Historically, work in medium energy nucleon-nucleus scattering physics started in the 1950s and has continued since. During the past ten years exciting new developments have occurred, and this work reviews these developments. Two distinct theoretical approaches tor describing the medium energy scattering process are discussed. The first is nonrelativistic and is based on approximate solutions to the many-body Schrodinger equation. The second is relativistic and is based on covariant meson exchange theory and the Dirac equation.A pedagogical discussion of nonrelativistic multiple scattering formalisms is presented, followed by a description of the approximation schemes used in numerical applications of the theory. Recent theoretical developments in the nonrelativistic approach, including medium corrections to the effective projectile-target nucleon interaction, off-shell contributions, and full integration ("full-folding") of the nucleon-nucleus optical potential are discussed in detail.The historical development of the relativistic scattering models for the nucleon-nucleus system is reviewed and each of the principal models developed during the past ten years is explained, starting with the original relativistic impulse approximation model.We show direct comparisons, some previously unpublished, between the predictions of the best available nonrelativistic and relativistic scattering models and the data. A number of specific proton-nucleus elastic scattering cases are considered, including p + O-16, Ca-40 and Pb-208 at incident proton laboratory energies of 200, 500 and 800 MeV. Both relativistic and nonrelativistic approaches provide surprisingly similar and fairly good overall descriptions of the data. Finally, possible areas of further theoretical work in this field are discussed.

Calculations are presented of the nuclear tensor term in the proton-nucleus optical model potential, generated by the relativistic impulse approximation. We first show that previously published expressions for this term make an unnecessary approximation, and second, clarify its effects in proton-nucleus elastic scattering at intermediate energies. The effects of the nuclear tensor term alone on the spin observables ${\mathit{A}}_{\mathit{y}}$ and Q for p${+}^{40}$Ca and $^{208}\mathrm{Pb}$ targets, at 650- and 800-MeV incident laboratory energy are shown. We find that the overall effect of the nuclear tensor term is in general quite small, except for the heaviest target considered.

We compute the analyzing power, ${\mathit{A}}_{\mathit{y}}$, and spin rotation, Q, for proton elastic scattering at 650 and 800 meV from target nuclei $^{16}\mathrm{O}$, $^{40}\mathrm{Ca}$, and $^{208}\mathrm{Pb}$, using both nonrelativistic multiple-scattering theory and a relativistic impulse approximation model. We show that the nonrelativistic theory, based on the Schr\"odinger equation with relativistic kinematics, and the relativistic model, based on the Dirac equation, provide very similar and equally good descriptions of these spin observables when electromagnetic spin-orbit contributions are included in both approaches. The nonrelativistic model calculations include contributions from nuclear medium effects (Pauli blocking and binding energy corrections) and also target nucleon two-body correlations. Medium effects and correlations are not expected to be significant in the relativistic model based on the Dirac equation, and were not included.

The sensitivity of intermediate energy ${\mathrm{K}}^{+}$ meson-induced elastic and inelastic differential cross section predictions to nuclear structure effects in the nuclear interior is examined for $^{40}\mathrm{Ca}$ and $^{208}\mathrm{Pb}$ targets. The observed sensitivity for ${\mathrm{K}}^{+}$ mesons is compared to that obtained with intermediate energy protons. In general, the ${\mathrm{K}}^{+}$ meson+nucleus elastic and inelastic scattering differential cross sections are an order of magnitude more sensitive to details of nucleon density distributions in the nuclear interior than corresponding proton-nucleus cross sections at comparable incident momentum. It is found that theoretical analyses of high quality ${\mathrm{K}}^{+}$ meson+nucleus data which extend to 3 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$ momentum transfer could, in principle, provide new information regarding neutron ground state and transition density distributions in the interiors of large nuclei.

Title of program:NUCLEAR SPECTRA Catalogue number: ABOM Program obtainable from: CPC Program Library, Queen’s University of Belfast, N, Ireland (see application form in this issue) Computer for which the program is designed and others upon which it is operable Computer: CDC 6600. Installation: The University of Texas Computer Center Operating system or monitor under which the program is executed:UT-2 Programming languages used: FORTRAN High speed store required: 77 777 words. No. of bits in a word: 60 Is the program overlaid?No

A comparison of the relative sensitivities of 800 MeV proton-nucleus and 444 and 991 MeV K+ meson-nucleus elastic angular distributions to realistic details of neutron density distributions is presented for nuclei 40, 48Ca. The quantitative conclusions agree with qualitative expectations that medium energy K+ mesons are potentially superior at probing the nuclear interior, while medium energy protons are superior at probing the nuclear surface region.

