| Author(s): |
David R. Penn; S Girvin; G D. Mahan; |
| Title: |
Dispersion Relation Approach to the X-Ray Edge Problem |
| Published: |
December 15, 1981 |
| 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 Nozi{egrave};res and De Dominicis is made. |
| Citation: |
Physical Review B (Condensed Matter and Materials Physics) |
| Volume: |
24 |
| Research Areas: |
Condensed Matter Physics |
