Approximate analytical solutions of the generalized Woods-Saxon potentials including the spin-orbit coupling term and spin symmetry

TL;DR

This paper derives approximate analytical solutions for the Dirac equation with the generalized Woods-Saxon potential, including spin-orbit coupling, using the Nikiforov-Uvarov method, and explores special cases and non-relativistic limits.

Contribution

It provides new closed-form solutions for the Dirac equation with the generalized Woods-Saxon potential considering spin and pseudospin symmetry.

Findings

Analytical bound state energy eigenvalues obtained

Solutions reduce to special cases like s-wave and non-relativistic limit

Comparison with previous non-relativistic results confirms validity

Abstract

We study the approximate analytical solutions of the Dirac equation for the generalized Woods-Saxon potential with the pseudo-centrifugal term. In the framework of the spin and pseudospin symmetry concept, the approximately analytical bound state energy eigenvalues and the corresponding upper- and lower-spinor components of the two Dirac particles are obtained, in closed form, by means of the Nikiforov-Uvarov method which is based on solving the second-order linear differential equation by reducing it to a generalized equation of hypergeometric type. The special cases $\kappa =\pm 1$ ($l=% \widetilde{l}=0,$ s-wave) and the non-relativistic limit can be reached easily and directly for the generalized and standard Woods-Saxon potentials. Also, the non-relativistic results are compared with the other works.