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Differential cross sections and analyzing powers have been measured for elastic and inelastic scattering of 800-MeV protons by /sup 16/O. Microscopic analyses utilizing the impulse approximation are used to study the ground-state neutron distribution of /sup 16/O, and to demonstrate the importance of the spin-orbit amplitudes for the inelastic transitions.

Elastic differential cross sections and analyzing powers for 800 MeV p+ /sup 48/Ca and /sup 54/Fe are analyzed to obtain the isotonic proton density difference. The calculations employ a local, spin-dependent, second order Kerman, McManus, and Thaler optical potential model; care is given to isovector, spin-unsaturated subshell, and phenomenological nuclear medium corrections. The results obtained here are compared with those from electron scattering experiments and theoretical expectations. The results of this analysis provide an overall consistency check on corresponding studies which start with known charge densities and determine neutron isotopic density differences.

Recent studies have demonstrated the enhanced sensitivity of K mesons to interior nuclear matter distributions compared to that of protons at similar momenta. An approximately model-independent error analysis technique, similar to that used in analyses of electron scattering data, has been applied to K -nucleus elastic scattering at 442 and 991 MeV. The primary result of this work is that the momentum transfer range and statistical quality of data necessary to provide meaningful new constraints on the distribution of nuclear matter in the interior of large nuclei is specified. The model dependence of this approach for hadron-nucleus scattering is considered and shown to be negligible.

A variety of nuclear structure and proton-nucleus dynamical effects are shown to significantly influence the behavior of the large angle 800 MeV p+ /sup 208/Pb elastic angular distribution. While coupled channels effects are found to be important, they are significantly smaller than recently suggested.

Neutron resonances in $sup 24$Na from E/subr/ = 0 to 1 MeV are studied with the $sup 23$Na(d, p)$sup 24$Na reaction at E/subd/ = 11.0 MeV using a biased quadrupole spectrometer. Fractionated single-particle states are identified via their forward angle cross sections, using distorted wave Born-approximation predictions with resonance state form factors for the residual $sup 24$Na system. Spectroscopic results are compared with those from (n, n) and/or (n, $gamma$) studies over the same region of excitation. (AIP)

A total of 21 states of $^{33}\mathrm{S}$ in the region of excitation from about 8.6 to 9.5 MeV have been studied using the reaction $^{32}\mathrm{S}(d, p)$ at 12 MeV incident deuteron energy and a biased quadrupole spectrometer. Fractionated single-particle states are identified via their forward-angle cross sections, using distorted-wave Born-approximation predictions with resonance state form factors for the residual $^{33}\mathrm{S}$ system. Results are compared with those from ($n, n$) and/or ($n, \ensuremath{\gamma}$) studies over the same region of excitation, where this is possible. It is shown that states strongly populated in ($n, n$) do not often show up in ($d, p$) spectra and vice versa.

