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

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 kappa. 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.