Elastic scattering of 80-180 MeV protons and the proton-nucleus optical potential

Abstract

Accurate and extensive measurements have been made of the differential cross sections for the elastic scattering of protons from $^{40}\mathrm{Ca}$, $^{90}\mathrm{Zr}$, and $^{208}\mathrm{Pb}$ targets over an energy range of 80-180 MeV, in the angular range from about 6\ifmmode^\circ\else\textdegree\fi{} to about 90\ifmmode^\circ\else\textdegree\fi{} (to 126\ifmmode^\circ\else\textdegree\fi{} for $^{90}\mathrm{Zr}$ at 135 MeV) in 0.5\ifmmode^\circ\else\textdegree\fi{} to 2.5\ifmmode^\circ\else\textdegree\fi{} steps. The most prominent general feature of the data, namely strong damping of the diffractive oscillations in the mid-angle region (roughly 30-60\ifmmode^\circ\else\textdegree\fi{}), was found to arise from the complex spin-orbit interaction which has a considerably greater influence on the differential cross section at these energies than at lower energies. These data, together with data of comparable quality from other sources in the energy range 60-180 MeV, were analyzed in terms of a 10-parameter phenomenological optical-model potential using relativistic kinematics and a relativistic extension of the Schr\odinger equation. Analyses with various parameter constraints were performed. A logarithmic energy dependence was found for the strengths of the real potentials (central and spin-orbit terms); the corresponding imaginary potentials were found to be essentially independent of energy. While individual model parameters were generally not uniquely defined by the cross section data, volume integrals of the central potentials were well determined. The spin-orbit parameterization was found to be relatively more uncertain, despite the enhanced sensitivity of the cross section to spin dependent terms in the potential at these energies and the inclusion of some existing polarization data in the analysis. Some features of the phenomenological potentials were compared with the predictions of microscopic potential models, and certain aspects of the proton-nucleus interaction at the higher energies have been found to be describable in terms of the free nucleon-nucleon interaction.