Approximate relativistic solutions for a new ring-shaped Hulth\'en potential

TL;DR

This paper derives approximate relativistic bound state solutions for a Dirac equation with a new ring-shaped Hulthén potential using an advanced method, providing explicit wave functions and energy levels.

Contribution

It introduces a novel approach to solving the Dirac equation with a generalized ring-shaped Hulthén potential using the Nikiforov-Uvarov method, including an exponential approximation for the centrifugal term.

Findings

Explicit energy eigenvalues derived for the potential.

Wave functions expressed in terms of Jacobi polynomials.

Reduction to Schrödinger solutions in a limiting case.

Abstract

Approximate bound state solutions of the Dirac equation with the Hulth\'en plus a new generalized ring-shaped (RS) potential are obtained for any arbitrary -state. The energy eigenvalue equation and the corresponding two-component wave function are calculated by solving the radial and angular wave equations within a recently introduced shortcut of Nikiforov-Uvarov (NU) method. The solutions of the radial and polar angular parts of the wave function are given in terms of the Jacobi polynomials. We use an exponential approximation in terms of the Hulthen potential parameters to deal with the strong singular centrifugal potential term Under the limiting case, the solution can be easily reduced to the solution of the Schrodinger equation with a new ring-shaped Hulth\'en potential.