Bound state solutions of Dirac equation: spin and pseudo-spin symmetry in the presence of the combined Manning–Rosen and Yukawa tensor potentials

In this study, the bound state solutions of the Dirac equation with spin and pseudo-spin symmetries are presented for the Manning–Rosen potential with Yukawa-like tensor interaction. In the supersymmetry quantum mechanics and Nikiforov–Uvarov methods framework, we obtain the relativistic energy eigenvalues associated with Dirac spinor components of wave functions. Next, the relativistic energy eigenvalues and corresponding radial wave functions are expressed as a recurrence relation in the Jacobi polynomials for arbitrary spin-orbit coupling quantum number κ . The parameter space of allowable bound state regions of potential strength V 0 is presented for the parameters of the exact spin and pseudo-spin symmetry limits. Adapting our results to specific potentials characterising different systems is also stated. The findings for particular cases exhibit a good agreement with the already reported results. In addition, the spin and pseudo-spin bound state energy spectra for various levels are investigated in the absence and the presence of tensor coupling. The energy levels are sensitive depending on arbitrary spin-orbit coupling quantum number κ , radial quantum numbers n , and screening parameter δ . It is also found that the tensor interaction eliminates the degeneracies between Dirac spin and pseudo-spin doublet eigenstate partners.