Approximately analytical solutions of the Manning–Rosen potential with the spin–orbit coupling term and spin symmetry

Abstract

In this Letter the approximately analytical bound state solutions of the Dirac equation with the Manning–Rosen potential for arbitrary spin–orbit coupling quantum number k are carried out by taking a properly approximate expansion for the spin–orbit coupling term. In the case of exact spin symmetry, the associated two-component spinor wave functions of the Dirac equation for arbitrary spin–orbit quantum number k are presented and the corresponding bound state energy equation is derived. We study briefly two special cases; the general s-wave problem and the equal scalar and vector Manning–Rosen potential.