Correlation Methods in Atomic Theory

Abstract

With respect to refining methods for recording atomic spectra, studying them near the threshold energies, and examining many-electron transitions and other anomalies, the development of effective, simple, and universal methods of accounting for the correlation between electrons is the most important problem in atomic physics, including the theory of electron and x-ray spectra. This chapter does not presume to be a systematic review of the various correlation methods. Methods of this type and variations of them have been proposed, but most of these are quite complex and are only used in practice for configurations containing either several electrons or closed electron shells. We will only describe the most widely used methods for describing electron and x-ray spectra — semiempirical and simple theoretical methods of accounting for correlations (Sec. 2.1), the many-configuration approximation and its variations, the method of configuration interaction (Sec. 2.2), stationary perturbation theory (Sec. 2.3), and the method that takes into account the interaction between a discrete state and a continuum, which is extremely important for highly excited states (Sec. 2.4). The various correlation methods in atomic theory have been thoroughly reviewed in the monographs [47, 45, 95, 96, etc.].