Calculations of K absorption edges in some heavy atoms

Abstract

The binding energy of a K electron in some heavy atoms is calculated to order Zα 2 mc 2 . This energy is considered in three parts: (i) the potential energy of the K electron in the Coulomb field of the nucleus, (ii) the interaction with the other K electron, and (iii) the Coulomb potential energy arising from the other (‘outer’) electrons. Although the potential due to the outer electrons is large, it varies little in the region of the K shell and may be written in the form V = a + b(r) , b (0) = 0, where a is a large constant potential and b(r) a small correction to it. For these the self-consistent field calculations are used. The nuclear potential and α are taken into account exactly and the remaining terms considered as small perturbations. The K electrons are treated relativistically. The change in the wave functions of the outer electrons when a K electron is removed is shown to give only a second-order change in the binding energy of a K electron. The results are found to be in good agreement with experiment.