Angular distributions based on the distorted-wave Born approximation taking into account the effects of finite range and exchange interaction have been calculated for four (p, n) and one (n, p) knockout reaction for target nuclei with atomic mass numbers between 13 and 91, for bombarding energies from 5.3 to 20 MeV and for a wide range of bound state orbital angular momenta. Finite range is treated both exactly and approximately, using various approximations and the results are compared with each other. An admixture of Wigner, Majorana, Bartlett and Heisenberg interactions with a Yukawa potential form factor is assumed for the neutron-proton interaction. The Woods-Saxon potential is used to evaluate the bound state wave functions. Experimental comparisons have been made for the 13C(p, n)13N and 28Si(n, p) 28Al ground state reactions. Neither the zero-range approximation, nor any of the other approximations considered yield results which quantitatively are consistently reliable. Many of the cross sections exhibit a great sensitivity to exchange mixtures at certain angles, as well as to the bound state wave functions and it may be possible in future investigations to take advantage of this property to determine nuclear parameters.

The first order, spin-dependent microscopic proton-nucleus optical potential of Kerman, McManus, and Thaler is used to analyze 800 MeV polarized proton elastic differential cross section and analyzing power data for target nuclei $^{58}\mathrm{Ni}$, $^{90}\mathrm{Zr}$, $^{116,124}\mathrm{Sn}$, and $^{208}\mathrm{Pb}$. Approximately model-independent target neutron density distributions are constructed in order to investigate the uncertainty in the deduced neutron densities resulting from the statistical error and the finite range of momentum transfer in the experimental angular distributions. Numerous other experimental and theoretical sources of error and uncertainty are considered to obtain a realistic estimate of the total error in the deduced neutron densities and their root-mean-square radii. The typical error in the root-mean-square radii is found to be \ifmmode\pm\else\textpm\fi{}0.07 fm. Impressive qualitative agreement is found between the deduced neutron matter densities and the corresponding densities predicted by Hartree-Fock calculations.NUCLEAR REACTIONS Proton-nucleus scattering, $E=0.8$ GeV; targets $^{58}\mathrm{Ni}$, $^{90}\mathrm{Zr}$, $^{116,124}\mathrm{Sn}$, $^{208}\mathrm{Pb}$; analyzing power; spin-dependent Kerman, McManus, and Thaler optical potential; model-independent densities; error analysis; neutron radii.

Angular distributions for the elastic and inelastic scattering of 0.8 GeV protons from /sup 12/C, /sup 13/C, and /sup 208/Pb have been measured. Reported are data for the ground, 4.4 MeV 2/sup +/, 7.6 MeV 0/sup +/, 9.6 MeV 3/sup -/, and 14.1 MeV 4/sup +/ states of /sup 12/C; the ground, 3.1 MeV 1/2/sup +/, 3.7 MeV 3/2/sup -/, 6.9 MeV 5/2/sup +/, 7.6 MeV 5/2/sup -/, and 11.9 MeV () states of /sup 13/C; and the ground, 2.6 MeV 3/sup -/, and 3.2 MeV 5/sup -/ states of /sup 208/Pb. Analyses of the elastic angular distributions are made using the partial wave formalism and the Kerman-McManus-Thaler approach to the nucleon-nucleus optical potential; a realistic spin-orbit term is included. The inelastic transitions are analyzed within the framework of the distorted-wave Born-approximation, using transition strengths consistent with previous low-energy studies of inelastic scattering. A simple single-particle-plus-excited-core model is used for /sup 13/C. In terms of this analysis, an assignment of J/sup ..pi../ = (5/2,7/2)/sup +/ is made for the 11.9 MeV state in /sup 13/C.

