Core polarization in inelastic scattering

Abstract

LBL-1951Inelastic scattering is a source of much useful information about core polarization effects in nuclei near closed shells. Although there have been many theoretical treatments of core polarization effects reported in the literature, the results of these calculations have rarely been applied to the interpretation of inelastic scattering data. In the present paper we review the microscopic models for the treatment of inelastic proton and electron scattering and the microscopic models for the treatment of core polarization.Estimates are made of core excited admixtures in the wave functions for low-1 . t t . 42c 50T. 89y 90z 207Pb and 209B 1 .• · y1.ng s a es 1.n a, 1. , , r, , The resulting wave functions are used to calculate theoretical (p,p') cross sections and (e,e') form factors for comparison with available experimental data. "Realistic" G matrix interactions are used as the starting point in both the structure and the (p,p') calculations. In the structure calculations the interaction is modified by means of a "bootstrap" prescription to account for important long-range core correlations and in the (p,p') calculations it is modified by the addition of an imaginary component. It is concluded that the overall features of the experimental data can be understood from these calculations. The concept of core polarization is quite well known in the shell model interpretation of nuclei in the vicinity of closed shells. In the shell model _, a nuclear state is described in a restricted configuration space which presumably contains the bulk of its wave function, but not all its significant components.This restricted configuration space, commonly called the model space, usuallyconsists of a few valence p,articles (holes) distributed among a small number of shell model orbitals outside (inside) an inert closed shell core. The term core polarization is generally associated with effects which are due to wave function admixtures not in the model space. The name arises because these admixtures most often will consist of core-excited configurations. Core polarization can be taken into account by defining effective operators in the model space which may be calculated by means of perturbation theory. 2These ideas first appeared in the literature about twenty years ago 'when it was first noted that there were discrepancies between the predictions of the simple shell model and the experimental values for nuclear magnetic moments, quadrupole moments, y-transition rates, etc. Two different models were proposed at this time. One is a hybrid model in which the core is treated as a liquid drop which can be set into oscillation by interaction with the extra-core nucleons. 1 The other is a completely microscopic model 2 in which the core is considered to be an assemblage of nucleons -any of which might be raised to higher, unoccupied levels as a result of the two body forces which couple them to the valence nucleons.In recent times this microscopic model has been pursued in considerably greater depth. The major impetus ...

Microscopic Effective Charges and theB(E2) Values of Terminating States in Mirror Nuclei51Mn and51Fe

“…A particle-vibration coupling model is used to give the perturbed wave functions under external probes in Eqs. 1and (2). In the RPA calculations the neutron and proton degrees of freedom are taken into account explicitly.…”

Inverse Kinematics Proton Scattering onN18eand Mirror Symmetry inARiley1, Jewell2, Cottle3 et al. 1999Phys. Rev. Lett.Self Cite15040View full textAdd to dashboardCite

“…2 [23,24], and core polarization, i.e., coupling to giant resonances [25][26][27], drives M p ͞M n toward Z͞N. However, Z͞N tends not to be achieved in single closed shell nuclei [28].…”