Exact Pseudospin Symmetric Solution of the Dirac Equation for Pseudoharmonic Potential in the Presence of Tensor Potential

Under the pseudospin symmetry, we obtain exact solution of the Dirac equation for the pseudoharmonic potential in the presence of the tensor potential with arbitrary spin-orbit coupling quantum number κ. The energy eigenvalue equation of the Dirac particles is found and the corresponding radial wave functions are presented in terms of confluent hypergeometric functions. We investigate the tensor potential dependence of the energy of the each state in the pseudospin doublet. It is shown that degeneracy between members of the pseudospin doublet is removed by tensor interaction. Furthermore, the radial node structure of the Dirac spinor is discussed. We have investigated the exact solution of the Dirac equation for the pseudoharmonic potential in the presence of the tensor potential under the condition of pseudospin symmetry. Energy eigenvalue equation and corresponding radial wave functions have been obtained for any spin-orbit coupling quantum number κ. Degeneracy between two states in the pseudospin doublet has been investigated in the presence and absence of the tensor potential. We have seen that tensor interactions remove all degeneracies between members of pseudospin doublets. Effects of the potential parameters as well as Cps on the energy levels of the each state of the pseudospin doublet have been presented. We have analyzed the upper and lower radial wave functions and their node structures. Consequently, we conclude from our results that tensor interaction is useful to study the pseudospin doublet splitting. (author)