Microscopic model analyses of the elastic scattering of 65 MeV protons from targets of diverse mass

Abstract

Nonlocal coordinate space optical potentials for the scattering of 65 MeV protons from nuclei ranging in mass from ${}^{6}\mathrm{Li}$ to ${}^{238}\mathrm{U}$ have been defined by folding a complex, medium-dependent effective interaction with the density matrix elements of each target. The effective interaction is based upon solutions of the Lippmann-Schwinger and Brueckner-Bethe-Goldstone equations having the Paris potential as input. The nuclear structure information required in our folding model is the one-body density matrix elements for the target and the single- nucleon bound state wave functions that they weight. For light mass nuclei, very large basis shell model calculations have been made to obtain the one-body density matrix elements. For medium and heavy mass nuclei, a very simple shell model prescription has been used. The bound-state single-particle wave functions that complete the nuclear density matrices are either Woods-Saxon or harmonic oscillator functions. The former are employed in most cases when large basis structure is available. For light nuclei $(Al~16)$ Woods-Saxon potential parameters and harmonic oscillator lengths are determined from fits to electron scattering form factors. For all other nuclei, we use harmonic oscillator functions with the oscillator lengths set from an ${A}^{1/6}$ mass law. Using this microscopic model, optical potentials result from which differential cross sections, analyzing powers, and spin rotations are found. In general the calculated results compare very well with data when the effective interactions are determined from a mapping of nucleon-nucleon g matrices. This is not the case when effective interactions built from a mapping of (free) t matrices are used.