# Bound State Solutions of the Dirac-Shifted Tietz-Wei Potential Plus a Generalized Ring-Shaped Potential with Spin and Pseudospin symmetry

## TL;DR

This paper derives approximate bound state solutions of the Dirac equation with a new shifted Tietz-Wei potential combined with a generalized ring-shaped potential, employing Nikiforov methods and Pekeris approximation for spin and pseudospin symmetries.

## Contribution

It introduces a novel approach to solving the Dirac equation with the shifted Tietz-Wei potential and generalized ring-shaped potential using advanced analytical methods.

## Key findings

- Eigenenergy equations derived for arbitrary quantum numbers.
- Wave functions expressed in terms of Jacobi polynomials.
- Solutions applicable to spin and pseudospin symmetric cases.

## Abstract

In this study, approximate bound state solutions of the Dirac equation with the newly proposed shifted Tietz-Wei (sTW) potential were obtained for any arbitrary quantum number. Using Generalized Parametric Nikiforov Methods, the eigenenergy equations as well as the upper and lower spinors of the wave function corresponding to spin and pseudospin symmetric solutions were obtained by solving the radial equation. The Pekeris approximation scheme in terms of the parameters of the shifted Tietz-Wei potential was used to deal with the spin-orbit coupling potential term k(k+1)/r^2. The solutions obtained for the radial and polar angular parts of the wave functions were written in terms of the well-known Jacobi polynomial.

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Source: https://tomesphere.com/paper/1903.10277