The relativistic theory of the auger effect

Abstract

In a recent paper by one of us the theory of the auger effect has been discussed and calculations carried out of the magnitude of the X-ray K series fluorescence yield for elements of atomic number low enough to justify the neglect of relativistic effects. The comparison of these theoretical results with experiment revealed effects. The comparison of these theoretical results with experiment revealed sufficiently good agreement to justify the extension of the theory to elements of high atomic number by taking account of relativistic effects. As the Auger effect is capable of direct and accurate experimental investigation any appreciable relativistic modification could be tested quantitatively. Such a test is of special importance owing to the somewhat meagre experimental evidence for the quantitative validity of Dirac's equations of the electron applied to atomic phenomena. Thus the predicted polarization of an electron beam on double scattering by heavy nuclei has received no experimental confirmation, and the theory has not provided exact agreement with the observed values of the internal conversion coefficients for γ-rays. On the other hand, the conspicuous success of the theory in its application to the fine structure of atomic spectra, the scattering of hard γ-radiation, and to pair formation in general makes it difficult to believe it can be markedly incorrect. Moreover, as the auger effect is concerned with the interaction of two electrons it can only be dealt with relativistically by an extension of Dirac's theory to two electrons. No exact method of doing this has as yet been discovered, but Mϕller, by a correspondence principle method, has obtained a relativistically invariant formula for the probability of transitions involving two electrons-including retardation effects and spin-spin interaction-which may be expected to hold to a first approximation. Comparison of observed auger coefficients with those calculated using Mϕller's formula thus provide a test, not only of Dirac's one-electron theory, but also of its extension in the first approximation to two electrons.