Using a liquid deuterium target, 800 MeV quasielastic $\stackrel{\ensuremath{\rightarrow}}{p}+n$ and $\stackrel{\ensuremath{\rightarrow}}{p}+p$ analyzing powers were measured over the center-of-momentum angular range 14\ifmmode^\circ\else\textdegree\fi{}-75\ifmmode^\circ\else\textdegree\fi{}. Elastic $\stackrel{\ensuremath{\rightarrow}}{p}+p$ analyzing powers were measured over the center-of-momentum angular range 10\ifmmode^\circ\else\textdegree\fi{}-47\ifmmode^\circ\else\textdegree\fi{} using a liquid hydrogen target, and elastic $p+p$ differential cross sections were obtained over the angular range 6\ifmmode^\circ\else\textdegree\fi{}-90\ifmmode^\circ\else\textdegree\fi{} using CH and C${\mathrm{H}}_{2}$ targets. The quasielastic $\stackrel{\ensuremath{\rightarrow}}{p}+p$ data are in good agreement with existing elastic $\stackrel{\ensuremath{\rightarrow}}{p}+p$ data, suggesting that the effects of final state interactions and Fermi motion averaging are small at this energy for the range of momentum transfer covered by these data. Results of phase shift analyses are reported, and the amplitudes important to microscopic analysis of 800 MeV $\stackrel{\ensuremath{\rightarrow}}{p}$+nucleus elastic differential cross section and analyzing power data are discussed. Use of these amplitudes to generate the microscopic Kerman-McManus-Thaler optical potential for 800 MeV $\stackrel{\ensuremath{\rightarrow}}{p}$+$^{40}\mathrm{Ca}$ elastic scattering does not resolve the problems encountered previously concerning nuclear size information and poor fits to the analyzing power data.NUCLEAR REACTIONS $^{2}\mathrm{H}(\stackrel{\ensuremath{\rightarrow}}{p}, pn)p$, $^{2}\mathrm{H}(\stackrel{\ensuremath{\rightarrow}}{p}, pp)n$, $^{1}\mathrm{H}(\stackrel{\ensuremath{\rightarrow}}{p}, p)$, $^{1}\mathrm{H}(p, p)$; ${E}_{p,\mathrm{inc}}=800$ MeV; measured $p+p$ elastic $\frac{d\ensuremath{\sigma}}{d\ensuremath{\Omega}}$ for $6\ifmmode^\circ\else\textdegree\fi{}\ensuremath{\le}{\ensuremath{\theta}}_{\mathrm{c}.\mathrm{m}.}\ensuremath{\le}90\ifmmode^\circ\else\textdegree\fi{}$; measured $\stackrel{\ensuremath{\rightarrow}}{p}+p$ elastic ${A}_{y}(\ensuremath{\theta})$ for $10\ifmmode^\circ\else\textdegree\fi{}\ensuremath{\le}{\ensuremath{\theta}}_{\mathrm{c}.\mathrm{m}}\ensuremath{\le}47\ifmmode^\circ\else\textdegree\fi{}$; measured $\stackrel{\ensuremath{\rightarrow}}{p}+p$ and $\stackrel{\ensuremath{\rightarrow}}{p}+n$ quasielastic ${A}_{y}(\ensuremath{\theta})$ for $14\ifmmode^\circ\else\textdegree\fi{}\ensuremath{\le}{\ensuremath{\theta}}_{\mathrm{c}.\mathrm{m}.}\ensuremath{\le}75\ifmmode^\circ\else\textdegree\fi{}$; CH, C${\mathrm{H}}_{2}$, liquid hydrogen and liquid deuterium targets; two arm coincidence for quasielastic; phase shift analyses; microscopic (KMT) optical model calculations for 800 MeV $\stackrel{\ensuremath{\rightarrow}}{p}$+$^{40}\mathrm{Ca}$.

The spin-rotation parameter Q(theta) was measured for 800 MeV p\ensuremath{\rightarrow}${+}^{16}$O, $^{40}\mathrm{Ca}$, and $^{208}\mathrm{Pb}$ elastic scattering for 2\ifmmode^\circ\else\textdegree\fi{}\ensuremath{\le}${\mathrm{theta}}_{\mathrm{lab}\mathrm{\ensuremath{\le}}21\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$. Microscopic ``relativistic'' (Dirac equation dynamics) and ``nonrelativistic'' (Schr\"odinger equation dynamics) optical model predictions are compared with the data. Slight preference for the relativistic impulse approximation approach is observed, but a marked mass dependence of the quality of the fit is evident. Other calculations are presented which suggest that inclusion of nuclear two-body correlation effects in the relativistic impulse approximation model might lead to better agreement with experiment.

We present results of calculations which suggest that several of the spin observables for elastic scattering of 500-MeV polarized protons from a polarized /sup 13/C target are sensitive to relativistic aspects of nuclear structure.

Elastic and inelastic angular distributions for 0.8 GeV $p$ + $^{154}\mathrm{Sm}$ and $^{176}\mathrm{Yb}$ are reported and analyzed using the distorted-wave Born approximation and the coupled-channels formalism where phenomenological deformed optical potentials are used in the latter analysis. As expected, the multipole moments extracted from the optical potentials are found to be in excellent agreement with those of the charge densities as obtained from electron scattering and Coulomb excitation experiments. The analysis also clearly demonstrates that multistep processes are important at 0.8 GeV and must be included for a proper description of the experimental data.

Intermediate energy (300\char21{}1000 MeV) proton-nucleus elastic observables, obtained using the relativistic and nonrelativistic impulse approximations, are compared to each other and with p${+\mathrm{}}^{40}$Ca, $^{48}\mathrm{Ca}$, and $^{208}\mathrm{Pb}$ data. Systematic, energy dependent differences between the model predictions and the data are observed and discussed. The underlying target densities are then adjusted in each model to obtain best fits to the differential cross section and analyzing power data at each energy. The variations in the resulting effective target density parameters show the deficiencies, with respect to the energy dependence, of the relativistic and nonrelativistic impulse approximations. Improvements which may eliminate some of the energy dependence are discussed.

