A] for charged currents, and so on.) If we look at deep inelastic scattering in a frame where the nucleon is moving very fast, and collinear with the photon, each of the partons must carry somepositive fraction x. of the momentum of the nucleon (E x. = 1). Thei 1structure of the nucleon is then described by the parton distributions P P Pu (x), d (x), s (x) etc., which give the number of up, down or strange quarks carrying a fraction x of the momentum of the nucleon. By charge symmetry we expect that the up distribution in the proton equals the down distribution in the neutron and so on. Then one needs one set of distri­butions, namely u(x) [ e  u P (x ) = dn(x)], d(x), s(x), u(x), d(x) and s(x).The final ansatz of the quark-parton model is that one can use the impulse approximation to describe the interaction of the quark with the incident boson. That is, the quark acts as though it is free during the collision. A very satisfying analogy is that of a collision between two billiard balls, one of which is attached to some point by a slack rubber band. The actual collision will look exactly like that of free billiard balls. Only after the projectile has left will the struck ball reach the end of its tether, and feel the effect of "final state interactions".The contraints of parity and gauge invariance imply that deep inelastic e or y scattering can be described by just two structure functions, F :F i(E m nW !) and F2(E v W2) where v is the energy lost by the lepton in the laboratory frame. In the quark-parton model, these structure functions are related to each other and to the momentum distributions f^(x) (i = 1 ,2, ... , 6, with f i(x) = u(x) etc.) by the relation:369370where q. is the charge of the type-i quark. Clearly we findandWe readily see that the electromagnetic interaction does not distinguish anti-quarks from quarks.For that purpose neutrinos are ideal. The V-A nature of the weak interaction means that only left-handed particles and right-handed anti­particles participate. It is then very easy to see that whereas the q-1 interaction will have an isotropic distribution in the c.m. system q-£ will behave as (1 + cos 0*)2. Indeed, the isotropic piece of the (v,y+ ) cross-section on an isoscalar target is proportional to qv (x), defined as,Quite a bit is known about the actual shapes of these momentum dis­tributions, but for our present purposes we simply cite the total momentum carried by each species. These total momenta are conventionally labelled by capitals asand so on. On the basis of the results of a series of measurements by the CERN-Dortmund-Heidelberg-Saclay (CDHS) group, we have the following p e r ­c e n t a g e s  o f  t h e  m o m e n tu m  o f  a  n u c l e o n  i n  F e  carried by each consti­tuent (15), (16), (17):gluons : 54% ,all quarks and anti-quarks : 46% , (3-6)q v  : 5.9 ± 0.4% .It is convention to define the valence quark distribution by subtrac­ting u(x) from u(x), and d(x) from d(x), leading to the sum rule^  + \ 0 eU ^ C - U 0 0 1  cl*0  0+- [o|<K) "  d(*>] d *  = 3. (3.?)Experimentally, the best value is currently 3.2 ± 0.5 (17). By definition, what remains is the sea distribution, consisting of all those quark-anti- quark pairs above the minimum required to reproduce the quantum numbers of the nucleon.In the early days of DIS it was common to assume that the sea wasSU(3)p symmetric (i.e. equal numbers of u, d, s ... ). Of course, becausethe strange quark mass is considerably larger than the up or down quarkmass, it was clear that this was a dubious approximation. However, it isonly in the last couple of years that the process    _  ~hV + 5  ^ C  +  J (3. s)L~7> yA.with its characteristic di-muon signal has allowed a direct measurement of the strange sea (16). The most recent CDHS results give the ratio of S to (0 + D) in Fe to be2 s / ( u + v )  = 0 . 5 1  t o .  0 7  , (3.7)showing clear SU(3)p breaking as expected from the difference in quark masses.Putting equations (3.6) and (3.9) together, we find (in Fe!)s') = 1.0 t 0.3 V  ; 3.W)Fe 2 * 'FeIt is interesting to compare this with the older estimate for a f r e en u c l e o n  which was made by Feynman and Field (FF) (18), namely371_ S  _  = 1 1  ^  (3.11)l i l )  = 1 . 8  2 . / > *Equation (3.11) would yield a value of 0.61 for the ratio 2S/(0 + D) in hydrogen. The comparison with the value measured in Fe is complicated372by the EMC effect (8), which we shall discuss in Section 5. For the pre­sent purposes, we merely note that the sea in Fe appears to be enhanced over that in a free nucleon by about 40%. (The enhancement of F2(x) is greater than or equal to 10% at x - 0.1, where the sea contributes about 25%.) If, as seems likely on the basis of our analysis [Section 5] (19),(20), the enhancement in Fe involves only the non-strange component, it would bring the value of {(0 + D)/2 - S } in a free nucleon down to 0.4 ± 0.45 from 0.95 ± 0.4 in Eq. (3.10). In view of all this, we shall use the FF value for {(0 + D)/2 - S) in a free nucleon, namely 0.7%.So far our discussion has had no relationship to the chiral bag models reviewed above. In order to see the connection we begin with the observa­tion by Sullivan (21) that there is a contribution to the nucleon structure function arising from the process shown in Fig. 1. This contribution canFig. 1N The contribution of the pion to the struc­ture function of the nucleonbe written asr±S F™Cy) = I  ^  ^where F ^  is the pion structure function and f(y) is the momentum distri­bution of the pion in an infinite momentum frame. (For the present purposeswe can omit the Q2-dependence of 6Folvl and F0 .)2N 2tt 'The physical interpretation of Eq. (3.12) is that we sum over all y the product of the probability [f(y)] of finding a pion carrying a fraction y of the momentum of the nucleon, with the probability [F^ (x/y)] of finding373a quark in the pion with a fraction x of the nucleon's momentum. Since Fp 1T(C) has been measured by the NA3 collaboration at CERN in the Drell-Yan process (22), (23), all we need is f(y). This is very easily calculated in terms of the ttNN coupling constant g, and the ttNN vertex function F(t) with t = q2 - q 02 = minus the 4-momentum transfer. For simplicity, we take a simple exponential for F(t)and seek to put some bounds on X. However, we should point out that in the CBM the form-factor is very well approximated (24) by Eq. (3.13) if X = 0.106 m 2R2_ with R the bag radius. The final expression for f(y) isA straightforward numerical calculation of Eq. (3.14) reveals two essential features (7). First, f(y) peaks at about 0.25 for any reasonable value of X. Second the maximum value of f(y) increases rapidly as X decreases. Returning to Eq. (3.12), we see that the pion structure func­tion is evaluated at x/y. As usual we expect that the valence component of the pion should dominate for x/y > 0.1. Since y is typically 0.25, this implies that the pionic contribution to the nucleon structure function for x > 0.03 involves only non-strange quarks. Thus, if the pion is an impor­tant component of nucleon structure, it should contribute to breaking the SU(3) flavour symmetry [SU(3)p] of the sea. Of course, as we mentioned earlier, it is generally expected that SU(3)p will be broken because of the larger strange quark mass, and it would be unreasonable to attribute the entire excess of non-strange sea quarks to the pion. Nevertheless, it seems quite reasonable to use any evidence for SU(3)p breaking to impose a limit on the pionic contribution to the nucleon structure function.Integrating Eq. (3.12) over x, we find that=  [ [  U 0 h  n  W -(3. i s )There is now quite good data on the pion structure (22), (23) from Drell-Yan, which gives / 6F2TT(^)d^ = 0.15 ± 0.04. Furthermore, from the definition of f(y) we recognize the second integral on the right of Eq. (3.15) as the average fraction of the nucleon momentum carried by the pion - (y) • If» as we argued above, the SU(2) excess in the sea makes a contribution,F N ov„occ> greater than that from the pion alone, we obtain the bound ^ll j CaLCj J< ^>n ~^ ; e .c.a  /  0. of). (i.iOFinally, if we use the FF value of 0.7% for the excess {(0 + D)/2 - S}, a simple calculation[c.f. Eq. (3.1)] gives F2N excess = 10/9 x 0.007 == 0.008. The bound from Eq. (3.16) is therefore<-y>1T ^ 5  t 1.5 ~°Z- , (3.17)In Fig. 2 we show the average fraction of the momentum of the nucleon carried by pions, y^ , as a function of the cut-off parameter X, at the374Fig. 2The average fraction of the nucleon's momentum carried by the pion as a function of X (or bag radius R).The shaded area represents the bound obtained in Ref. (7).375NNtt vertex. Clearly Eq. (3.17) is a very strong constraint on that para-+ 0 . ° 1 2meter. It is not possible to accept a value of X smaller than 0.039 _0.006- We also show in Fig. 2 the CBM radius corresponding to each value of X. The lower bound on the bag radius in the CBM is R = 0.87 ± 0.10 fm. Of course, there are many defects in the static bag model, and one cannot insist too strongly on an absolute value of R. One expects the bag to have some sur­face thickness, and this together with centre-of-mass and recoil corrections could change the simple relationship between R and X. Nevertheless, we expect this upper bound to be a good indication of the size of the region within which quarks are confined in the nucleon. The concept of a little bag with a size of order (0.3-0.5) fm is definitely excluded.Let us finish by trying to put this result in perspective. From the measurements on Fe we know that the valence quarks carry some 36% of the momentum of the nucleon, while the whole sea carries about 10%. Our bound says very simply that the pionic contribution should not be more than about 20% of the sea. (The quarks carry about 40% of the pion's momentum, and 0.40 x 0.05/0.10 = 0.20.) Even this may seem quite large to a number of high-energy physicists 14 - APPLICATIONS OF THE CLOUDY BAG MODELA fairly recent summary of results from the CBM can be found in Refs. (4) and (25). It is not unreasonable to say that in every case where pionic corrections have been computed the agreement with experiment is as good as, and usually better than, the original MIT bag model. Of course, it must be said that the major underlying defect of the bag, namely the spurious c.m. motion is not solved by adding pionic corrections. Thus for magnetic moments, and particularly for the charge radii there are correc­tions at the level of 10% or greater, upon whose sign there is no general agreement. It remains to be seen whether a thorough theoretical analysis can lead to a generally acceptable correction procedure, or whether what we really need is a better relativistic model of confinement. For the present, agreement of any bag model calculation at a level better than (5-10)% must be regarded as random. At that level, however, its success is still striking.Because of the fact that the CBM results have been reviewed elsewhere, we