Relativistic perturbation theory. III. A new perturbation approach to the two-electron Dirac-Coulomb equation

Abstract

For pt.II see ibid., vol.19, p.3431 (1986). Using the methods described by A. Rutkowski in pt.I (ibid., vol.19, p.149, 1986). A new perturbation approach is extended to two-electron problems. In this approach the Dirac-Coulomb equation is partitioned into an equivalent of the Schrodinger equation and a perturbation. The two perturbations involved each include a different negative power of the velocity of light. The relevant perturbation equations and formulae for the corrections to energy are derived. The method preserves some of the advantages of the Rayleigh-Schrodinger perturbation theory. A relativistic version of the variational perturbation method is formulated. In order to demonstrate the correctness of our two-electron relativistic perturbation theory, particular attention has been given to the exposition that the two-electron approach is consistent with the one-electron approach. It is shown that for the exact non-relativistic wavefunction the author's first-order energy correction is equal to the sum of appropriate quasirelativistic corrections. Numerical results are presented for the ground-state of helium-like atoms.