Solution of the Dirac equation for the Woods-Saxon potential with spin and pseudospin symmetry

The s(s˜)-wave Dirac equation is solved exactly for a single particle with spin and pseudospin symmetry moving in a central Woods-Saxon potential. The corresponding radial wavefunctions for the two-component spinor are obtained in terms of the hypergeometric function, and the energy spectra of the bound states are presented as the solutions to the given equations with boundary constraints. The condition of existing bound states is analyzed in the limit of pseudospin symmetry.