shall restrict our discussion to just two examples, and these will be brief.4.1 - The Z~ magnetic momentThis is of particular interest for the chiral bag models because of the so-called Pilkuhn-Eeg effect (26). That is, the pionic correction for the Z" is twice as big as that for most other baryons, because as well as the process Z" -* Z°tt", one has also Z" -+■ AtT. In the CBM, using the same bag parameters as the MIT bag model, we find p(Z“ ) = -1.08 n.m. (The MIT bag value, also including the Donoghue-Johnson c.m. correction (27), is -0.81 n.m.) On the other hand, the little bag model gives about -0.58 n.m. (28).Until recently, the experimental situation was unclear, with older atomic physics measurements giving -1.41 ± 0.27 n.m. and a Z"-beam measure­ment giving -0.89 ± 0.14. The new generation of Z_-atom measurements made by the William and Mary group have made an order of magnitude improvement in this.Indeed, the accuracy of the most recent value of y(Z") (29), namely -1.09 ± 0.03 n.m., is too good for the present theory! Nevertheless, the confirmation of the CBM prediction is very welcome.4.2 - Exotic bag statesOne of the more exciting possibilities raised by the MIT bag model was that there might be stable, exotic states. For example, it was suggested that the so-called H-dibaryon (a A-A state) might be bound by (50-80) MeV (30). In view of the relatively large self-energy corrections associated with pions for single hadrons (4),(24), it is reasonable to ask how those corrections affect the masses of exotic states.In order to check this in a scheme consistent with the philosophy of the CBM, Mulders and Thomas (31) refitted the usual hadron spectrum with the phenomenological form376Here Eg, Ey and E^ are respectively the standard kinematic energy, volume and colour magnetic contributions to the bag energy. The last term, Ep , is a phenomenological representation of the pion self-energy which has the form377The spin-isospin structure corresponds to keeping only the lowest orbital in the intermediate state, and treating all such states as degenerate. Finally, p is a phenomenological constant.There were several notable features associated with the best fit parameters. As expected from the earlier discussion of the N-A splitting the colour coupling constant was reduced by about 35%. The strange quark mass also came down to 218 MeV (from 279 MeV) -- a little closer to the usual current algebra value of 150 MeV. Lastly, we observe that, although treated as an adjustable parameter, the value of p agreed very well with that calculated for a nucleon in the chiral bag models.For the non-strange, B = 2, exotic bag states, the pionic corrections had little effect. In 3Sfl and 1SQ the bag masses were 2.18 and 2.24 GeV respectively (c.f. 2.16 and 2.23 in the original MIT bag model). Since ' these lie well above the appropriate thresholds they will be quite broad, and should not have dramatic experimental consequences.On the other hand, for the doubly strange H-dibaryon the change is dramatic. The combination of decreased colour attraction (smaller ac), and the R"3 dependence of the pionic self-energy result in a larger mass for the H —  2.22 instead of 2.15 GeV. Thus the H is almost certainly unbound (31), and it is no longer a mystery why recent searches have failed to reveal it (32).5 - THE EMC EFFECTThe general picture of the structure of the nucleus to which we have been led is quite radical (4),(5). We picture a collection of relatively large nucleons (R ^ 0.8-1.0 fm) moving independently some of the time, but also merging and fissioning. Thus at any given instant there will be a non-negligible probability of finding a given quark in a six-quark rather than a three-quark bag. It is therefore quite gratifying that recent data from the European Muon Collaboration (EMC) has revealed a dramatic dif­ference in the effective structure function of a nucleon in Fe compared with that in D (8). (Throughout the rest of this discussion, we shall not distinguish between the structure function of a free-nucleon and that of a nucleon in deuterium —  because of the latter's low density.)Essentially the EMC data, which has been partially confirmed at SLAC (9), shows a softening of the structure function in Fe. For x < 0.1, F^n (x ) is enhanced by about 15%, while at x ^ 0.6, it is depressed by thesame amount. Eventually at large-x fermi motion takes over and the ratio rises above one.Late last year, it was suggested by Llewellyn Smith (19), on the basis of Eq. (3.12), that an increase in the number of pions per nucleon in Fe could explain the enhancement at small-x. To see this we evaluate Eq. (3.12) at x = 0, with the result378Here we used the result F2tt(0) ^ FzN(0). We also recognize the r.h.s. of Eq. (5.1) as the number of pions. Thus an extra 0.15 pions per nucleon in Fe would explain the observation.In fact, reference to eq. (3.14) shows that the typical pion momentum is |q| '"v 300-400 MeV/c, which is exactly the region where an enhancement of the pion field has been expected for some time. The mechanism for this enhancement is illustrated in Figs. 3(b) and 3(c). It is generally believedFig. 3 Illustration of (a) the basic pion contribution to the nucleon structure function (the Y * tt vertex involves the structure function of pion itself); (b) and (c) other coherent processes involving pion re­scattering in the nucleus which lead to enhancement for |q| ^ 300-400 1 (d) and (e) the phenomenological short-range repulsion which damps the enhancement arising from (b) and (c).(a)(d) (e)379XFig. 4 The fractional increase in the ratio of the structure function in Fe compared with D, as a function of x (= Q2/2mNv), caused by the multinucleon pion emission graphs of Figs. 3(b)-(e). The data are from the EMC collabora­tion, and the shaded area indicates possible systematic errors. The standard input (solid curve) for Fe is kp = 1.30 fm-1, g^N = g^A = g^A = 0.7, a bag radius of 0.7 fm in F(q2), and T(q2) is a dipole of mass 1.67 GeV. We show in the other curves the effect of altering any single one of these parameters.that iterating those processes would lead to pion condensation at nuclear matter density if it were not for a short range repulsive interaction which is conventionally parametrized as the Landau-Migdal parameter g' -- see Figs. 3(d) and 3(e).Our intention is not to pursue the justification of the Landau-Migdal force, or to discuss its consequences in the famous suppression of Gamow- Teller strength (33). We merely note that as shown by Ericson and Thomas (20) it is possible to generalize Eq. (3.14) to the nuclear case by introducing the nuclear spin-isospin response function. Then, within the conventional RPA, with g' 'v 0.7, we obtain the solid curve of Fig. 4. Clearly the shape and380magnitude of the enhancement of the sea is reproduced. In view of the controversy over the microscopic calculation of g ^ ,  we point out that any value of this parameter significantly less than 0.7 would give an enhance­ment that was far too big.Let us now consider the depression of the structure function at large x. It was first pointed out by Jaffe that the presence of 6-quark bags in a nucleus could produce such an effect (34). However, one does not need the bag model; the result can be derived quite generally. The Drell-Yan- West relation (14) in fact tells us that the structure function of a 6-quark state must behave as (l-x/2)9, while that of a 3-quark bag goes as (1-x)3.It is then trivial to show thathas a minimum at x = 0.5 —  exactly as in the data.Clearly the essential qualitative features of the data can be under­stood. The real difficulty is to make the analysis quantitative. For example, even the fermi motion corrections seem to be fairly model depen­dent. A program of careful experiments to map out the dependence of this effect on A and N/Z, as well as looking at inclusive hadron spectra in coincidence will be required to test our ideas (20). Nevertheless, we should allow ourselves a little enjoyment of the present. It is conceivable that we are seeing the beginning of a new and far deeper understanding of the structure of the nucleus than we have ever had before.It is a pleasure to acknowledge the stimulating conversations that I have enjoyed with a number of theoretical colleagues, and in particular, M. Ericson, T. Ericson, P. Guichon, C. Llewellyn Smith, G.A. Miller,P. Mulders, H. Pirner and W. Weise. I am also indebted to J. Boucrot,F. Eisele, E. Gabathuler, J. Steinberger and R. Welsh for taking the time to discuss their data with me.(1) Proceedings of Baryon '80, ed. N. Isgun (U. Toronto Press)(2) E.V. SHURYAK, CERN report 83-01 (1983)(3) K. JOHNSON, Acta. Phys. Polonica B6 p. 865 (1975)(4) A. THOMAS, TRI-PP-82-29 and CERN TH-3368 (1982), to be published inAdv. in Nucl. Phys. 21 (1983)ACKNOWLEDGEMENTSREFERENCESG.A. MILLER, S. THEBERGE and A.W. THOMAS, Comm. Nucl. Part. Phys. 10 p. 101 (1981)(5) G.A. MILLER, Proc. IUCF Workshop (Nov. 1982), CERN TH-3516 (1983)(6) G.E. BROWN and M. RHO, Phys. Lett. 8213 p. 177 (1979)V. VENTO et al., Nucl. Phys. A345 p. 413 (1980)(7) A.W. THOMAS, CERN TH-3352, to be published in Phys. Lett. B(8) J.J. AUBERT et al., CERN EP/83-14 to be published in Phys. Lett. B(9) A. BODEK et al., Rochester preprint UR 841/C00-3065-348, SLAC-PUB-3041(1983)(10) A. CHODOS et al., Phys. Rev. DIO p. 2599 (1974)(11) T.J. GOLDMAN and R.W. HAYMAKER, Phys. Rev. D24 p. 724 (1981)(12) G. T'HOOFT, Phys. Rev. D14 p. 3432 (1976)(13) R. BROCKMANN, W. WEISE and E. WERNER, to be published in Phys. Lett. B(14) F. Close, An Introduction to Quarks and Partons (Academic Press, NewYork, 1979)(15) H. ABRAMOWICZ et al., CERN-EP/82-210 (1982)(16) H. ABRAMOWICZ et al., Zeit. Phys. Cl_5 p. 19 (1982)(17) F. EISELE, J. de Phys. C3 p. 337 (1982)(18) R.D. FIELD and R.P. FEYNMAN, Phys. Rev. Dl_5 p. 2590 (1977)(19) C.H. LLEWELLYN SMITH, Oxford preprint 18-83 (1983) and in Proc. SPSWorkshop (December 1982)(20) M. ERICSON and A.W. THOMAS, CERN TH-3553(21) J.D. SULLIVAN, Phys. Rev. D5 p. 1732 (1972)(22) I.R. KENYON, CERN-EP/82-81, to be published in Rep. Prog. Phys.(23) J. BADIER et al., CERN-EP/82- (March 1983).(24) S. THEBERGE and A.W. THOMAS, Nucl. Phys. A393 p. 252 (1983); Phys. Rev.D25 p. 284 (1982)(25) A.W. THOMAS, 7° Session D 1Etudes Biennale de Physique Nucleaire Aussois,p. C.16.1 (Uni versite de Lyon, 1983)(26) J.O. EEG and H. PILKUHN, Z. Phys. A287 p. 407 (1978)(27) J.F. DONOGHUE and K. JOHNSON, Phys. Rev. D21_ p. 1975 (1980).