Local Optical Model Potential Research Articles

A nonlocal optical model for neutron scattering from light 1p-shell nuclei

Nonlocal effects result in complications when predicting scattering observables. This is usually seen when one analyses the data for nucleon scattering off light 1p-shell nuclei using local optical model potentials. In this work we employ the nonlocal optical model of Perey and Buck (1962) [10] to study the neutron-light nucleus scattering process. By fitting the individual elastic angular distributions we determine energy-dependent, target-specific potential parameters. Then, for each nucleus, a constant set of nonlocal parameters is obtained by simultaneously fitting the corresponding elastic angular distributions. The good quality of the fits prompted us to search for a global constant set of nonlocal parameters by simultaneously fitting a large number elastic angular distribution sets for neutron scattering off light nuclei from 6Li to 18O over the energy range 9 to 35 MeV. We also show that the implicit inclusion of nonlocality in the optical model does not fully remove the need for energy-dependent potential parameters. This is achieved by expressing the nonlocal imaginary volume and surface depths of the constant global set as linear functions of energy and the asymmetry term. The effectiveness of this set is tested by applying it to additional light nuclei and energies outside the fitted range. The predicted elastic angular distributions compared well with the measured data.

Nonlocal nucleon-nucleus interactions in (d,p) reactions: Role of the deuteron D state

Theoretical models of the (d,p) reaction are exploited for both nuclear astrophysics and spectroscopic studies in nuclear physics. Usually, these reaction models use local optical model potentials to describe the nucleon- and deuteron-target interactions. Within such a framework the importance of the deuteron D-state in low-energy reactions is normally associated with spin observables and tensor polarization effects - with very minimal influence on differential cross sections. In contrast, recent work that includes the inherent nonlocality of the nucleon optical model potentials in the Johnson-Tandy adiabatic-model description of the (d,p) transition amplitude, which accounts for deuteron break-up effects, shows sensitivity of the reaction to the large n-p relative momentum content of the deuteron wave function. The dominance of the deuteron D-state component at such high momenta leads to significant sensitivity of calculated (d,p) cross sections and deduced spectroscopic factors to the choice of deuteron wave function [Phys. Rev. Lett. {\bf 117}, 162502 (2016)]. We present details of the Johnson-Tandy adiabatic model of the (d,p) transfer reaction generalized to include the deuteron D-state in the presence of nonlocal nucleon-target interactions. We present exact calculations in this model and compare these to approximate (leading-order) solutions. The latter, approximate solutions can be interpreted in terms of local optical potentials, but evaluated at a shifted value of the energy in the nucleon-target system. This energy shift is increased when including the D-state contribution. We also study the expected dependence of the D-state effects on the separation energy and orbital angular momentum of the transferred nucleon. Their influence on the spectroscopic information extracted from (d,p) reactions is quantified for a particular case of astrophysical significance.

Systematic nonlocal optical model potential for nucleons

Based on the Perey–Buck nonlocal optical model potential, F. Perey and B. Buck, Nucl. Phys. 32 (1962) 353, we obtain a new set of nonlocal optical model potential (NLOMP) parameters for proton and neutron scattering off nuclei. The experimental angular distributions of nucleon scattering off nuclei ranging from 27 Al to 208 Pb with incident energies around 10 MeV to 30 MeV are adopted in the fitting procedures. This NLOMP is energy independent. The chi-squares χ2 obtained in the fittings are comparable to those from the KD03 phenomenological local optical model potentials (OMP) A. Koning and J. Delaroche, Nucl. Phys. A 713 (2003) 231. Good agreement is found in comparisons between optical model calculations using this NLOMP and KD03 in their reproduction to the experimental angular distributions of elastic scattering cross-sections and analyzing powers.

Unified treatment of scattering and cluster structure in alpha +closed shell nuclei: 20Ne and 44Ti.

