Inverse Scattering Problem for Separable Potentials

Abstract

A method for constructing a separable potential directly from the two-nucleon phase shifts is presented. The solution of the inverse scattering problem is extended to include both a long-range attraction and the important strong, short-range repulsion. The occurrence of both an attraction and a strong repulsion in a single separable potential is shown to require that the phase shifts satisfy a modified Levinson theorem. Construction of a noncentral separable interaction directly from known eigenphase shifts and coupling parameters is also discussed. Using the construction procedure described in this paper, the task of repeated phase-shift fitting is avoided, and one can more easily test the sensitivity of nuclear structure calculations to various aspects of the two-nucleon interaction.