(28) G.E. BROWN et al., Phys. Lett. 97B p. 423 (1980)(29) L. ROBERTS and R. WELSH, private communication (1983)(30) R.L. JAFFE, Phys. Rev. Lett. 38 p. 195 (1977)(31) P.J. MULDERS and A.W. THOMAS, CERN TH-3443 (1982)381(32) G. D 1AGOSTINI, Nucl. Phys. B209 p. 1 (1982)(33) J. DELORME and W. WEISE, Proceedings of this conference(34) R.L. JAFFE, Phys. Rev. Lett. 50 p. 228 (1983)382V. FUTURE DIRECTIONS AND EXPERIMENTAL POSSIBILITIESPOLARIZATION PHENOMENA IN N-NUCLEUS SCATTERINGJ. M. Moss Los Alamos National Laboratory Los Alamos, New Mexico 87545"Polarization observables will play an increasingly important role in future studies of nuclei with medium-energy (ME) protons." This may be stated without much chance of future contradiction. Beyond that, however, it is impossible to foresee. There are many isues in nucleon-nucleus physics that could be dramatically affected. I will present a couple of current examples of polarization experiments. Then I will discuss two future experiements in which qualitatively new informtion will be obtained. The emphasis here will be on physics that cannot be obtained from other hadronic or electromagnetic experiments.From an experimental perspective, it is apparent that ME protons offer a large advantage over low-energy protons (E < 100 MeV) when it comes to proton polarization. The much longer range of the higher energy particles results in scattering efficiencies in the 10~* range at 500 MeV compared to 10“  ^at 50 MeV. The advantage for ME neutrons is not nearly as striking. However,efficiencies are sufficient to allow (p, n) studies to be performed.One can already observe my prejudice for polarization transfer (PT) experiments. Indeed, experiments in which polarimetry is required will be the main subject of this talk. Measurement of analyzing powers (not requiring polarimetry) is so routine today that I will assume these measurements need no special justification or discussion. Spin correlation experiments cannot presently be performed in any general way on complex nuclei. Future machinessuch as the IUCF cooler should offer a wide variety of possiblities for spincorrelation experiments, so the time is approaching when one should begin to think about the physics that might result.384In t r o d u c t io nPolarization Transfer ExperimentsIn general, there are five parity conserving PT observalbes in spin 1/2 incoming-spin 1/2 outgoing reactions. They are D^, dlL'» DSS' » DSL'» anc* °LS' in modern notation.* Additionally, one has the independent quantities, the polarization, P^, and the analyzing power, Ajj. The subscripts refer to the spin projections indicated in Fig. 1, with L, S, N = longitudinal, sideways, and normal. The relations between the new definitions and older systems used by Wolfenstein^ and Ohlsen^ are given in Table I.385TABLE INew*oWolfenstein^ Ohlsen^°NN DDSS' R *5'°LL' A' Kz'dl s' A Kz'd s l' R' *xIn order to measure for example , one needs a longitudinally polarizedbeam and a measurement of the S' outgoing component. Then =p||-na-*-/p£n^t^a-*-. The expression for D^j is more complicated and requires Ajgand P{j as well.^’^  Finally, it is often convenient to think in terms ofspin-flip probabilities. These are related to the Ds viaHi ■ ■j - °ij>The Ss v a ry  from 0 to  1 , as th e  Ds v a ry  from +1 to  - 1 .Elastic ScatteringElastic scattering from a 0+ target is particularly simple to Parity and time-reversal arguments limit the scattering amplitude to aM(q) = A + C oN ,(where N is the normal component defined previously). Ignoring anphase, three measurements suffice to determine M(q).Two of these are the differential cross section, o and> oequivalently P^); the third, commonly called the Q parameter^ polarization transfer. In terms of the previously defined quantities,oQ = A2 + C2 , oqAn = 2 Re AC* , ooQ = 2 Im AC* ,with the symmetries,AN = PN »Q = DLS = DLS' cos 9lab + DSS' sin 9lab *= -DSL = DLL' sin 9lab “ d SL' cos 9lab *The first measurement of the Q parameter for a complex nucleus was performed with the focal-plane polarimeter-* of the high-resolution spectrometer at LAMPF. Figure 2 shows the Q data for the reaction ^Ca(p,p)^Ca afc MeV. These data, along with A^ data at the same energy, show definite evidence for the inadequacy of impulse approximation calculations based on the386analyze. formoverallAn (or requiresSchroedinger equation (dashed curve, Fig. 2). This has led to the suggestion^ that the nuclear medium modifies the free N-N interaction even at this relatively high energy. A much better fit to the data could be obtained by Ray et al.^ if the free N-N spin orbit term were reduced by ~20% at small q.An alternative proposal, which has received considerable attention recently, is that relativity plays a role beyond the kinematic constraint built into the intrinsically nonrelativistic Schroedinger-equation-based approaches. In particular, Sherpard, McNeil, and Wallace^ have achieved a phenomenal success with an impulse approximation approach based on the Dirac equation. The results of the two approaches for the Q parameter are shown in Fig. 2. It is entirely plausible that the need for more careful consideration of relativistic affects is seen in measurements of polarization observables. After all, in the Dirac equation spin enters at a fundamental level. More experiments of this type are required before one can really assess the succeses of the Dirac equation approaches.Inelastic Scattering and Charge-ExchangeThere is great potential for new physics in polarization transfer studies of inelastic scattering and charge exchange reactions. Here the full complexity of the NN-interaction is allowed. Although detailed studies of these observalbes in the Dirac impulse approximation are only beginning, it seems safe to predict that important differences will arise between this approach and the Schroedinger-equation-based models.The physics obtainable from polarization observables is most apparent when one uses the eikonal impulse approximation m o d e l . E x p r e s s i o n s  for the PT observalbes closely resemble those for free NN experiments. The major approximations necessary are:3871) Eikonal propagation through the nuclear medium.2) Static NN interactions only.3) Reaction Q value «  beam energy.These approximations are fairly accurate for most problems of interest forbombarding energies above 200 MeV.The main observation we wish to emphasize here is that there are only twoform factors measurable for unnatural parity inelastic transitions.Combinations of the PT observables may be formed that isolate, respectively, the transverse, X^, and axial longitudinal, X^, form factors. Specifically,4 p2 " 7  °o^ “ °NN + DSS/ “ DLL') *xlr 2 = ao^ 1 " °NN ” DSS' + DLL'^ *The coefficients E and F are taken from the impulse approximation NN amplitudesin the notation of KMT.** The transverse form factor is identical to thatmeasurable in electron scattering. The axial longitudinal is not present in electromagnetic interactions and thus represents new physics obtainable from polarized nucleon experiments. This form factor is, of course, present in the semileptonic weak interaction. * 2 Hence, inelastic scattering and charge-exchange experiments may well provide interesting information in several areas of weak interaction physics. A final note on Eqs. (1) and (2) relevant to the experiments discussed shortly is that they are valid (within the approximations noted) even if unnatural parity excitations are present. Thus, it is not necessary to know, for example, that a (p,p') reaction occurs only through unnatural parity channels.388Recently, considerable attention has been paid to understanding the NN-effective interaction in terms of meson-exchange models.*3,14 ^ discussionof these approaches is beyond the scope of this talk. Crudely speaking, for the isovector case the axial longitudianl part of the NN interaction results from pion exchange and the transverse part from rho-meson exchange.I will briefly discuss two planned experiments that attempt to exploit the "new" physics contained in PT experiments to learn something about the axial and transverse nuclear responses.The first experiment, the *3C(p,n*)*3N reaction at Ep = 160 MeV is part of an approved proposal at Indiana (Fig. 3). The target was selected becausethere is accurate data from *3C(e,e') yielding the transverse form factor* 3(Fig. 4). If our simple model has its expected range of validity, we should be able to find the same information from the (p,nQ) reaction to the mirror state1 Oin iJN. The axial longitudinal form factor will be completely new information. Figure 5 shows calculations of the axial and transverse form factors for this transition using DWBA-70 with the Love-Franey interaction. The nearby curves are the same calculations employing the eikonal model in which Eqs. (1) and (2) are exact. Normalization of the two types of calculations was made at zero degrees. It is apparent that the neglect of distortion and nonstatic interactions is unimportant even at this relatively low energy.An experiment scheduled to run at LAMPF this fall will employ the HRS polarimeter to make the first (p,p') measurements of the transverse and axial longitudinal nuclear response functions. This will be accomplished bymeasuring the entire spectrum of inelastic scattering of 800-MeV protons from 0 to 100 MeV of excitation energy. At each excitation energy the PT observables will be recorded thus allowing one to use Eqs. (1) and (2) to project thecorresponding response functions. Figure 6 shows calculations of these389response functions in a model that incorporates some of the fascinating spin physics involved when mesons propagate in the nuclear medium.^ Note that at small q both the axial and transverse functions are suppressed with respect to the free (noninteracting) Fermi gas calculation. At larger q the axial response shows an enhancement, which if it were an order of magnitude larger, might be called a precursor of pion condensation. Clearly this kind of experiment will have a lot to say about the current critical issues of delta-hole effects, short range interaction (g')» and enhancement of meson fields in nuclei.^In conclusion, it is easy to make a strong case for emphasizing polarization observables in future (p,p') and (p,n) experiments. We have attempted to do this by stressing the new nuclear structure physics obtainable from PT experiments. One may also argue that the effective NN interaction, medium effects, relativistic approaches, etc., are equally interesting frontiers for future study.390References1. R. Fernow and A. Krish, Ann. Rev. Nucl. and Part. Science 31_, 107 (1981).2. L. Wolfenstein, Ann. Rev. Nucl. Sci. 6^ 43 (1956).3. G. G. Ohlsen, Rep. Prog. Phys. _35^  717 (1972).4. R. J. Glauber and P. Osland, Phys. Lett. 8013, 401 (1979).5. A. Rahbar et al., Phys. Rev. Lett. 47_, 1811 (1981).6 . G. W. Hoffmann et al., Phys. Rev. Lett. 47, 1436 (1981).7. J. R. Shepard, J. A. McNeil, and S. J. Wallace, Phys. Rev. Lett. 50.