Analytical bound state solutions of the Dirac equation with the Hulth\'en plus a class of Yukawa potential including a Coulomb-like tensor interaction

TL;DR

This paper analytically solves the Dirac equation with a combined Hulthén and Yukawa potential including tensor interaction, revealing how tensor coupling affects energy spectra and degeneracies in relativistic quantum systems.

Contribution

It introduces an improved analytical approach to solve the Dirac equation with complex potentials, incorporating tensor interactions, and compares two methods for consistency.

Findings

Energy spectra depend on quantum numbers and potential parameters.

Tensor interaction removes degeneracies between spin and pseudospin states.

Results are consistent with previous studies and applicable to various physical systems.

Abstract

We examine the bound state solutions of the Dirac equation under the spin and pseudospin symmetries for a new suggested combined potential, Hulten plus a class of Yukawa potential including a Coulomb-like tensor interaction. An improved scheme is employed to deal with the centrifugal (pseudo-centrifugal) term. Using the Nikiforov-Uvarov and SUSYQM methods, we analytically develop the relativistic energy eigenvalues and associated Dirac spinor components of wave functions. We find that both methods give entirely the same results. Modifiable of our results into some particular potential cases, useful for other physical systems, are also discussed. We obtain complete agreement with the findings of previous works. The spin and pseudospin bound state energy spectra for various levels are presented in the absence as well as the presence of tensor coupling. Both energy spectrums are sensitive with regards to the quantum numbers $\kappa$ and $n$, as well as the parameter $\delta$. We also notice that the degeneracies between Dirac spin and pseudospin doublet eigenstate partners are completely removed by the tensor interaction. Finally, we present the parameter space of allowable bound state regions of potential strength $V_0$ with constants for both considered symmetry limits $C_S$ and $C_{PS}$.