Static and Dynamical Effects of Core Holes in KLV Auger, SXE, and SXA Spectra of Simple Metals

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We examine the effect of the core hole on several spectroscopies used to explore the conduction band of simple metals. We show that the static effect on the valence electrons is very strong and discuss under what circumstances this effect may be seen experimentally. In KLV Auger spectra a core hole is present in both initial and final states. Thus, there will be almost no dynamical effect, but the static effect must be accounted for in any quantitative calculation. We here present a full effective one-particle calculation for the KL1 V and KL2,3V spectra of sodium, that for the first time explain the "mystery" structure seen in experiment, by attributing this effect to the presence of a core hole. The agreement with experiment is gratifying although some discrepancy remains. For the main band of soft X-ray emission spectra the core hole is present in the initial state but not in the final state, yet the experimental spectra do not show the strong effect found in KLV. This is explained in terms of the Final State Rule, according to which rather accurate spectra can be obtained from a one-particle calculation provided final-state wave functions are used in the transition matrix elements. The dynamical switching of the core hole potential causes a singular behavior of the X-ray edge, which according to the Final State Rule can be accounted for by mutliplicative power-law factors. For the satellite emission band there is an additional core hole in both initial and final states, and, by the Final State Rule, the spectrum should show the static effect of precisely one core hole. This is confirmed by the good agreement between theory and experiment that we obtain for the L2,3 SXE satellite spectrum of sodium. The Final State Rule is also used to explain the similar shapes of the main band and the satellite in the case of Li K emission, and for the interpretation of alloy spectra.