*(1983).8 . J. R. Shepard and F. Rost, private communications.9. J. M. Moss, Phys. Rev. C 26, 727 (1982); J. M. Moss, Proc. of theInternational Conf. on Spin Excitations, Telluride, CO, 1982, Plenum Press (to be published).10. M. Bleszynskl et al., Phys. Rev. C _26_, 2063 (1982).11. A. K. Kerman, H. McManus, and R. M. Thaler, Ann. of Phys. 8_, 551 (1959).12. T. W. Donnelly and W. C. Haxton, Atomic and Nucl. Data Tables _23, 103(1979).13. J. Speth et al., Nucl. Phys. A343, 282 (1980).14. W. G. Love, M. A. Franey, and F. Petrovich, Proc. of the Int. Conf. onSpin Excitations, Telluride, CO, 1982, Plenum Press (to e published).15. R. S. Hicks et al., Phys. Rev. C 26_, 339 (1982).16. W. Albercio et al., Nucl. Phys. A379, 429 (1982).17. W. Weise, Nucl. Phys. A374, 505 (1982).Fig. 1. Summary of the allowed polarization transfer observables.Fig. 2. Q parameter data for 4 0Ca(p,p)40Ca at 500 MeV. The curves arecalculations from Ref. 7.Fig. 3. Schematic layout of the proposal ($,n) experiment at IUCF.Fig. 4. Transverse form factor for the 13C ground state from Ref. 15.Fig. 5. DWIA and eikonal calculations for the transverse and axial longitudinalcross sections for the 13C(p,nQ)13N reaction at 160 MeV.Fig. 6 . Calculations of the nuclear response functions from Ref. 16.392F ig u re  Captions393Polarization Transfer Experiments (Wolfenstein param.)Parity conserving observables are:dl l ”  ds s ”  dn n ’ dl s ”  ds l ,; p ’ aEx: PS1 = Pi °LS'Except: f p ,Qv + pi Di  =  N  N N I------1 + P A(0)L = Longitudinal S = Sideways (in plane) N = Normal ^Spin-flip Prob Sab ' 1 /2 (1-Dab>- 1 ±  Dab i  1 1 ±  Sab > 0N N (°4- + a-+ °ij13(au_u + CT_+ " a+_ “ 0ij ijP - A  =(a++ + a+_ _ - o— ) a  a±j- o+J/Z ijF ig u re  1394F ig .  2395P<D I WM TAxHsfew* ^  Cp, *0 .,—-V——  — !■ ■■ — -    —■■ «Los /llay*A.0t - X  -£>k.io Co (It«S.pot At l*A.«4« Xr£ p l a v h c  tot+W 2 P M ^c r ^ —1  77------ /oj--Kp/f/( i5d r■fatty t*f*p©/. pra-f** taavv*.^ -p N IW . SWJVVwfj  ©V- ^F ig .  3H i c k .  J - t ;  , " I t ' " * - ' -^ C c e . e )q ( f m ' 1)Fig. 4397T = 160 HeV PCKWF (bH()=l .59 fm) ^WIA^DWIA . 1 *a t  0O13C ( p , n )13N ( g s ) Long. DWtALong. PW ( tTran. DWI fitTran. PW (  £<0. 10. 20. 30.6cm <de^F ig .  5398»a f b t r t t *  , £ r ,c J ^ ( /  / & W  A s ? 9<r.t 1?IF#V*U*t' <&«.$6 fl\Mj IJ T  rciMA txvse,(j'te.t?)E>F ig .  6399Future Directions in Proton Physics G.E. WalkerNuclear Theory Center and Physics Department Indiana University, Bloomington, Indiana 47405The outline of my talk is as follows:1. Brief summary of present emphasis.2. Additional possibilities in the 'near' future.3. Selected theoretical topics:( a )  ( p . tt)(b) Coupled channels for 't' embedded in many-body environment(c) Corrections due to energy dependence of t.4. Proton physics above 1 GeV.5. Anti-nucleon - nucleus physics.6 . Conclusions.The basic capabilities of the present intermediate energy high quality proton microscopes are shown on the next page. Also shown is a brief summary of Professor Olmer's talk as well as an indication of some of the effects that should influence the spin observable P-A. The large arrows indicate topics I will discuss in more detail later in the 'theoretical topics' section of my talk. One should keep in mind the goal of mapping out the nuclear response as a function of momentum transfer (q) and nuclear excita­tion co for a variety of proton energies E. By nuclear response we refer tospin observables as well as the traditional differential cross section.400BASIC CAPACILITIES: Experimental - Energy range 100 - 800 MeV (variable energy)Beam current highExcellent energy resolutionMeasure spin observables (P-A, P+A, Dij)Limited data base now[OLMER] P-A results sensitive to tensor interaction (sometimes to densitydependence = DD)Little sensitivity to distortions High precision needed.[Availability of spin polarized along any direction] -*-But interpretation?P-A sensitive to 'non-local effects'(a) exchange (different interactions?)(b) energy dependence of interaction(c) multi step processes DD(d) Relativistic effects?(e) Traditional nuclear structure (etc.)u s401Below I have Indicated the subjects of Professors Hutcheon's and Scott's talks in the parallel sessions yesterday. I have also indicated the poss­ibility and desirability of using excellent energy resolution proton beams to study, in detail, vibrational and rotational levels in heavier nuclei.The use of neutron beams to study T> giant resonances, MI resonances and isospin mixing in nuclei is also summarized.[HUTCHEON] TRIUMF (p,p'), (p,P) °nNuclei A < 58 (p ,p '»Y) D(p,2p)(p,p') inclusiveyA contrib.Why?A - h states <==study collective properties of nuclei (Giant resonance in sd shell nuclei)Medium effects < = =[SCOTT] - Studies of sensitivity of (p,p')Ay shapes to p and n structure - importance of DD forces.(A) Excellent energy resolution AE <_ = 30 keV'Really' study vibrational and rotational nuclei (as opposed to (a  ,xn), (c,xn) etc.)(a) IBA(b) particle-like interlopers vs. collective states(spin observables)(c) Mixing of vibrational band sIU, PAULI, US proposals(B) (n,p), (n,n')(a) Study T> giant resonances in N > Z nuclei(b) 'Ml" transitions enhanced by An&j -*■ (n+l)£j (Virginia Brown)different than GT states but 1+(c) (p,p') - (n,n') like (tt+ ,tt+ ’) - (tt- ,tt- f)402Since there have been several references at this conference to the role of A ' s  in nuclei, I thought you might be interested in seeing some recent results (Iqbal and Walker to be submitted for publication) for the (p,7T) process in a model using finite range forces and an intermediate propagating, interacting A. The results, as shown by the following trans­parencies, show little sensitivity to the input parameters. The code is quite long to run but in addition to providing a meaningful comparison between theory and experiment should allow one to test the validity of various approximations.Reactions involving A formation Consider (p ,tt)TNM - finite range interactionPropagating intermediate A that interacts with medium - realistic distortions for p and tt(p) . [S + P wave now - res. included]Results: - Javed Iqbal1. Sensitivity to distortions2. Sensitivity to orbitals3. Sensitivity to width of A4. Which diagrams dominate5. Comparison with data.INON-RtSON antno403C OOC404tX*-~aV -4<P r -HU lK IOcv. •%n o*u—4u H i•-7  *• o• •u.O• au i IU l I Iu. 1 |u.U t» n  t i l l  I  I  I m l i  i  I  « | | « I I  i  » « i  l i m i t  l  t  1 1 I I  «7o To8M W I  Vt/*9405406'oOJsnvwwK Mn (js/qu) up/joplUCf 966p,r407410n030)1—14-JXI CJca a) 0)> CO CDu a) C/30) uto 0>Xo a) •a rHc G •H•H 0) cdD. 13 u03 G CDa)X00 Phc CD G•H X •H■U03 COi-i 00 GCX J-l OP CD*Hcu G 4-J■u CD uc <D•H <DJd3-44-J OO O>4-1 O4-1Jd4-1 uc G 3cd O CO■u •Hn 4-JXo •H (DCX T3 J-ie X CDcdX•HQJ G COX •H Gs-/ Oacd XS •H CDU >X 4J cdu G jC•H gX M& 4-JX* GCO i cdGO CD•H CD aU Jd •Hcd 4-1 Ur—1 P-i3 <4-1a O <DrH /"Ncd CD •H •a U S MG 00<1 (D oH X •rHg: Go CD g Ga. M XX 0) CD•HU X 4-1 Ucd 3x CDrHG 00 00 rHcd G (D4J CD cdHCO G JdCD o 1o X4-1 a) (D UJd CDg 4-1 CDo Jd rH•H g 4-1 cd4-1 O £O <4-4Cl)MH‘O •tilM CO (D •O 4-» COoCJrH 33 cd oCD CO a COG CD CD rHO rO G411In order to test the importance of intermediate A states in the N-N t matrix embedded in the many-body environment (with regard to such things as Pauli-blocking, i.e. Density depence) and also to provide a more com­plete multistep (coupled channels) pion-production operator we (Boris Blankleider and G.E. Walker) have been considering the following exten­sions of existing two-body coupled channels theories as shown below.(1) Corrections to (p,p')and(p,n) due to target nucleon fermi motion and 'energy' dependence of the t matrix.[t(s,t)](a) t(E,q)3t= t(E0sq) + (E-E o)3E+ ------Eo3t~t(E0,q) + [ap22 + 6q*P2 + YPi* P2] x 9^1 V 'long & trans. contributions(b) Fermi averaging inadequate(c) Allows toC to contribute to non-normal parity transitions(p-A) (T(d) Detailed correction suitable for existing codes under wayTypical 'corrections'3t0t c ■+ t cax *a2 + -^ra a 3E Pi *P2 E=E0(2) Coupled Channels (Blankleider)NN -*■ NA NN + NN NN -> NN7T(a) Include backward going pions(b) Put in fermi gas model(c) Uses separable representation and form factors as in put(d) Also applicable to strangeness exchange reactions412Now let us briefly consider what might be learned from nucleon- nucleus reactions above ~ 2 GeV. A summary of the total N-N reaction channel cross sections as a function of Plab is shown below. We also list some conclusions regarding nucleon-nucleus investigations in this higher energy regime.Nucleon-Nucleus Interactions at Higher EnergiesA. Total cross sections [aT(mb)] for selected N-N channels as a function of Piab(~^)Channel Plab2 j4 8 Channel 4 8^total 48 42 40A + +nA 5 2PP 22 13 10 > >t O 2pNTT+ 18 10 4 pN*(1470) .6 .4+ -ppir it 1 3 2.5 pn*(1520) .7 .3+ + —pnir it it 1 2 pN*(1688) .7 .5PPP - . 1 pAK+ .05 .05ppU) .09 .15 pEK .03 .02ppn .1 .1B. Inelastic ScatteringNo novel sensitivityC. Meson Production(p,p) very high q (> 1 )short distance behavior (quarks, bag but also complicated multinucleon reaction mechanism?D. Resonance production + propagationE. Hyperon (hypernuclei) production high spin states Essential to have variable E capability413In anticipation of the forthcoming data from LEAR on N-N and N-Nucleus scattering, Dover, Sainio and I have been studying different models for the N-N t matrix suitable as input for existing DWIA codes.We summarize some salient features regarding N-N and N-NucleusN-N and N-Nucleus A. Selected N-NReactionschannels ,GeV. Plab c ) aT (mb)\P PT^3 _^ 8 300 100 “  J  100P_Pel_70 50 30(pp+nn) (13.1) (8) (4)pp-*-total pion [31 (3 ^ ) ]  c— + —pp-*TT IT .7 .3 .06+ + — — o-*-TT 7T 7T TT TT [13.6 (~1 — )] cpp->K+K~ .08 .1 .02-►total kaon [ 5 (1.6 ~ ) ]— + -*pn7T [ 1 (1.6 — -)]+AA [.05 (1.6 ^ ) ]B. N on Nuclei (large energy deposit, strong absorption, no exchange, part of N-N related to N-N).(p,p') and (p,n)1. Anticipated data from LEAR2. Different but related to ^ N(G parity exchanges Strong T=0[tt,w ] => tensor(strong W) Weaker L ‘S(no exchange) than NN(different energy dependence)V(*)3. Recent theoretical results (Dover, Sainio, Walker)(*)tT »  t T TLS order of magnitudeLStoSince our main purpose here is to compare the N-N t matrix results with the N-N transition operator we show the central terms in the N-N t matrix in the next transparency.Ep (MeV)(Franey-Love)We show selected N-N results in the next three transparencies.\/ex*»c*l br€rtVc,.’Oso^■Nc»!^ 766 056s//////±c ' '  " /  '/  "  ' " ' ‘ N r !fsl-hl ccrs)1:r*l t  c o m p o s e ^ ' T s  O(S/ior'fY'Arvg c  Sp***-isospi *V/  W a W N j .'*°® * ° ° O v \ e v >  a l s o416417Momentum Transfer Dependence of N-N t Matrix Components E = 210 MeV(MeV/c)q = 0 140 250 350Componentto 893 730 480 228tC 73 53 23 4atC 63 40 12 11TtC 78 31 15 9OTt 50 58 44LSt 11 7 5LSttT 8 17 22tTT 49 52 35418The results show that for the Paris N-N annihilation potential, the resulting t matrix has a strong t£ component capable of exciting AS = 1, isoscalar resonances. This result is sensitive to the spin-dependence assumed for the imaginary; potential. Other interesting similarities and differences between N-N and N-N t matrices are evident from the trans­parencies. Note the characteristic signatures of the various spin and iso-spin channel asymmetries.