The model of an \ensuremath{\alpha} cluster orbiting a closed shell core provides a highly successful description of low lying bound and resonant states of $^{20}\mathrm{Ne}$ and has been successfully extended to $^{44}\mathrm{Ti}$ by various authors. This description is closely related to \ensuremath{\alpha} scattering from the relevant closed shell core, and although the scattering has previously been reasonably well reproduced with a local optical model potential, few attempts have been made to link the two phenomena. In this paper, a universal \ensuremath{\alpha}-core interaction is given which describes the spectra, B(E2\ensuremath{\downarrow}) transition strengths, \ensuremath{\alpha}-decay widths, and differential elastic scattering cross sections for the systems corresponding to $^{20}\mathrm{Ne}$${=}^{16}$O+\ensuremath{\alpha} and $^{44}\mathrm{Ti}$${=}^{40}$Ca+\ensuremath{\alpha}. This potential has only a single free parameter, the radius, whose value is kept fixed for each nucleus.

Surface contributions to the complex neutron-208Pb mean field between -20 and +20 MeV.

Phenomenological analyses of the experimental n${\mathrm{\ensuremath{-}}}^{208}$Pb differential, total, and polarization cross sections with local optical-model potentials indicate that the radial shape of the surface absorption depends upon energy below 10 MeV: The corresponding diffuseness decreases and the radius parameter increases with decreasing neutron energy. Because of the dispersion relation that connects the real and imaginary parts of the mean field, these features imply that the real potential contains a surface component whose radial shape also depends upon energy. This radial shape is calculated numerically for typical parametrizations of the energy dependence of the surface absorption; it turns out to be quite complicated for neutron energies between 0 and 15 MeV. In this domain, the predicted differential cross sections are sensitive to the radial shapes of both the real and imaginary surface components of the mean field even though their volume integrals are exactly the same in all the investigated models. The best agreement with the experimental data is obtained for parametrizations in which the radial shape of the surface absorption depends only weakly upon energy. It is shown that good fits to the experimental data can also be obtained in the framework of models in which the radial shape of the surface absorption is independent of energy but in which the strength of the surface absorption depends upon the orbital angular momentum of the incoming neutron. Tentative physical interpretations of these features are proposed.

Energy dependence of neutron scattering fromPb208in the energy range 7—50 MeV

Elastic neutron scattering from $^{208}\mathrm{Pb}$ has been measured at 22.0 and 24.0 MeV and remeasured at 7.0 and 20.0 MeV with greatly improved precision. The present results and other neutron data in the energy range 7---50 MeV are analyzed in terms of a conventional, local optical model potential with the aim of studying energy dependence of the potential well depths. We find that the very detailed measurements of the present work made unusual demands on the geometrical parameters of the model. Improvements, if any, resulting from extension of the optical model parametrization to include a real surface term and imaginary spin-orbit term are tested. Concurrently with the elastic scattering experiments, inelastic scattering to the ${3}^{\ensuremath{-}}$ state at 2.615 MeV was measured at 7.0, 20.0, and 22.0 MeV. A distorted-wave Born approximation analysis is made of these data to extract octupole deformation parameters.

Elastic and inelastic scattering of 100 MeV protons from the even-even titanium isotopes

The differential cross sections for elastic and inelastic scattering to the first excited (${2}^{+}$) states of 100 MeV protons from $^{46,48,50}\mathrm{Ti}$ were measured. The angular ranges covered were 9\ifmmode^\circ\else\textdegree\fi{} to 110\ifmmode^\circ\else\textdegree\fi{} for $^{46,50}\mathrm{Ti}$ and 9\ifmmode^\circ\else\textdegree\fi{} to 168\ifmmode^\circ\else\textdegree\fi{} for $^{48}\mathrm{Ti}$. The elastic scattering data were analyzed with a local optical model potential. The quality of fits to the data covering the smaller angular range ( 110\ifmmode^\circ\else\textdegree\fi{}) is good for all three isotopes, with $\frac{{\ensuremath{\chi}}^{2}}{N}\ensuremath{\sim}1.5$; whereas the fit to the large angle data of $^{48}\mathrm{Ti} (\ensuremath{\lesssim}{168}^{\ensuremath{\circ}})$ is not as satisfactory ($\frac{{\ensuremath{\chi}}^{2}}{N}\ensuremath{\sim}3.75$). Various modifications to the Woods-Saxon shape of the real central potential showed no real improvement. Nevertheless, the large angle data appear to favor a slightly sharper falloff in the real central potential near the surface, such as the Woods-Saxon-squared potential. Systematics of the phenomenological optical model potential of 100 MeV protons were studied. The derived volume integrals and rms radii seem to follow the usual $A$ dependence. The isospin dependence of the real potential was also extracted. The mean free paths computed directly from the imaginary potential strength have large uncertainties due to the insensitivity of the data to the central region of the imaginary potential. Distorted-wave Born approximation and coupled-channels Born approximation calculations for the collective excitation of the target nuclei to the first ${2}^{+}$ states provided deformation parameters, ${B}_{2}$, in agreement with those from other proton and alpha scattering data and electromagnetic measurements.