Differential cross section and analyzing power data for elastic scattering of 0.8-GeV polarized protons from $^{12}\mathrm{C}$, $^{58}\mathrm{Ni}$, $^{90}\mathrm{Zr}$, and $^{208}\mathrm{Pb}$ have been analyzed in terms of the Kerman-McManus-Thaler formalism using spin-dependent nucleon-nucleon scattering amplitudes. The derived results for nuclear matter densities are in good agreement with theoretical predictions. Uncertainties in the deduced neutron distributions are discussed.NUCLEAR REACTIONS $^{12}\mathrm{C}$, $^{58}\mathrm{Ni}$, $^{90}\mathrm{Zr}$, and $^{208}\mathrm{Pb}$ ($p, p$), $E=0.8$ GeV; cross section and analyzing power; Kerman, McManus, and Thaler spin-dependent optical potential analysis; deduced neutron densities and rms radii; errors in radii given.

Angular distributions for the elastic and inelastic scattering of 0.8 GeV protons from $^{12}\mathrm{C}$, $^{13}\mathrm{C}$, and $^{208}\mathrm{Pb}$ have been measured. Reported are data for the ground, 4.4 MeV 2+, 7.6 MeV 0+, 9.6 MeV ${3}^{\ensuremath{-}}$, and 14.1 MeV 4+ states of $^{12}\mathrm{C}$; the ground, 3.1 MeV $\frac{1}{{2}^{+}}$, 3.7 MeV $\frac{3}{{2}^{\ensuremath{-}}}$, 6.9 MeV $\frac{5}{{2}^{+}}$, 7.6 MeV $\frac{5}{{2}^{\ensuremath{-}}}$, and 11.9 MeV (?) states of $^{13}\mathrm{C}$; and the ground, 2.6 MeV ${3}^{\ensuremath{-}}$, and 3.2 MeV ${5}^{\ensuremath{-}}$ states of $^{208}\mathrm{Pb}$. Analyses of the elastic angular distributions are made using the partial wave formalism and the Kerman-McManus-Thaler approach to the nucleon-nucleus optical potential; a realistic spin-orbit term is included. The inelastic transitions are analyzed within the framework of the distorted-wave Born-approximation, using transition strengths consistent with previous low-energy studies of inelastic scattering. A simple single-particle-plus-excited-core model is used for $^{13}\mathrm{C}$. In terms of this analysis, an assignment of ${J}^{\ensuremath{\pi}}={(\frac{5}{2}, \frac{7}{2})}^{+}$ is made for the 11.9 MeV state in $^{13}\mathrm{C}$.NUCLEAR REACTIONS $^{12,\phantom{\rule{0ex}{0ex}}13}\mathrm{C}$, $^{208}\mathrm{Pb}(p, {p}^{\ensuremath{'}})$, $E=0.8$ GeV; measured $\ensuremath{\sigma}(\ensuremath{\theta})$; enriched targets; resolution \ensuremath{\geqslant} 80 keV, ${\ensuremath{\theta}}_{\mathrm{c}.\mathrm{m}.}=2\ensuremath{-}40\ifmmode^\circ\else\textdegree\fi{}$, $\ensuremath{\Delta}\ensuremath{\theta}=0.2\ifmmode^\circ\else\textdegree\fi{}$. Optical potential analysis, DWBA, inelastic deformation lengths, ${\ensuremath{\beta}}_{l}R$.

The first elastic-scattering analyzing-power (A/sub y/) data at 0.8 GeV are presented and discussed. Angular distributions of A/sub y/ over the range 2/sup 0/ to 20/sup 0/ (30/sup 0/ for /sup 1/2C) have been obtained for /sup 1/2C, /sup 5/8Ni, /sup 9/0Zr, and /sup 2/08Pb using the high-resolution spectrometer at the Clinton P. Anderson Meson physics Facility. The analyzing powers osillcate sharply over positive values in qualitative agreement with expectations.

Differential cross section and analyzing power data for elastic scattering of 0.8 GeV polarized protons from 116Sn and 124Sn are analyzed in terms of a spin-dependent Kerman-McManus-Thaler formalism. Neutron matter densities and rms radii are deduced with careful attention to sources of error, and found to be in good agreement with Hartree-Fock predictions.

Distorted-wave Born-approximation calculations for medium-energy proton inelastic scattering to collective states, which use microscopic, spin-dependent optical potentials that properly describe proton elastic analyzing powers, show that inclusion of the deformation or collectivity of the spin-orbit term in the inelastic transition matrix element has an important effect on predictions for the available inelastic angular distributions and analyzing powers.