An approximate {\kappa} state solutions of the Dirac equation for the generalized Morse potential under spin and pseudospin symmetry

TL;DR

This paper derives approximate analytical solutions for the Dirac equation with a generalized Morse potential under spin and pseudospin symmetry, employing an improved approximation scheme and the Nikiforov-Uvarov method, covering special cases and limits.

Contribution

It introduces an improved approximation scheme to solve the Dirac equation with the generalized Morse potential for arbitrary spin-orbit quantum number, providing analytic bound state energies and wavefunctions.

Findings

Derived explicit energy eigenvalues and wavefunctions for the Dirac equation with generalized Morse potential.

Analyzed special cases including l=0 and non-relativistic limits.

Compared results with other existing methods for validation.

Abstract

By using an improved approximation scheme to deal with the centrifugal (pseudo-centrifugal) term, we solve the Dirac equation for the generalized Morse potential with arbitrary spin-orbit quantum number {\kappa}. In the presence of spin and pseudospin symmetry, the analytic bound state energy eigenvalues and the associated upper- and lower-spinor components of two Dirac particles are found by using the basic concepts of the Nikiforov-Uvarov method. We study the special cases when {\kappa}=\pm1 (l=l=0, s-wave), the non-relativistic limit and the limit when {\alpha} becomes zero (Kratzer potential model). The present solutions are compared with those obtained by other methods. Keywords: Dirac equation, spin symmetry, pseudospin symmetry, generalized Morse potential,