Approximate analytical solutions of the Dirac–Manning–Rosen problem with the spin symmetry and pseudo-spin symmetry

Abstract

By employing an improved new approximation scheme to deal with the centrifugal term and pseudo-centrifugal term, we solve approximately the Dirac equation with the Manning–Rosen potential for the arbitrary spin–orbit quantum number κ. Under the condition of spin symmetry and pseudo-spin symmetry, the bound state energy eigenvalues and the associated two-component spinors of the Dirac particle are obtained approximately by using the basic concept of the supersymmetric shape invariance formalism and the function analysis method.