Two approximations to the bound states of Dirac-Hulthen problem

TL;DR

This paper derives approximate solutions for the bound states of the Dirac-Hulthen problem, incorporating spin and pseudospin symmetries, and introduces improved approximation schemes for the centrifugal and orbital terms.

Contribution

It presents two novel approximation methods for solving the Dirac equation with the Hulthen potential, enhancing accuracy for all angular momenta.

Findings

Derived bound state energy spectra and wave functions.

Included spin and pseudospin symmetry considerations.

Extended solutions to wider energy spectra with improved approximations.

Abstract

The bound state (energy spectrum and two-spinor wave functions) solutions of the Dirac equation with the Hulthen potential for all angular momenta based on the spin and pseudospin symmetry are obtained. The parametric generalization of the Nikiforov-Uvarov method is used in the calculations. The orbital dependency (spin-orbit and pseudospin-orbit dependent coupling too singular 1/r^{2}) of the Dirac equation are included to the solution by introducing a more accurate approximation scheme to deal with the centrifugal (pseudo-centrifugal) term. The approximation is also made for the less singular 1/r orbital term in the Dirac equation for a wider energy spectrum. The nonrelativistic limits are also obtained on mapping of parameters.