* U V  )i  i *  “, * •O ■ --.1>■1-+•300( M e vV419In summary the prospects for new and exciting data from intermediate energy proton machines is considerable. I have tried to point out some additional experiments (involving collective states or n and p probes) that should provide additional useful information. I have discussed briefly my own interests in three theoretical topics (detailed (p,Tr) predictions, energy dependence of the t matrix, and coupled channels NN, NA, and NNtt transition operators) whose study, I hope, will aid the interpretation of the anticipated high precision data. We have discussed the role of higher energy nucleon-nucleus reactions. Here the emphasis will probably be on heavier meson or baryon resonance production and the role of the many body medium in influencing the production and propagation of these more exotic 'particles.' Since these processes tend to be very high momentum transfer (~ 1 GeV/c) the results may be very sensitive to models involving short distances (bags QCD). On the other hand the necessity for including multi­nucleon mechanisms will probalby significantly complicate the issue.Finally we have discussed the N—N t matrix in comparison with the familiar N-N transition operator. The possibility of exciting AS = 1,AT = 0 nuclear states via the N-N t£ term is noteworthy. As mentioned previously the t channel (meson exchange) parts of the N—N and N—N potential are related by the G parity transformation. The different strong components and energy variation between the N—N and N—N t matrices, as well as the important role of absorption (N-N) and exchange (N-N) for the different operators should make N—nucleus and N-nucleus results interesting to com­pare in the future.The prospects for important additional information being distilled from the anticipated proton-nucleus data appear excellent. Especially if both theorists and experimentalists co-operate in analyzing future experiments using more realistic models.RAPPORTEUR TALKS AND SUMMARY421THEORY OF EFFECTIVE INTERACTION AND MULTIPLE SCATTERING*P.C. TandyDepartment of Physics Kent State University Kent, Ohio 44242AbstractPapers presented in the parallel session under the above title are summarized and discussed. Some general comments on contemporary methods for relating nucleon-nucleus reactions to nucleon-nucleon scattering are made with reference to the underlying multiple scattering theory context.Parallel Session (1): Theory of Effective Interactionand Multiple ScatteringSix short papers were presented at this session, three on elastic scattering and three on inelastic scattering. In two of these papers, initial results were presented for inelastic scattering calculations based upon extensions of the Dirac equation description of elastic scattering summarized earlier in the Workshop by Ray and McNeil.Besides introducing a more justified treatment of spin, the four- component nature of the relativistic formulation introduces a more complex dependence of scattering observables and wave functions upon the nuclear shape. Much work remains to be done before the full impact of relativistic effects upon our understanding of the microscopic description of the effective interaction and the dominant reaction mechanism can be clarified. As the other papers in this session show, the full impact of the first-order non-relativistic treatment of elastic and inelastic scattering is by no means completely explored. The related effects of non-locality, antisymmetrization, and large-angle mechanisms were addressed. There is not yet a definitive answer for how such effects should be treated below several hundred MeV even for a first-order multiple scattering theory. A summary of the contributed papers will be followed by some general remarks.4221. Orbiting in Proton Elastic Scattering - H.V. Von GerambPredictions of large-angle analyzing powers for elastic scattering from heavy targets at beam energies of 200 to 400 MeV were presented.The predicted oscillatory behavior in the backward hemisphere was interpreted as due to an "orbiting" phenomena. In this picture, the imaginary part of the spin-orbit optical potential acts as a very efficient spin filter on trajectories which orbit around the surface of the nucleus to emerge in the backward hemisphere. The interference effect of such orbiting trajectories with direct backward scattering trajectories which traverse much less nuclear matter produces the large- angle oscillatory behavior of the analyzing power. A brief description of these predictions was given in the survey talk by Von Geramb at the beginning of this Workshop. These predictions apparently hold for both microscopic first-order optical potentials and for phenomenological optical potentials. The intrinsic non-locality of the employed microscopic optical potentials was suppressed in favor of local approximations. The dependence of these predictions on the form and nature of the localization procedure is an interesting question which should be addressed.32. p- He Scattering with Full-Spin Dependence and Some Antisymmetry - R.H. LandauResults based on first-order microscopic optical potential calculations were presented. In this work, the full spin h (*) h structure of the system was retained with three types of tensor terms appearing in the optical potential along with the central and spin- orbit terms. The NN t-matrix was determined on-shell from NN phase423shifts and extended off-shell through separable form factors taken from a separable potential model. The momentum-space tp factorized form was employed for the optical potential and the Lippman-Schwinger integral equation for the scattering was solved in momentum space.The antisymmetrization effects included were those accounted for by use of the free NN t-matrix. Comparisons of differential cross sections and analyzing powers with data at 200, 515, 600, 715, and 1000 MeV were presented. The parameter-free cross-section calculations reproduce the qualitative trends of the data over this wide energy range, but do not quantitatively describe the first diffraction minimum. Analyzing powers beyond the first minimum are also not well- reproduced. The back angle rises in the cross-section data at 515 and 600 MeV are quite wel1-described and in this region the importance of the exchange symmetry of the NN t-matrix and the tensor terms of the optical potential were pointed out. Further details of this work can be found in a forthcoming paperJ Other Pauli exchange mechanisms are likely to be important for this few-nucleon system. The "heavy- particle stripping" mechanism discussed in the contribution byH. Sherif is one example.43. Exchange Effects in Larqe-Angle p- He Scattering - H.S. SherifAn investigation of the role of the heavy-particle stripping exchange mechanism in the back-angle excitation function was presented. The usual direct and knock-on contributions to the scattering amplitude were taken to be accounted for by use of a phenomenological optical potential. The resulting forward-peaked amplitude was supplemented by a DWBA form of the stripping amplitude. The required424proton-triton overlap function was obtained from the He charge form factor through several models and the sensitivity to the large momentum components was investigated. Systematic improvement over a range of energies between 0.1 to 1.0 GeV was noted for the back-angle cross- section when the charge form factor with meson exchange corrections was employed. In almost all cases, the region where the optical model amplitude and the heavy-particle stripping amplitude just begin to interfere, namely, the second diffraction minimum or shoulder, the calculations significantly underestimate the data and lead to a diffraction minima which is too pronounced. This could be a signature of an incorrect phase relation between the two independently calculated mechanisms. The general behavior of the large backward angle cross section is reproduced by this approach. The heavy-particle stripping has an effect on the large-angle polarization, but does not lead to improved agreement with data. The description of spin effects for large-angle scattering is still an open question. This work has been recently published. The assumption in this work that the scattering amplitude generated by a conventional optical model adequately represents the knock-on NN exchange process is doubtful in view of3the earlier results of Alexander and Landau. These latter authors have shown that a microscopic first-order optical potential calculated with an NN t-matrix containing the correct exchange symmetry produces a back-angle rise in the cross section. The optical model scattering amplitude employed by Sherif et al. is monotonically decreasing with angle in the backward hemisphere.42544. Non-Locality in Inelastic Scattering - E.F. RedishIn this paper, some important consequences of the intrinsic non­locality of the nucleon-nucleon t-matrix in treatments of inelastic scattering were pointed out and discussed. The source of non-locality addressed here derives from the dependence of the t-matrix upon the initial and final momenta (or conjugate coordinates) of the two nucleons. The energy parameter of the t-matrix was taken to be fixed.A similar discussion has been presented by Walker^ for the implication of the non-locality arising from the coupling of the effective energy of the t-matrix with the kinematics describing the inelastic excitation.The form obtained for the DWIA matrix element when the NN t-matrix is a local function in coordinate space isL . IaK  a*. - ,..(+)T = d rod rl*f (ro )¥ rl)t (V l )xi (ro)*i(rl) • (,)Redish contrasted this form with that which arises when the NN t-matrix has the more general (non-local) form t(x;R) where x = ^ (r+r') and R = ( r - r ‘) and (r,r‘) are the initial and final relative momenta of the two nucleons. In momentum space this becomes t(q;<) with q = k1 - k, k = 2 (k1 + k) where k and k 1 are the initial and final NN relative momenta. As was pointed out, a non-locality (dependence-Vupon < or R) is always present in the solution for two-particle scattering even if the potential is local and the particles are distinguishable. The form of the DWIA inelastic matrix element with a non-local NN t-matrix becomesThe two forms of the DWIA matrix will be identical ift(rQ -r^;R) = t^(r - r^  )6(R). It was pointed out that since <t>^ andpeak at different values of their arguments, the transition density^ -y -vmatrix <j>^(r-] + |-)<t>.j(ri - ^ ) can take on much larger values than the localtransition density ^(r^ )<)>. (r-j). The magnitude predictions of DWIAcalculations can be strongly affected.The above non-locality can also alter angular momentum selectionrules. Expansion about zero range for a Gaussian non-locality givest ( V V ’K) ^ t ^ o - V n  - 1  e2v26(R)] and the DWIA amplitude becomesT = T*- + TN .