Nonlocal potentials and inadequacies of the Jost function in the description of nuclear phenomena

Abstract

This paper considers the conceptual problem of describing the physics of a many body system in terms of a two body $S$ matrix. Projection of the many body problem onto a two body channel results in a potential which is nonlocal. We demonstrate that for a nonlocal potential the analytic structure of the Jost function differs from that associated with a local potential. Moreover, the Jost function, and thus the $S$ matrix, is shown to be an incomplete description of the information in the two body channel. This is accomplished by considering Fredholm determinants associated with scattering integral equations.NUCLEAR REACTIONS Scattering by a nonlocal potential, Jost functions, $S$ matrices, and Fredholm determinants and their analytic character in the complex plane.