Title: FREQUENCY MOMENTS: FINE STRUCTURE OF X-RAY SPECTRA IN METALS AND OTHER APPLICATIONS
Authors: A.G.Salistra (Odessa State University, Theoretical Physics Department, 42 Pastera St., UA-270100 Odessa, Ukraine)

Fine structure of the edges of X-ray lines (absorption, emission, photoemission) in metals is admitted to frequently possess an asymptotic power law singularity I(omega)->A(omega-omega_{edge})^{-alpha} on the line threshold due to the analogue of the infrared catastrophe. This happens due to the quasicontinuity of energy spectra of metals. In this paper the leading term of this power law's exponent is combined with first exact frequency moments of the relevant spectrum. The moments are obtained from an exact explicit expression and the use is made of the results of the power moments' problem on the half-axis to restore approximate line forms beyond the edge asymptotic region: i.e. to find the so-called generalized power law I(omega)=C omega^{-alpha(omega)}. Applying the method to a model alkali metal we show that the postasymptotic form strongly depends on the long-range asymptotics of the potential of a core hole (where an electron excited by a quantum has been). Later on Tchebycheff-Markov inequality is shown which enables us to find some parameters of spectra with a number of absorption and nonabsorption regions. This method also requires only a few first moments. It can be applied to spectra for wide frequency regions.

Comments: Figs. 2, Refs. 6, Tabs. 0.