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.

New and/or corrected 800 MeV $p+^{40,42,44,48}\mathrm{Ca}$ elastic angular distributions are presented. The data, together with analyzing power measurements, are analyzed to investigate the isotopic neutron and matter density differences between these four calcium isotopes. The analysis employs a local, spin-dependent form of the second order Kerman, McManus, and Thaler optical potential in which approximately model-independent forms for the neutron densities are assumed. Nucleon-nucleon amplitude uncertainties which occur at 800 MeV are taken into account in determining the empirical isotopic density differences. The deduced neutron and matter density differences are compared to the results of other intermediate energy proton and alpha particle scattering analyses and to Hartree-Fock predictions. The various empirical results are generally in good agreement with each other and with the Hartree-Fock predictions, except for $^{48}\mathrm{Ca}$ where the results obtained here and elsewhere suggest that the $^{48}\mathrm{Ca}$ neutron excess is not distributed at quite as large a radius as predicted by Hartree-Fock theory.NUCLEAR REACTIONS Proton elastic scattering cross sections; targets, $^{40,42,44,48}\mathrm{Ca}$; ${E}_{\mathrm{lab}}=800$ MeV; second order Kerman, McManus, and Thaler optical potential; neutron and matter isotopic density differences.

Deformed spin-orbit, coupled-channels effects are investigated for 800 MeV proton inelastic scattering from 24 Mg and 154 Sm. The influence of the spin-orbit potential on the inelastic angular distributions and on the deduced multipole moments of the optical potential is shown to be small. The predicted 4 + and 6 + inelastic analyzing powers are, however, significantly affected by deformed spin-orbit coupling, multistep processes, and the large intrinsic quadrupole deformation of these two nuclei.

New, large-momentum-transfer 0.8 GeV p+/sup 208/Pb elastic analyzing power data are presented and compared to optical model predictions using the Kerman-McManus-Thaler microscopic optical potential. This comparison provides an important test of multiple scattering theories since the predictions are quite sensitive to the assumed nucleon-nucleon scattering amplitudes and are not sensitive to the details of the nuclear densities. We show that improvement in the agreement between experiment and a parameter-free theoretical prediction is obtained when the calculation includes the electromagnetic spin-orbit potential which arises from the coupling of the projectile proton's magnetic moment and the Coulomb field of the target nucleus. The sensitivity of the predicted analyzing power to the various ingredients of the theory is also investigated, and the importance of the inclusion of target-nucleon correlations (in the second-order Kerman-McManus-Thaler potential) for proper explanation of the data is discussed.

Experimental elastic and inelastic angular distributions for 0.8 GeV $p+^{12}\mathrm{C}$ are reported for momentum transfers up to $q=7.1$ ${\mathrm{fm}}^{\ensuremath{-}1}$. At the largest angle the elastic cross section is \ensuremath{\sim}2.0\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}8}$ mb/sr. The data are analyzed using the distorted-wave Born approximation and the coupled-channels formalism, where phenomenologically deformed optical potentials are used in the latter analysis. The multipole moments extracted from the optical potentials are found to be in fair agreement with those of the charge densities as obtained from electron scattering.NUCLEAR REACTIONS $^{12}\mathrm{C}(p,{p}^{\ensuremath{'}})$, $E=0.8$ GeV; measured $\ensuremath{\sigma}(\ensuremath{\theta})$; natural targets; resolution 100 to 650 keV, ${\ensuremath{\theta}}_{\mathrm{c}.\mathrm{m}.}=3.9\ifmmode^\circ\else\textdegree\fi{}\ensuremath{-}67.2\ifmmode^\circ\else\textdegree\fi{}$, ${q}_{max}=7.1$ ${\mathrm{fm}}^{\ensuremath{-}1}$. Optical model potential, DWBA and coupled channels analyses, rotational model, coupling parameters, multipole moments, inelastic deformation lengths ${\ensuremath{\beta}}_{l}R$.

The first calculations of p-bar-nucleus elastic scattering using the relativistic impulse approximation are presented and compared with the recent 46.8-MeV p-bar-/sup 12/C elastic scattering data. The calculated cross sections agree well with the data. The differences between relativistic and nonrelativistic impulse approximation calculations using the same input are small.

