Dirac equation with coupling to 1/r singular vector potentials for all angular momenta

TL;DR

This paper derives an approximate analytic solution to the Dirac equation with a 1/r singular vector potential for all angular momenta, broadening the applicability to a wider energy spectrum, exemplified by Hulthen and Eckart potentials.

Contribution

It introduces a novel approximation method for the Dirac equation with 1/r singular potentials applicable to all angular momenta, extending previous approaches.

Findings

Solution valid for a wider energy spectrum

Applicable to Hulthen and Eckart potentials

Provides approximate analytic solutions for all angular momenta

Abstract

We consider the Dirac equation in 3+1 dimensions with spherical symmetry and coupling to 1/r singular vector potential. An approximate analytic solution for all angular momenta is obtained. The approximation is made for the 1/r orbital term in the Dirac equation itself not for the traditional and more singular 1/r^2 term in the resulting second order differential equation. Consequently, the validity of the solution is for a wider energy spectrum. As examples, we consider the Hulthen and Eckart potentials.