Approximate Solutions of The Dirac Equation with Screened Kratzer-Hellmann Problem Including Generalized Tensor Interaction

The Dirac equation presents better perspective of understanding the motion of particles in region of relativistic quantum mechanics. In this regard, we examine the approximate bound state solutions of the Dirac equation under the spin and pseudospin symmetries for the screened Kratzer-Hellmann potential including generalized tensor interaction. By using the Nikiforov-Uvarov functional analysis method and an approximation scheme, the analytical, numerical and graphical 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 generalized tensor interaction and these degeneracies were removed with the help of the generalized tensor interaction, which is made up of the Coulomb, the Yukawa and the Hulthen potentials. The variations of the energy eigenvalues with screening parameter for spin and pseudospin symmetries were studied for various values of the quantum numbers. The increase and decrease of the energy eigenvalues are observed for both symmetries, indicating tightly bound and loosely bound states, respectively. Our study shows that the obtained energies are very sensitive to the screening parameter and quantum numbers.