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

TL;DR

This paper derives approximate analytical solutions for the Dirac equation with Rosen-Morse and Pöschl-Teller potentials including tensor interactions, showing that tensor interactions lift degeneracies in spin and pseudospin doublets.

Contribution

It provides new approximate solutions for the Dirac equation with specific potentials including tensor interactions, highlighting the removal of degeneracies.

Findings

Tensor interaction removes degeneracies in spin and pseudospin doublets.

Solutions are obtained using Pekeris-type approximation.

Results apply to Rosen-Morse and modified Pöschl-Teller potentials.

Abstract

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.