Analytic perturbation theory for screened Coulomb potentials: Relativistic case

Analytic expressions for relativistic screened Coulomb radial wave functions, including bound-state energy eigenvalues as well as bound and continuum wave-function shapes and normalizations, are given explicitly as series in $\lambda \simeq \alpha Z^{\frac{1}{3}}$. The method employed is a direct generalization of an approach previously used for the nonrelativistic case. The analytic expansions which we obtain are compared with exact numerical solutions of the Dirac equation for relativistic Hartree-Slater potentials. Low-, intermediate-, and high-$Z$ cases are considered for a wide range of energies and angular momenta. In general, excellent agreement is found for both inner bound states and for relativistic continuum states.