Approximate Spin and Pseudospin Solutions of the Dirac equation with Rosen-Morse Potential including a Coulomb Tensor Interaction

By applying the Pekeris-type approximation to deal with the (pseudo or) centrifugal term, the spin and pseudospin symmetry solutions of the Dirac equation for the Rosen-Morse potential including a Coulomb-like tensor potential with arbitrary spin-orbit coupling quantum number $\kappa$ are obtained by standard method. It has been shown from the numerical results that the degeneracies between spin and pseudospin state doublets are removed by the tensor interaction. Special case of this potential, that is, the spin and pseudospin solutions of the Dirac equation with the modified P\"{o}schl-Teller potential including a tensor interaction is also considered. The results obtained in this case show that the tensor interaction removes the degeneracies between the members of doublets states in spin and pseudospin symmetries.