Theory of Auger core-valence-valence processes in simple metals. I. Total yields and core-level lifetime widths

There is a considerable disagreement in the literature on the description of lifetime effects arising from core-valence transitions in solids. We calculate here Auger and radiative widths of shallow core levels in Li, Be, Na, Mg, and Al with use of principles consistent with dynamical theories of secondary-emission processes developed earlier. The lifetime has no simple relation to the usual self-energy but is instead directly related to emission yields. The problem of choosing reliable approximations for Auger rates and matrix elements is analyzed theoretically and computationally. We also comment on some earlier approaches. Much of our discussion pertains also to calculations of Auger line shapes from first principles. For long hole lifetimes the total and partial level widths obey an initial-state rule and follow from wave functions perturbed by a static core hole. To obtain these impurity wave functions we perform self-consistent supercell calculations. The core-hole screening increases the Auger rates by factors of the order 2–4 compared with results from ground-state orbitals but has never been properly included before. The width of the 1s level in Li is rather accurately known because it monitors large effects of incomplete lattice relaxation. For Li we obtain here a width 17 meV in excellent agreement with the value 16 meV deduced earlier from measurements by Callcott et al.