Empirical density-dependent effective interaction for nucleon-nucleus scattering at 500 MeV

We report new cross-section and analyzing-power data for the excitation by 498-MeV protons of all narrow normal-parity states of ¹⁶O below 12.1-MeV excitation. In addition, spin-rotation measurements for elastic scattering and depolarization measurements for the 1₁^-, 2₁⁺, and 3₁^- states of ¹⁶O have been performed. These data are used in conjunction with existing data for ⁴⁰Ca to study medium corrections to the effective interaction for nucleon-nucleus scattering at 500 MeV. Systematic differences between the data and nonrelativistic impulse approximation calculations based upon either the free t matrix or a recent density-dependent effective interaction are interpreted within the framework of the local-density approximation. An empirical effective interaction has been constructed which parametrizes the density dependence of the medium modifications in a simple form amenable to phenomenological analysis of data.

The parameters of the interaction are adjusted by fitting to data from many transitions simultaneously, including inelastic transitions sensitive to both the surface and the interior of the nucleus. We find that the empirical effective interaction provides a good description of both the fitted inelastic-scattering observables and elastic-scattering observables not included in the fit. Furthermore, we find that the empirical effective interaction fitted to inelastic-scattering data for ¹⁶O provides an excellent description of both elastic- and inelastic-scattering data for ⁴⁰Ca at 500 MeV. The most significant difference between the empirical interaction and the theoretical interaction is that absorption is enhanced at higher density, contrary to expectations based upon Pauli blocking. We find also that the empirical interaction has a stronger repulsive core than expected in nonrelativistic models of the effective interaction. Nevertheless, the optical potentials are very similar to the Schrödinger-equivalent potentials from a relativistic impulse approximation model, showing that the empirical density dependence is comparable to the equivalent density dependence due to elimination of lower components from this relativistic model of the nucleon-nucleus interaction. These results are also compared with global optical potentials from Dirac phenomenology, which suggest even stronger repulsion in the real central interaction.