Approximate bound state solutions of Dirac equation with Hulth\'{e}n potential including Coulomb-like tensor potential

TL;DR

This paper derives approximate analytical solutions for the Dirac equation with Hulthén and Coulomb-like tensor potentials, revealing energy spectra and wavefunctions under spin and pseudospin symmetry, applicable to relativistic quantum systems.

Contribution

It provides new closed-form solutions for the Dirac equation with combined Hulthén and tensor potentials using the Nikiforov-Uvarov method, including non-relativistic limits.

Findings

Analytic energy spectra for various quantum states.

Wavefunctions for upper and lower spinors derived.

Effect of tensor coupling on energy levels analyzed.

Abstract

We solve the Dirac equation approximately for the attractive scalar $S(r)$ and repulsive vector $V(r)$ Hulth\'{e}n potentials including a Coulomb-like tensor potential with arbitrary spin-orbit coupling quantum number $\kappa .$ In the framework of the spin and pseudospin symmetric concept, we obtain the analytic energy spectrum and the corresponding two-component upper- and lower-spinors of the two Dirac particles by means of the Nikiforov-Uvarov method in closed form. The limit of zero tensor coupling and the non-relativistic solution are obtained. The energy spectrum for various levels is presented for several $\kappa $ values under the condition of exact spin symmetry in the presence or absence of tensor coupling.