A nonrelativistic distorted wave Born approximation analysis, using a phenomenological effective proton-nucleon interaction to generate both optical and transition potentials, is made of new 500 MeV (p-arrow-right,p') data for excitation of low-lying states in /sup 40/Ca, /sup 48/Ca, /sup 90/Zr, and /sup 208/Pb. The data, differential cross section and analyzing power angular distributions for 5/sup 0/ less than or equal to theta/sub c.m./ less than or equal to 30/sup 0/, are well described using this effective interaction. Calculations using the impulse approximation to generate the optical and transition potentials do not adequately describe the data. As a further test of the 500 MeV empirical effective interaction, model-dependent neutron transition densities are deduced for excitations which are expected to be purely isoscalar, such as the first 3/sup -/ states of /sup 40/Ca and /sup 208/Pb. These are found to be qualitatively similar in strength and overall shape to the renormalized (x N/Z) model-independent proton densities determined from analysis of (e,e') data. Model-dependent neutron transition densities are also deduced for other excitations and are in reasonable agreement with results of analyses of other hadron plus nucleus scattering data. These results indicate that the 500 MeV isoscalar effective interaction is better than themore » free proton-nucleon scattering amplitudes (impulse approximation) as a starting point for analysis of (p,p') data aimed at detailed extraction of neutron transition densities and other nuclear structure information.« less

Inclusive quasielastic {ital {rvec p}}+{sup 2}H analyzing-power and spin-rotation depolarization ({ital D}{sub {ital ij}}) data are reported for the nucleon-nucleon center-of-momentum angular ranges 46.9{degree}--118.0{degree} and 58.3{degree}--110.0{degree} at 647 and 800 MeV, respectively. Exclusive quasielastic {ital {rvec p}p} and {ital {rvec p}n} analyzing-power data and exclusive {ital {rvec p}p} {ital D}{sub {ital ij}} data are also presented. A simple isospin weighting model successfully describes the inclusive data and is used to estimate the free {ital {rvec p}n} {ital D}{sub {ital ij}} values. The new data are compared with those of previous experiments and with predictions of phase-shift analyses. The deduced {ital {rvec p}n} {ital D}{sub {ital ij}} values extend the angular range of previous 800 MeV data and provide entirely new information at 647 MeV.

Elastic and inelastic $p+^{40}\mathrm{Ca}$ observables are calculated using a relativistic impulse approximation model for the diagonal optical potential and a simple collective ansatz for the transition potentials. The calculations were performed using Dirac coupled channel codes. Agreement with large angle elastic-scattering data is greatly improved by the inclusion of strongly coupled, lowlying collective states.

The first application of the Kemmer-Duffin-Petiau wave equation for spin-0 particles to meson-nucleus scattering is given. A relativistic impulse approximation using the Kemmer-Duffin-Petiau formalism is used to calculate meson-nucleus optical potentials. Comparison with the nonrelativistic impulse approximation is given.

Scattering models with either relativistic or nonrelativistic dynamics are used to predict elastic scattering observables in the forward angle, Coulomb-nuclear interference region for 500 and 800 MeV ${\mathrm{p}+}^{16}$O, $^{40}\mathrm{Ca}$, and $^{208}\mathrm{Pb}$. At 500 MeV the differential cross sections for the relativistic model are 15--25 % larger than those of the nonrelativistic model. Ambiguities in the theoretical predictions which arise from empirical input used by the models and from approximations made in numerically evaluating higher order corrections are estimated and found to contribute \ifmmode\pm\else\textpm\fi{}2%--\ifmmode\pm\else\textpm\fi{}6% to the uncertainty of the differential cross sections in the forward angle region at 500 MeV for ${\mathrm{p}+}^{40}$Ca and $^{208}\mathrm{Pb}$. The sensitivity of the relativistic model cross sections to the use of a variety of relativistic nuclear structure models and different prescriptions for the virtual NN\ifmmode\bar\else\textasciimacron\fi{} pair process for the projectile is investigated and found to be largest at 500 MeV.

The sensitivity of intermediate energy K/sup +/ meson-induced elastic and inelastic differential cross section predictions to nuclear structure effects in the nuclear interior is examined for /sup 40/Ca and /sup 208/Pb targets. The observed sensitivity for K/sup +/ mesons is compared to that obtained with intermediate energy protons. In general, the K/sup +/ 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 K/sup +/ meson+nucleus data which extend to 3 fm/sup -1/ momentum transfer could, in principle, provide new information regarding neutron ground state and transition density distributions in the interiors of large nuclei.

