Core Level X-Ray Spectra of Simple Metals: Deviation from the Asymptotic Theory

Abstract

An analytic treatment is given for the deviations of XAS and XPS intensities from the asymptotic power-law behaviors given by Nozières and de Dominicis (ND). In deriving the formulae, the core-hole potential is assumed to be of contact-type and the energy dependences of physical quantities such as the phase shift and the dispersion integrals are taken into account up to linear terms with respect to the energy. It is shown that the deviations from the asymptotic formulae are expressed by introducing several new quantities which are derived from the first principle. It is also found that the deviations can be incorporated in the framework of the generalized (frequency-dependent) power-law. By comparing with the exact numerical results, the obtained formulae are demonstrated to have much wider applicability in the frequency space than the asymptotic ND formulae.