Empirical effective interaction for 135 MeV nucleons

A model for medium modifications to the two-nucleon effective interaction, based upon the results of nuclear matter theory, is proposed for the analysis of proton inelastic scattering to normal-parity isoscalar states of self-conjugate nuclei. An empirical effective interaction is fitted to cross section and analyzing power data for the excitation by 135 MeV protons of six states of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ simultaneously. Transition densities determined by electron scattering minimize uncertainties due to nuclear structure. Distorted waves are generated from the self-consistent optical potential computed from the same effective interaction, corrected for rearrangement effects. We find that a unique effective interaction provides a good global fit to all inelastic scattering data and is consistent with data for elastic scattering, which were not included in the fit. The density dependence of the empirical interaction is similar to, but somewhat smaller than, that of the Paris-Hamburg G matrix. However, we also find that the interaction strength is reduced at zero density. These comparisons suggest effects due to nonlocal density dependence beyond the local density approximation.