Bound states of the Dirac equation for the generalized Woods–Saxon potential in pseudospin and spin symmetry limits

Abstract

Bound state solutions of the Dirac equation for the generalized Woods–Saxon potential are examined for arbitrary κ states by using the approximation to the Coulomb and centrifugal potentials in pseudospin symmetry (PSS) and spin symmetry (SS) limits, respectively. The energy eigenvalues and corresponding eigenfunctions are obtained in closed forms. Some numerical examples are given for proton or anti-proton in a nucleus. The correlations between the energy splitting and some parameters of the effective potential in PSS limit are examined for several pseudospin doublets.