In this paper, potentialhyphen;dependent transformations are used to transform the fourhyphen;component Dirac Hamiltonian to effective twohyphen;component regular Hamiltonians. To zeroth order, the expansions give second order differential equations (just like the Schrouml;dinger equation), which already contain the most important relativistic effects, including spinndash;orbit coupling. One of the zero order Hamiltonians is identical to the one obtained earlier by Chang, Pelissier, and Durand lsqb;Phys. Scr.34, 394 (1986)rsqb;. Selfhyphen;consistent allhyphen;electron and frozenhyphen;core calculations are performed as well as first order perturbation calculations for the case of the uranium atom using these Hamiltonians. They give very accurate results, especially for the onehyphen;electron energies and densities of the valence orbitals.
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