Approximate Analytical Solutions of the Pseudospin Symmetric Dirac Equation for Exponential-type Potentials

TL;DR

This paper derives approximate analytical solutions for the Dirac equation with exponential-type potentials under pseudospin symmetry, using the Nikiforov-Uvarov method, applicable to Morse, Hulthen, and q-deformed Rosen-Morse potentials.

Contribution

It introduces a parametric generalization of the Nikiforov-Uvarov method to solve the Dirac equation with exponential potentials under pseudospin symmetry, providing solutions for any spin-orbit quantum number.

Findings

Derived energy eigenvalues for Morse, Hulthen, and q-deformed Rosen-Morse potentials.

Obtained Dirac spinors for these potentials within an approximation to the spin-orbit coupling.

Solutions applicable for all values of the spin-orbit quantum number .

Abstract

The solvability of The Dirac equation is studied for the exponential-type potentials with the pseudospin symmetry by using the parametric generalization of the Nikiforov-Uvarov method. The energy eigenvalue equation, and the corresponding Dirac spinors for Morse, Hulthen, and q-deformed Rosen-Morse potentials are obtained within the framework of an approximation to the spin-orbit coupling term, so the solutions are given for any value of the spin-orbit quantum number $\kappa=0$, or $\kappa \neq 0$.