Electron-interaction effects on the soft x-ray emission spectra of metals. II. Renormalized theory with application to sodium

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Abstract
Details of a renormalized theory of the soft x-ray emission spectrum of a light metal are presented. The resulting spectrum shows structure in the plasmon satellite band and the parent band which did not appear in the first-order theory. The structure in the plasmon satellite band arises from the excitation of the plasmaron mode as suggested by Hedin. In addition there is a peak of intensity near the high-energy edge of the parent band, which is related to the threshold effect discussed by Nozières and others. The calculated spectrum differs considerably from what would be expected for noninteracting electrons. It also departs considerably from what could be considered a generalized density of states of the interacting conduction electrons. The transient effect of the disappearance of the core hole makes it impossible to relate the spectrum to the density of states in any simple way. Careful study of the experimental spectra of light metals could serve as a check of the approximations made here, and provide important information about electron correlations in metals.