Scattering phase shift for relativistic exponential-type separable potentials

TL;DR

This paper derives analytic expressions for the relativistic scattering phase shifts of exponential-type separable potentials using the J-matrix method, connecting relativistic and nonrelativistic results and providing a way for numerical evaluation.

Contribution

It introduces a method to analytically compute phase shifts for specific relativistic exponential potentials and explores their nonrelativistic limits.

Findings

Analytic phase shift expressions for potentials with n=0,1,2

Nonrelativistic limit matches known phase shifts

Numerical evaluation method for higher order potentials (n>2)

Abstract

The J-matrix method of scattering is used to obtain analytic expressions for the phase shift of two classes of relativistic exponential-type separable potentials whose radial component is either of the general form r^(n-1)exp(-r) or r^(2n)exp(-r^2), where n = 0, 1, or 2. The rank of these separable potentials is n + 1. The nonrelativistic limit is obtained and shown to be identical to the nonrelativistic phase shift. An exact numerical evaluation for higher order potentials (n > 2) can also be obtained in a simple way as illustrated for the case n = 3.