Relativistic effects in the screened Coulomb potentials

The expansion of wavefunction into Sturmian functions is used to compute nonrelativistic energies for the Yukawa and Hulthen potentials. Using nonrelativistic solutions, the first-order relativistic corrections for bound states with n <= 4 Dirac particles bounded in these potentials are calculated in the framework of direct perturbation theory. The dependence of the relativistic energy shifts and the fine structure splittings on the parameters of the potentials for several states are examined.