A perturbation analysis of current methods of calculating relativistic energies

The principal methods of calculating relativistic corrections are analysed from the point of view of the relativistic perturbation theory. The conditions under which the Breit-Pauli method is consistent with the relativistic perturbation method of Layzer and Bachall (1962) are formulated. Difficulties arising in the application of perturbation expansions in terms of 1/Z to relativistic Hartree-Fock equations, are demonstrated. Some typical numerical data are examined in the light of these discussions.