Nonlocality corrections to the mean free path of a nucleon

We discuss the relationship between recent estimates of the following three quantities: The imaginary part of the local optical-model potential, the mean free path of a nucleon, and the mean lifetime of a quasiparticle.NUCLEAR REACTIONS Mean free path of a nucleon and imaginary part of the optical-model potential.

Limits on model-independent descriptions of elastic alpha-particle scattering

Nearly unconstrained parametrizations of local optical-model potentials are used to investigate potential shapes which best reflect experimental data. The model dependence of optical-model analyses is investigated by removing as much of the parametrization bias as is practical, so that the analyses are mostly dependent on the sensitivity of the alpha-nucleus interaction and the precision of the experimental data. It is found that real- versus imaginary-potential correlations are the dominant limitation on model-independent analyses using local potentials; correlations decrease the effective sensitivity of the interaction to the interior of the real potential and are responsible for ambiguous solutions to the problem.NUCLEAR REACTIONS $\ensuremath{\alpha}$-nucleus optical potentials; model-independent parametrization. $^{50}\mathrm{Ti}(\ensuremath{\alpha}, \ensuremath{\alpha})$, ${E}_{\ensuremath{\alpha}}=140$ MeV.

The proton optical-model potential near the Coulomb barrier

Proton elastic scattering data from 197Au, 208Pb and 209Bi at energies near the Coulomb barrier are analyzed. The energy dependences of the real volume and imaginary surface-derivative potential depths V R and W SF of a local optical-model potential with fixed geometric parameters are found to be much more rapid than at higher energies. The strong energy dependence of V Rnear the Coulomb barrier is explained in terms of the non-locality of the nucleon-nucleus interaction.

Pion-nucleus total cross sections from 88 to 860 MeV

Total cross sections for π + and π − mesons on 6Li, 7Li, 9Be and C have been measured in the energy range from 90 to 860 MeV, and for oxygen from 88 to 228 MeV. The results of calculations with Kisslinger and local optical model potentials, using different sets of parameters, are compared with the data for 6Li, C and O.

Dispersion relation for the equivalent local optical-model potential

Feshbach's dispersion relation for the generalized optical potential is used to obtain, in an approximate way, a dispersion relation for the equivalent local optical-midel potential. The dispersion relation is found to be fairly applicable to the phenomenological local potential. The applicability of the Kramers-Kronig dispersion relation to the nuclear case is considered and it is found to be inappropriate.

Elastic scattering of 3He from 12C from 18 to 24 MeV

Angular distributions of 3He nuclei elastically scattered from 12C were taken at 3He beam energies of 18.6, 20.0, 22.2 and 23.9 MeV and analysed with a six-parameter local optical-model potential having either volume or surface absorption terms. It was not possible to account well for the data over the full angular range examined, but several sets of parameters which produced good predictions to the 20.0, 22.2 and 23.9 MeV data at forward angles were obtained by restricting the analyses to c.m. angles less than 85°. The real well depths of these parameter sets appeared to cluster around mean values of 75, 130 and 210 MeV. No substantial distinction seems evident in the quality of the fits between the volume and surface type analyses, but perhaps more consistent sets of real well depths were obtained in the surface case. The quality of the fits to the data appeared to improve with higher bombarding energy.

The optical model of light nuclei

A derivation of the optical model operator is presented for a nucleus of any mass number A ≥1. The special case of A = 1 is considered. The formalism is extended to include com ­ pound incident particles, and particles, such as K~ mesons, for which true absorption processes are important. An approximate evaluation is made for K +— 4He elastic scattering at a number of energies. Both real and imaginary parts of the potential are non-local. The radial dependence of each non-locality is calculated. The accuracy of the impulse approximation for K +— 4He scattering is investigated. Correlations in the 4He ground-state wave function are shown to be important in the interpretation of both the empirical local optical model potential and the charge distribution determined b y high-energy electron scattering.