Anomalous Effects of a Localized Inner-Shell Hole upon Soft X-Ray Spectra in Metals. I. Generalized Power Law

Abstract

Theoretical study of Mizuno and Ishikawa on emission spectra is extended beyond the behavior precisely at threshold. Following them, the perturbation series of the spectral density functions are calculated up to the third-order term for L₂₃ spectra while up to the fourth-order for K, the perturbation being a static potential caused by a localized inner-shell hole that is present only before emission. In the present paper, however, the part, which goes to zero at threshold, of each of the terms is also calculated out explicitly without approximation.
After rearrangement of the obtained ill-behaved perturbation series, it is found that spectral densities below threshold may be expressed in the form of a generalized power law:
w(ω)=γ(ω)|ω_F−ω|^α(ω).
Here, ω is a frequency of emitted photon, ω_F being the value at threshold. Both α(ω) and γ(ω) denote certain well-behaved functions which are regular in particular about ω=ω_F.