Relativistic perturbation theory. I. A new perturbation approach to the Dirac equation

Abstract

A new perturbational approach useful in the relativistic theory of atomic structure is formulated. In this approach the Dirac equation is partitioned into an equivalent of the Schrodinger equation and a perturbation. The relevant perturbation equations and formulae for the corrections to the energy are derived. For the ground state of hydrogen-like atoms all the differential equations arising are solved directly. The power series in Z2/c2 obtained coincide with the exact solution of the Dirac equation. A relativistic version of the variational perturbation method is formulated. In order to demonstrate the usefulness of this approach to the problem of optimising non-linear parameters, the first-order wavefunctions for the ground state of the hydrogen-like atoms have been approximated in terms of exponential basis functions. The minimum value of the appropriate functional is very close to the exact second-order correction to the energy.