An energy-independent nonlocal potential model for bound and scattering states

Abstract

The general expression of the nucleon-nucleus optical potential has been obtained using Watson's multiple scattering theory and Wolfenstein's parametrization of the nucleon-nucleon scattering amplitude. The resulting theoretical potential is nonlocal and consists of an energy-independent central volume plus surface real and imaginary potential and of a Thomas-like spin-orbit term. The analysis has been restricted to N = Z spherical nuclei, so that neither isospin-isospin nor spin-spin interactions have been included. The widely used Perey-Buck, Greenlees, and Watson expressions of the optical potential are easily obtained as particular cases. For practical purposes, the nonlocal potential has been parametrized in the Frahn-Lemmer form, using Woods-Saxon radial form factors, and the equivalent local potential (ELP) has been calculated by a Perey-Buck-like transformation. The ELP has a radial behavior very similar to the original nonlocal one, but the potential depths and radii are energy dependent. The six free parameters in the ELP have been adjusted to fit the available experimental data in the −70 to + 150 MeV range of interest in nuclear reactions, namely, energies of single hole and single particle states, charge distributions, proton elastic scattering cross sections, and polarizations. The fitted potential depths show an energy dependence in remarkable agreement with the model predictions with a central nonlocality range β ≅ 1 F and a spin-orbit nonlocality range β 3 ≅ 0.8 F. The relative importance of surface and volume dependence in the real central potential in also discussed.