Target nucleon correlation contributions to intermediate energy proton-nucleus elastic scattering observables are explored within the context of a semirelativistic multiple scattering model. A general, nonlocal expression for this second-order relativistic optical potential model is derived and discussed. Use is made of the local, projectile-target nucleon interaction given by the relativistic impulse approximation together with a shell model target nucleus wave function represented in a suitable, four-component form. For this initial investigation a simplified model is then assumed in which only the scalar and time-like vector components of the projectile-nucleon interaction are retained and in which the lower components of the target wave function are omitted. Intermediate propagation of positive and negative energy projectile states are included, as are important nonlocalities arising from the Dirac propagator for the projectile. Numerical estimates are provided for several cases of interest. Individual terms in the correlation contribution to the optical potential are fairly large; significant cancellations occur, however, resulting in relatively small changes in the calculated proton-nucleus elastic scattering observables. The differential cross section predictions are increased in magnitude at forward angles, although to a lesser degree than in nonrelativistic models of correlation effects. Analyzing powers and spin rotation functions, which are generally described quite well by the first-order relativistic impulse approximation model, are not significantly affected by these corrections, except at large scattering angles. These results indicate that the semirelativistic impulse approximation model considered here is stable with respect to higher-order multiple scattering contributions, at least to the level of two-body target nucleon correlations. The erroneous target mass dependence of the first-order relativistic impulse approximation model is not corrected by these effects, however.

Using a liquid deuterium target, 800 MeV quasielastic parrow+p and parrow+n spin-rotation and -depolarization parameters (D/sub S/S,D/sub S/L,D/sub L/S,D/sub L/L,D/sub N/N ) were determined over the center-of-momentum angular range 14.3/sup 0/--69.2/sup 0/. The parrow+p results are in good agreement with existing elastic results and predictions from phase shift analysis. The parrow+n results, in general, are not in agreement with predictions from phase shift solutions. Small corrections to previously reported parrow+p elastic observables are also discussed.

We present a description of the spin-one Kemmer-Duffin-Petiau equations. An effective second-order equation is obtained for various types of interactions. An argument is given for the use of one particular form of interaction for deuteron-nucleus scattering. This provides the basis for a generalization of the standard Watanabe model in which Dirac scalar and vector nucleon-nucleus potentials are used as input. Parameter-free calculations are performed using both phenomenological and microscopic nucleon-nucleus potentials, and results are compared with deuteron-nucleus elastic scattering data at 400 and 700 MeV. Qualitative agreement is generally obtained. A good description of the forward-angle vector analyzing power data is achieved.

500 MeV p\ensuremath{\rightarrow}+p elastic and quasielastic, and p\ensuremath{\rightarrow}+n quasielastic, analyzing powers (${A}_{y}$) and spin-rotation-depolarization parameters (${D}_{\mathrm{SS}}$, ${D}_{\mathrm{SL}}$, ${D}_{\mathrm{LS}}$, ${D}_{\mathrm{LL}}$, ${D}_{\mathrm{NN}}$) were determined for center-of-momentum angular ranges 6.8\ifmmode^\circ\else\textdegree\fi{}\char21{}55.4\ifmmode^\circ\else\textdegree\fi{} (elastic) and 22.4\ifmmode^\circ\else\textdegree\fi{}\char21{}55.4\ifmmode^\circ\else\textdegree\fi{} (quasielastic); liquid hydrogen and deuterium targets were used. The p\ensuremath{\rightarrow}+p elastic and quasielastic results are in good agreement; both the p\ensuremath{\rightarrow}+p and p\ensuremath{\rightarrow}+n parameters are well described by current phase shift solutions.

We present a description of the spin-1 Kemmer-Duffin-Petiau equations and make an application to deuteron-nucleus scattering. Comparison with d${+}^{58}$Ni elastic scattering data at 400 MeV shows that the Kemmer-Duffin-Petiau model reproduces experimental spin observables quite well.

The differential cross sections and analyzing power are calculated for p+/sup 40/Ca and p+/sup 208/Pb elastic scattering with a tensor term included in the relativistic impulse approximation optical potential.(AIP)