^ Redish pointed out that one part of the non-localcorrection term involves use of the transition operatort*"(r - r,)v • v in the otherwise local form of the DWIA. Since ° °_> r!the operator v carries quantum numbers L11 = l", the strong spin­'llindependent central component of the t-matrix can in this way contribute to the abnormal parity transitions which are usually attributed solely to the much Weaker spin-flip components of the t- matrix. The extracted Gamow-Teller strength for 0+ ->-l + transitions can be modified by these considerations. Further details can be found in a recent preprint.^The form of the NN t-matrix parameterizations developed by Love6 7 8and Franey, Picklesimer and Walker, and Von Geramb contain non­localities and fit within the general form considered here by Redish. However, in these models the non-locality arises solely as a device to accommodate the exchange symmetries of the t-matrix. The t-matrix is written as a sum of a purely local component and a purely non­local component so that they can be employed separately in standard DWIA codes such as DWBA70. In the notation used here, these models have the structure t(x;R) = 6(R)t(x ) ± s(2x)t(R/2) where the sign427depends on whether the spin-isospin channel is spatially even or odd.The cross section magnitude effects and the selection rule effects addressed by Redish will be included when employing t-matrices of this form. It remains to be investigated whether forms for t(x,R) which are more in accord with the intrinsic structure of the t-matrix arising from solving the NN Lippmann-Schwinger equation introduce important non-local effects over and above those which are routinely incorporated in present day calculations.5. A Dirac Version of the DWIA - E. RostMicroscopic inelastic calculations which employ distorted waves from the Dirac equation treatment of elastic scattering were described. Some preliminary results were presented for the ^0(p,p') 3 reaction at 500 MeV. The DWIA matrix element is calculated in the formTfi = < 4 _) $f |tD | ^ +)$i> (3)where now each distorted wave 'V and bound state $ are Dirac spinors having both upper and lower components. The nucleon-nucleon t-matrix operator t^ is expressed in terms of Lorentz invariants in the same manner as is described earlier in this Workshop by McNeil. The components of t^ having different Lorentz character are identified by requiring that <u-|U2 |tp|u-|U2 > describe on-shell NN scattering as deduced from phase shift compilations. These inelastic calculations represent a straight-forward extension of the microscopic Dirac equation approach to elastic scattering begun recently by Shepard,McNeil, and Wallace.^428For the natural parity excitation of the 3 state of ^ 0  at 500MeV, Rost pointed out that the coupling of the lower components ofthe initial and final distorted waves through the Lorentz scalar andvector parts of t^ had an important effect on the magnitude and shapeof the effective spin-orbit contribution to the excitation. This ispresumably the inelastic counterpart of the improved description ofspin-dependent observables that arises in Dirac treatments of elasticgscattering at this energy. It was pointed out also that for unnatural parity excitations, the spin-flip mechanisms that enter when the pseudo-scalar (y ) term of tg couples upper to lower components should add a new perspective to the studies of spin-modes of nuclear exci tation.6. Collective Excitations with Dirac Distorted Waves - H. SherifThe coupled channel nature of the Dirac equation for elastic scattering leads to unconventional shapes for the effective single­channel optical potential. The shapes are similar to the "wine- bottle" forms that have recently been suggested from studies of nuclear-matter-based medium dependence of the effective nucleon-nucleonOinteraction. Sherif presented results from an investigation of theextent to which the extracted & parameters for collective excitationsare sensitive to these new descriptions of the distorted waves. Ina recent paper,^ Satchler has suggested that the inelastic crosssections can often be reduced by as much as a factor of 2 whenoptical potentials of the "wine-bottle" shape are employed.40The excitation of the first 3 state of Ca by 181 MeV protons is studied here. The approach followed is the phenomenological429description of elastic scattering via a Dirac equation which is reduced to an effective Schrodinger equation for the upper components. The non-linear dependence on the nuclear shape is prescribed in this way. The effective central and spin-orbit potentials are both then deformed due to nuclear shape deformations and the inelastic transition potential is then identified. In the recent investigation by Satchler, the spin-orbit potential was not deformed. Sherif found no substantial change in the angular distributions for the cross section and analyzing power. The extracted value of 6 was0.285 compared to the value 0.230 which obtains when optical potentials of standard shape are employed. The electron scattering result is 6 = 0.35.General RemarksThe theoretical framework underlying almost all microscopic treatments of intermediate energy elastic and inelastic nucleon- nucleus scattering is first order in the multiple scattering expansion. The folding of a nucleon-nucleon t-matrix with the nuclear density provides the optical potential in the case of elastic scattering and the transition potential in the case of inelastic scattering. This model has been subjected to a great deal of close scrutiny in recent years due to the availability of increasingly accurate spin-dependent data on a large variety of nuclear excitations. On one hand, the model has proved remarkably resilient; on the other hand, clear deficiencies are evident. As originally formulated, the multiple scattering expansion introduces the free space NN t-matrix. While this leads to reasonably satisfactory430descriptions of elastic nucleon-nucleus data at energies above several hundred MeV, the resemblance to elastic data deteriorates markedly as the energy is lowered. For inelastic scattering at IUCF energies, the DWIA with a free t-matrix fares significantly better. However, for spin-dependent measurements of natural parity excitations which sample the nuclear interior, medium-modified NN t-matrices obtained from angextension of Brueckner nuclear matter theory to the scattering sector provide consistently better results. This density dependence which follows from antisymmetrization effects on the low-energy effective NN interaction is expected on physical grounds because of the connection to bound-state descriptions. Further research in this area should continue to emphasize the derivation and use of NN t-matrix or g-matrix interactions which are free of adjustable parameters; otherwise, the ability to make interpretations in terms of microscopic mechanisms is lost. Below several hundred MeV, the reliability of truncating multiple scattering expansions of the elastic optical potential or the inelastic transition potential at first order is not obvious. For this reason, it is important to make the connection between multiple scattering theories and bound-state perturbation theories much clearer than is now the case.Traditional methods of formulating multiple scattering theory under the constraints of identical particle symmetries are really suited only for the high-energy regime. The Pauli exchanges can be distributed throughout the terms of the expansion so that each term contains only the exchanges relevant to the active particles of that term.^ The NN t-matrix of the first-order term will contain only two-particle antisymmetrization effects. A more physical organization for lowerenergies would have the many-particle antisymmetrization effects presentin each term in an expansion in orders of the number of particles activein strong interaction. Until such an organization is developed, therewill remain theoretical ambiguities in how anti symmetrized effectiveinteractions based on bound-state perturbation theory are to beemployed for scattering calculations.An example of such an ambiguity arises in the use of the BruecknerNN g-matrix to provide the effective interaction for nucleon-nucleusscattering including antisymmetrization effects amongst the A+lnucleons where A is the mass number of the target. The g-matrix isdefined in bound-state perturbation theory where the (unperturbed)basis states already satisfy the constraints of antisymmetry amongstall nucleons. The Bethe-Goldstone type of equationg(u>) = v + vG0(w)Qg(w) therefore needs only to have the antisymmetryconstraint built into the operator Q which projects intermediatestates off the unperturbed ground state of the system. When g isused as the effective interaction for scattering of the projectileand bound nucleon and the unperturbed (asymptotic) states of the systemare taken to involve a free plane wave for the projectile, animportant part of projectile-nucleus antisymmetrization is overlooked.As an illustration, the contribution of lowest order in v for theAscattering or effective interaction is thus <k'|«f>f| J  v0j 1 > I k>Awhereas it should be <k'|«j)f | £ Av . |<t>->|k>. Here and a . aret j=i oj-Vantisymmetrized target states, the |k> are plane waves, A is theAantisymmetrizer 1 - £ EQ . where EQ  ^ exchanges the projectile (o)with target nucleon (i). The antisymmetrization effects for first-order432nucleon-nucleus scattering would be fully included through the use of the g-matrix if the asymptotic states of the employed nucleon-nucleus wave equations were governed by a Hamiltonian which is symmetric in all nucleon coordinates. This is, however, difficult to arrange in scattering problems and has not been accounted for in the variety of medium-dependent effective interactions that have been developed to date. This symmetry of the reference (or unperturbed) Hamiltonian is automatic in bound-state applications and the lack of it is basic to the very definition of a reaction channel.Part of the effect of these extra exchange processes which should be incorporated into the use of the g-matrix for the effective interaction is related to the heavy-particle stripping mechanism mentioned in the contributed paper by Sherif. A less difficult aspect from a practical point of view is the replacement of the asymptotic plane wave states of the continuum particle by states which at least have the constraint of being orthogonal to each occupied single­particle bound state of the target. A simple model for such12"orthogonality scattering states" is available. A multiple scattering13theory built upon these basis states is being formulated.At 500 MeV, the effects of antisymmetrization of the projectile nucleon with the constituents of the nuclear medium are presumably small. There is this hope of achieving a calculation of first-order multiple scattering theory as a bench-mark for making extensions to handle the increasingly important pion channels as the energy is raised, and the coherent medium effects as the energy is lowered. The recent improvement in quality of the spin-dependent observables calculated4339with the relativistic treatment of the first-order optical potentialbrings this hope closer to a reality. The relativistic results presented earlier in this Workshop by Ray show that the improvement for higher and lower energies are not as compelling as at 500 MeV, especially for the differential cross section. Nevertheless, analyzing powers are improved on the average and the quantitative sensitivity to relativistic effects has been demonstrated.The coupled channel nature of the Dirac equation introduces a non-linear dependence of the effective single-channel optical potential on the nuclear density. The extent to which this can provide an alternative view of at least part of the density dependence of the effective interaction at the lower energies should be investigated. It is important to identify the extra physical reaction mechanisms that enter in a Dirac description so that the implications for the development and wider use of a microscopic underlying theory can be highlighted.The extra degree of freedom introduced by a Dirac descriptionof the motion of the projectile compared to the non-relativistic wave equation is the availability of negative energy plane wave intermediate states in the scattering process. The integral form of the Dirac equation can be expressed as+  +  + +  + +  T  +  +  .  +T = u + u r+T + u r_TT'+ = U"+ + U'+r+T++ + U""r_T“+where the various quantities are operators in the momentum space of the projectile. The superscripts (+) identify the employed basis states as either positive or negative energy free particle Diracspinors. The r+ represent the projections of the Dirac propagator(for a nucleon and a ground-state target) onto the corresponding partsof the Hilbert space. That the negative energy intermediate states(of the projectile) described by r_ account for almost all of theimprovement in the analyzing power at 500 MeV has been verified by14solving Eq. (4) with and without the r_ contribution. Let us consider the potential U, taken from a first-order multiple scattering picture, to be435Here u and u are positive-energy free-particle spinors, <j>Q is the ground state of the target (which for simplicity we here consider to be a collection of non-relativistic nucleons), and tp is the operator for on-shell nucleon-nucleon scattering appropriate to this basis.This operator is such that in the limit where the target is a single nucleon, the above matrix element reproduces nucleon-nucleon scattering data. Hence, all possible free-particle intermediate states (positive and negative energy) for the scattering amplitude of a given pair of nucleons are implicitly included. The contributions to T++ which are higher than first order in U involve two different active target nucleons. Identification of the standard single-channel optical potential by folding back the negative energy states of the projectile yields<k'|U+ + |k> = u(k' )<k' ,<l»0 1tQ |4»0 ,k>u(k) (5)(6 )where( 7 )The first term in the above expression for W++ is essentially the standard non-relativistic first-order optical potential <£ tQi->, and the second term can be described schematically as< V t .r t .>. This is the lowest order correction which comes from\ h  0 1 ' 0Ja relativistic description of the projectile and leads to a profound change in the physical picture of a first-order optical potential.In the non-relativistic formalism, the first-order optical potential can be described as either a) the sum of all scattering interactions of the projectile with one active target nucleon at a time, or b) the sum of all scattering interactions of the projectile which do not rely on nucleon-nucleon correlations in the target. These two descriptions are equivalent since the optical potential must contain only excited intermediate states of the system and since the internal structure of the projectile is being ignored, the target must be excited. In the relativistic formulation the descriptions a) and b) are not equivalent and only description b) is appropriate. The enlargement of the Hilbert space available to the projectile introduces "non-elastic" intermediate states of the system in which the target remains in its ground state while the projectile is in a negative energy plane wave state between collisions with two different nucleons of the target. These intermediate states (in r_) are off-shell by at least twice the nucleon mass, but nevertheless have a sizable effect since the strengths of U+ and U + , especially in the spin-dependent parts, are significant fractions of the nucleon mass. The above considerations rely on specific assumptions for inferring U ", U+ , and U"+ from knowledge of U++, a quantity which is constrained by NN436scattering data. The main assumption is that the spinors u and/or u may be replaced by the negative energy spinors v and/or v to obtain U”", U+” , U + from U++. Since in a field theory the negative energy states can be interpreted as anti-nucleons, off-mass shell considerations for the two-body t-matrix should be brought in. The spihors are essentially projection operators and the extension of U++ to the other orthogonal parts of the space should be constrained by relationships between two-body scattering for nucleons and anti­nucleons.AcknowledgementThe author is grateful to A. Picklesimer and R.M. Thaler for valuable discussions on some of the topics mentioned in this presentation.437References1. M.J. Paez and R.H. Landau, Oregon State University preprint,1983, submitted to Phys. Rev. C.2. H.S. Sherif, M.S. Abdelmonem, and R.S. Sloboda, Phys. Rev. C27, 2759 (1983).3. Y. Alexander and R.H. Landau, Phys. Lett. 84B, 292 (1979).4. G.E. Walker, Proceedings of the Telluride Conference, 1982, to be published.5. E.F. Redish and K. Stricker-Bauer, University of Maryland preprint #83-108, to be published.6. W.G. Love and M.A. Franey, Phys. Rev. C24_, 1073 (1981 ).7. A. Picklesimer and G.E. Walker, Phys. Rev. C17., 237 (1978).8. H.V. Von Geramb, AIP Conf. Proc. No. 97: The Interaction between Medium-Energy Nucleons in Nuclei - 1982, ed. H.O. Meyer (AIP Press, New York, 1983), p. 44.9. J. Shepard, J.A. McNeil, and S.J. Wallace, Phys. Rev. Lett. 50,1443 (1983); see also B.C. Clark, S. Hanna, R.L. Mercer, L. Ray,and B.D. Serot, Phys. Rev. Lett. 5£, 1644 (1983).10. G.R. Satchler, Nucl. Phys. A394, 349 (1983).11. A. Picklesimer and R.M. Thaler, Phys. Rev. C23, 42 (1981).12. R.R. Scheerbaum, C.M. Shakin, and R.M. Thaler, Ann. Phys. (NY) 7£, 333 (1973).13. K. Maung, P.C. Tandy, and R.M. Thaler, in preparation.14. M.V. Hynes, A. Picklesimer, P.C. Tandy, and R.M. Thaler, to bepublished.438439NUCLEAR REACTIONS P. KltchingUniversity of Alberta, Edmonton, Alberta and TRIUMF, Vancouver, B.C.There were no contributions to this discussion session, so the convener gave some personal impressions of progress already made and future directions.In the area of quasi free scattering, it is clear that polarization studies which can now be done provide important tests of DWIA theories used to analyze these reactions. Past experiments have been plagued by mediocre energy resolution, but this will change with the new spectrometers being built at TRIUMF and Indiana, which will enable experiments to be performed with an overall energy resolution approaching ~100 keV. This is an order of magnitude improvement, which will need to be matched by better calculations and theory.The most urgent need is to remove the factorisation approximation and to incorporate the effect of the nuclear medium on the interaction between the two nucleons. A promising line of attack would be to use effective interactions of the kind we have heard so much about at this conference.There seems to be no technical reason by this should not be done, giving quasi free scattering a new lease of life as a source of information on single particle wave functions, nuclear medium effects, etc. A particularly interesting paper, presented by Manfred Dillig, has even suggested that the role of the A in quasi free scattering may be much more important thanpreviously expected(when the kinematic conditions are chosen appropriately).If Dillig's preliminary calculations hold up, quasi free scattering may provide us with a tool to study the A-nucleus interaction.I can make a few remarks on the pion production reaction. Firstly, a large amount of data now exists, and it is clear that the reaction is very complicated. No single model describes the reaction completely, although it seems to be understood in some circumstances (e.g. when the kinematics are chosen to make the A dominate). Recent discoveries at Indiana of systematic features of the ( p , tt- )  reaction suggest that the (p,iT) process is simpler than the ( p , tt+ )  and may be a better choice for testing microscopic models of the reaction mechanism. Further experiments are probably more urgent, therefore, for (p,ir_), particularly in the resonance region. Couvert's comparison of (p,Y) and (p, it)  data showed some interesting regularities when the appropriate variables are chosen, and more analysis of this type would be useful.Greben's talk on (p,d) reactions showed that theoretical models are being developed from first principles. Data exists from TRIUMF for both cross sections and analyzing powers for a few nuclei, and have been compared with DWBA calculations such as DWUCK. It is clear that while such calculations do not disagree too much with the rather featureless cross section data, they are in violent disagreement with the polarization measurements. We need better theoretical models, rather than more data. (This conclusion was strongly disputed by some members of the audience. After some discussion the speaker conceded that more measurements of spin observables in deuteron-nucleus scattering would be useful as input to the (p,d) calculations. These meas­urements may be made at Saclay in the near future).440CONFERENCE SUMMARYEdward F. Redish Department of Physics and Astronomy University of Maryland, College Park MD 20742This meeting covered a wide variety of developments in proton-nucleusscattering in the intermediate energy regime (IER: 300 MeV < E < 1 Gev) and inthe transition region (TR: 100 MeV < E < 300 MeV). The range of subjectscovered was well represented in elegant and complex flow charts in many talks.These are summarized in Fig. 1. The talks indicated that a number of importantthings have been learned already, and that further interesting topics are understudy. In some cases, good progress has already been made and criticalexperiments are planned for the near future. In other cases, indications weregiven that interesting physics can be learned in a few years, but considerablework is needed, both experimental and theoretical.I. OVERVIEWI classify the results which were presented as follows:Solid Accomplishments:(1) Gamow-Teller strengths have been extracted from the (p,n) reaction in the forward direction. These confirm the results found in the study of weak decays, namely, that