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Dispersion Relation Approach to the X-Ray Edge Problem



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


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.
Physical Review B (Condensed Matter and Materials Physics)


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 April 21, 2024)
Created December 14, 1981, Updated October 12, 2021