An approximate solution of Dirac-Hulthén problem with pseudospin and spin symmetry for any κ state

Abstract

For any spin-orbit quantum number κ , the analytical solutions of the Dirac equation are presented for the Hulthén potential by applying an approximation to spin-orbit coupling potential for the case of spin symmetry, Δ ( r ) = C = const , and pseudospin symmetry Σ ( r ) = C = const . The bound state energy eigenvalues and the corresponding spinors are obtained in the closed forms.