Dirac bound state solutions of spherically ring-shaped q-deformed Woods-Saxon potential for any L-state

TL;DR

This paper derives approximate bound state solutions of the Dirac equation for a q-deformed Woods-Saxon potential with a ring-shaped component, applicable to any L-state, using the Nikiforov-Uvarov method and Jacobi polynomials.

Contribution

It introduces a new approximation for the centrifugal term and provides solutions for the ring-shaped Hulthén and standard Woods-Saxon potentials within a unified framework.

Findings

Derived energy eigenvalues and wave functions for the potential.

Expressed solutions in terms of Jacobi polynomials.

Extended solutions to ring-shaped Hulthén and Woods-Saxon potentials.

Abstract

Approximate bound state solutions of the Dirac equation with -deformed Woods-Saxon plus a new generalized ring-shaped potential are obtained for any arbitrary L-state. The energy eigenvalue equation and corresponding two-component wave function are calculated by solving the radial and angular wave equations within a shortcut of the Nikiforov-Uvarov method. The solutions of the radial and polar angular parts of the wave function are expressed in terms of the Jacobi polynomials. A new approximation being expressed in terms of the potential parameters is carried out to deal with the strong singular centrifugal potential term L(L+1)/r^2. Under some limitations, we can obtain solution for the ring-shaped Hulth\'en potential and the standard usual spherical Woods-Saxon potential (q=1).