Approximate solutions of the Dirac equation with deformed Woods-Saxon potential including a Hellmann-like tensor interation

An Approximate bound state solutions of the Dirac equation under the spin and pseudospin symmetries for the deformed Woods-Saxon potential with a Hellmann-like tensor interaction was examined. With the help of the Nikiforov-Uvarov functional analysis (NUFA) method and an approximation scheme, the analytical and numerical energies of the combined potential were obtained for both symmetries, for different quantum numbers. Degeneracies were observed in the energy values in the absence of the tensor interaction and these degeneracies were removed with the help of the Hellmann-like tensor interaction. The variations of the energies for spin and pseudospin symmetries were studied for various values of the quantum numbers and deformation parameters. Our study shows that the relativistic energies obtained are very sensitive to the quantum numbers and the deformation parameter.