The relativistic J-matrix theory of scattering: an analytic solution

TL;DR

This paper develops an analytic solution for the relativistic J-matrix in Coulomb-free scattering with spin-dependent potentials, connecting it to the non-relativistic case and demonstrating relativistic effects on phase shifts.

Contribution

It introduces an analytic solution for the relativistic J-matrix in scattering problems, extending the non-relativistic framework to relativistic regimes.

Findings

Analytic recursion relation for the relativistic J-matrix derived.

Non-relativistic limit matches the traditional J-matrix.

Relativistic effects on phase shifts quantified.

Abstract

The relativistic J-matrix is investigated in the case of Coulomb-free scattering for a general short-range spin-dependent perturbing potential and in two different L2 bases. The resulting recursion relation of the reference problem, in this case, has an analytic solution. The non-relativistic limit is obtained and shown to be identical to the familiar non-relativistic J-matrix. Scattering examples are given to verify the non-relativistic limit and calculate the relativistic effects in the phase shift.