the axial vector coupling strength is "quenched" inside a nucleus. The mechanisms responsible for this are still controversial, though a numberof plausible suggestions have been made. (Rapaport)(2) Angular distributions in (p,p') to the continuum permit a sharp identi­fication of giant resonance strengths up to L=4. (Bertrand)Both of these results clearly show the value of proton scattering experi­ments in the TR and IER for the extraction of information about nuclear struct­ure and the properties of nuclear matter.In Progress:(1) Elastic and inelastic proton scattering is being used to study the effective interaction of nucleons in the nuclear medium. This subject was addressed by a number of speakers from both theoretical and experimental points of view. Experimental results and prospects were discussed by Bacher, Moss, and Olmer. Semi-phenomenological approaches to the effective inter­action were presented both in the Schroedinger framework (Love) and in the relativistic Dirac picture (McNeil, Ray, Rost, Sherif). An attempt to derive the effective interaction from Breuckner theory was also presented (von Geramb). As this is the subject which is currently most controversial, and which is receiving a great deal of attention, I will discuss it extensively.Future Possibilities;(1) Coincidence spectrometers are being built at some accelerators and pro­posed at others. This promises high quality (p,2p) data in a few years. Pol­arization and cluster knockout experiments are also planned. These experiments may be very sensitive to the details of the single particle and cluster wave functions in a nucleus. In order to extract this information, both the effect­ive interactions and the reaction mechanisms need to be better understood than they are at present. Better theory and calculations must be developed to go with the improved apparatus. (Chant)(2) Calculations were presented to indicate that A's may be much more important than had previously been expected. Will we be able to study the A-nucleus interaction with this reaction, or will the uncertainties in the single particle wave functions and effective interactions get in the way? (Dillig)The treatment of distortions in the presented calculation was somewhat crude and a more careful treatment could reduce the strength of the effect. More extensive studies of this subject will be needed before we can be really com­fortable about what we are going to learn from the new knockout experiments.442(3) There is quite a  bit of data available on (p,Y) and ( p , t t  ) reactions. There are some tantalizing regularities, but the theory to understand them is not yet in place. More analysis is needed. (Couvert)(4) Theories of the (p,d) reaction are beginning to be developed from funda­mental many-particle scattering theories. At present, the severest difficulty is the lack of adequate deuteron data, especially with the spin observables measured. There are also ambiguities in how one distributes physical pro­cesses in a complete theory. There are some striking discrepancies between standard DWBA calculations and data in the neighborhood of 100 MeV. (Greben)(5) It was pointed out that one could possibly have a sensitive probe of A's in the nucleus and meson exchange currents via a study of 0+ -*■ 0- transitions. (Khanna)(6) The experimental details of developments at TRIUMF were presented.(Miller)And Now For Something Completely Different(1) One talk discussed the quark structure of the nucleon. The European Muon Collaboration (EMC) has studied the distribution of quarks in nuclei as com­pared to the distribution in the deuteron, and found it to be substantially different from that expected if nuclei are made up of nucleons and the dis­tribution of quarks in the nucleus just arise from folding their distribution inside the nucleon with the nucleon's fermi motion. (Thomas) This result has recently been confirmed by analysis of electron scattering data at SLAC and in the Soviet Union. These workers are diligently undermining the basic assumptions of nuclear physics. This has severe implications for nuclear physics in general, and for how IE physics is done in particular. About this, more anon.443I I .  EFFECTIVE INTERACTIONSSince such a la rge  propor t ion of the talks -  and of  the discussions -  was devoted to the quest ion of  the e f f e c t i v e  in teract ion ,  and since this is a topic o f  current invest igat ion ,  I am devot ing a substantial  propor t ion  of my summary to an analysis  of this topic.A NUCLEAR MATTER METHODSThe f i r s t  talk of the meeting,  and the one that attempted tc o f f e r  the most " fundamental"  approach to the e f f e c t i v e  in teract ion  was that of Geramb. In his approach one takes a r ea l i s t i c  potentia l (e g . ,  Pa r i s  or  Hamada-Jchnston) as input The Brueckner theory  of nuclear matter  is  then used to construct  a local ,  dens ity dependent in te rac t ion .  Th is  interact ion is then used with theore t i ca l  or  phenomenological  densi t ies (and trans it ion  densit ies )  for  f in i te  nucle i  to construct  optical  potentia ls  (and DWIA t rans it ion  matr ix elements fo r  ine last ic  scatter ing*.At the present time this is the closest  thing we have to a theory  of  the optical potentia l that goes beyond on-shel l  multiple scat ter ing  methods (Glauber theory  or the impulse approximation to KMT).  Since on-shel l  multiple scat ter ing  methods (05M5M) only use informat ion about the long-d istance  nucleon-nucleon r e la t i v e  wave function (the phase sh i f t ) ,  when they work we learn l i t t l e  about how two nucleons behave when they are  close together  inside nuclear matter  *When the data begins to deviate  from 05MS calculations we have the chance to learn  something important.  How does the e f f e c t i v e  in teract ion  of two nucleons d i f f e r  when they are inside a nucleus? Even in standard nuclear*  We do learn something. The e f f e c ts  from the short  range behavior  must not be so la rge as to mess up the on-shel l  f i t .444physics we expect  a number of in te res t ing  modi f icat ions e f f e c t s  of the Pauli p r inc ip le ,  e f f e c ts  of th ree -body  fo rces ,  etc.  I f  we can measure these,  we can test  our fundamental assumptions about how the many-body theory  of nuclear matter  should be arranged  To do this,  we need to have a theory  that permits us to include the re l evant  co rrec t ions .  I t appears that the Erueclcner theory  at pos it ive  energ ies  may prov ide  such a theory .Since the informat ion obtained from these calculations is  so important it essent ia l  that we examine the approximations and assumptions with great  care Upon such considerat ion ,  I  f ind a number of quest ions about the present form of the approach.(ij Which Potential?Th is  is a problem with all o f non - re la t i v i s t i c  nuclear physics in its standard form I f  the shor t - ranged  part of the potent ial  is to be constructed phencmenclogical ly ,  what are  the appropriate forms of  other  operators  in the theory ,  in part icu lar ,  those associated with the e lectromagnet ic  current and meson exchange co rrec t ions*Th is  becomes painful ly obvious i f  one cons iders the der ivat ion of the the Pa r is  potent ia l Cll I t  begins with a d ispers ion  theore t i c  treatment of the 2-picn exchange contr ibut ion tc the nucleon-nucleon potent ial  Th is  y ie lds an on-shel l  matr ix element only.  An Ansatz is then made to extend this of f  shel l in a way which yie lds a local potent ia l (TPEP )  Th is  (and the tai l  o f omega meson exchange) is added to OPEP to g ive  the medium and long range part of the fo r c e .  The short  range part is taken to be essent ia l l y  f lat and a smooth t rans it ion  made to OPEP+TPEP at 0 8 f  The height of  the in t e r i o r  is  adjusted to f i t  the two-nucleon data. I t is found empir i ca l ly  that the height in the in t e r i o r  is wel l  f i t  by a l inear  form The two-nucleon Schroed inger  equation then looks l ike  the fo l lowing:(1) Cp2//m ♦ (V + EW."IO = E ’i'445Rewr it ing  this by br ing ing  EV to the r ight  ancf introducing the trans format ion(2) ♦ = /l-V 1> y ie lds the equation(3) [ ( 1 - W % z!2m ( 1 - W &  V/(l -V> 3<j> = E * .I f  we now expand the rad ica ls  ( (1 -V )  = l+V/2 + . . . )  we get an e f f e c t iv emomentum dependent potential:(4) C p 2/2m + (p2V+Wp2 )/4m + V/(l-W3<|> = E<CTh is  is the potent ial  used Unfor tunately ,  <f> d i f f e r s  from V at shortdistances This means that the energy  dependent and momentum dependent ve rs ions  of  the potent ial w i l l  have d i f f e ren t  o f f - s h e l i  cont inuations and th e r e f o r e  d i f f e ren t  resu lt s  in a many-body calculation When we are calculating an elect romagne t ic  current opera tor  including meson exchange e f f e c t s  which ve rs ion  of the potential should be used? These fundamental quest ions are not dealt with in any form of  standard potent ial  theory  and wi l l  cause uncerta int ies whenever short  ranged e f f e c ts  are  important.( i i l  Nuclear Matter?The next class of  problems are associated with the use of nuclear matter  as an in termed iate step. Were we to begin with the Brueckner theory  of a f in i t e  nucleus and t ry  tc use the G-matr ix as an e f f e c t i v e  in teract ion  we would f ind that the e f f e c t iv e  in teract ion  is nucleus dependent. Th is would be a great  burden I t s  much n icer  to have an e f f e c t i v e  in teract ion  which depends on one parameter (the density )  which can be calculated once and fo r  al l ,  and then used in a va r ie ty  of nuclei.T h e r e  is ,  however ,  a deep problem invo lved in using G-matr ices taken from nuclear matter  in scat ter ing  theory The essence of scat ter ing  theory  is  that i t  is a comparison between two hamiltonians: the “ f r e e "  hamiltonian act ing in the asymptotic reg ion ,  and the " fu l l "  hamiltonian which d i f f e r s  from the f r e e  in  the scat ter ing  volume [23. The matching of the wave function across the446boundary of the two reg ions  produces the scat ter ing  In nuclear matter ,  however ,  there  is  nc asymptot ic reg ion.  As a resu lt ,  the treatment of  the e f f e c t i v e  in teract ion  in the nuclear surface has to be analyzed with some c a r e .One test  f o r  the va l id i t y  of the nuclear matter  approximation has beenproposed by Mahaux C33 He suggested that the strength of the densi ty-dependentin teract ion  should not change much over  a distance correspond ing  to the rangeof the densi ty -dependent fo rce .  Th is  leads to the condit ionr «  Iv |o dr dp 1 1where  r  is  the range of the e f f e c t i v e  in teract ion .  In the nuclear sur face ,  the odensity changes from 0 to near ly  nuclear matter  density in about 1 f  The range o f  the e f f e c t i v e  in teract io