Golden-rule approach to the soft-x-ray-absorption problem. II. The effect of a bound state

Abstract

The soft-x-ray-absorption problem is examined in the case where a bound state exists in the final state. The analysis is based on the Fermi-golden-rule approach developed in a previous paper [Phys. Rev. B 28, 6833 (1983)]. It is found that the present method leads quite naturally to the conclusions of Combescot and Nozières (CN), who first examined this problem. Besides reproducing the results of CN, the present analysis gives exact expressions of the integrated intensities of the optical absorption for both absolute and secondary absorption bands. The formulas reveal that there should be a marked difference between the x-ray-photoelectron spectrum (XPS) and optical-absorption spectrum in the intensity of the secondary band. Also, the present work leads to expressions for the critical amplitudes, the prefactors of the power-law spectra, of the main and secondary thresholds, which are exact for a contact-type core-hole potential. For these two quantities some numerical results are presented for a model conduction band.