Dispersion Relation Approach to the X-Ray Edge Problem

Published

December 15, 1981

Author(s)

David R. Penn, S Girvin, G D. Mahan

Abstract

We present a dispersion relation formulation of the open-line amplitude for the x-ray edge problem within the contact potential model. Using both multiple-scattering and determinant techniques, we find that to a very good approximation the many-body effects can be described within a single-particle transition-rate expression using a renormalized matrix element. This renormalized matrix element may be expressed exactly in terms of a frequency integral over the scattering phase shift for the core-hole potential. There are small corrections to the transition rate due to multiple particle-hole-pair final states, and a systematic series expansion for these is presented. This series is summed at threshold to yield an exact expression for the critical amplitude multiplying the power-law singularity. Our analytic results given an exact description at threshold and are shown to be quite accurate away from threshold. Comparison with the asymptotic expression of Noziegrave};res and De Dominicis is made.

Citation

Physical Review B (Condensed Matter and Materials Physics)

Volume

24

Pub Type

Journals

Citation

Penn, D. , Girvin, S. and Mahan, G. (1981), Dispersion Relation Approach to the X-Ray Edge Problem, Physical Review B (Condensed Matter and Materials Physics) (Accessed October 22, 2025)