Theory of Auger satellite energy shifts

A theoretical model is described for calculating energy shifts of Auger satellites--- Auger transitions that occur in the presence of "spectator" vacancies. The shifts arise through a combination of direct and indirect (or relaxation) interactions between spectator and regular hole states. Both can be expressed in terms of two-electron Coulomb and exchange integrals, and approximate pairwise additivity of the shifts owing to holes or spectator vacancies is demonstrated. An approximate method, based on the "equivalent-cores" approximation, is employed to estimate numerical values of the indirect term using only tabulated two-electron integrals for atomic ground states. Satellite shifts for the L₃M₄₅M₄₅(M₄₅) transition are thereby estimated for elements with 70≤Z≤100. The predicted value of -38 eV for bismuth is in excellent agreement with the experimental value -36 ± 5 eV reported for ²¹⁰Bi by Haynes, Velinsky, and Velinsky. For americium the predicted value is -61 eV; Freedman and Porter reported an experimental value -56 eV. Other predicted satellite shifts in bismuth also show reasonably good agreement with less accurate experimental values. These results thus strongly support previous interpretations of satellite shifts and appear to provide a fairly accurate and very easy method for predicting these shifts in deep core levels.