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

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 $C_{PS}$.

arXiv comment21 pages, 9 figures, 2 tables

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• Arbitrary $\ell$-state solutions of the Klein-Gordon equation with the Eckart plus a class of Yukawa potential and its non-relativistic thermal properties
• Eigensolutions and thermodynamic properties of generalized hyperbolic Hulthen and Woods-Saxon potential