Final-state effects in x-ray photoemission spectra

In this work, we use von Barth and Grossmann’s (BG) exact results and their model as guidelines for examining several approximate methods. The main concern is the resonance structure in Minnhagen’s kernel α(u) due to final-state effects at frequency u∼${\epsilon }_f$—where we believe the dynamic Coulomb effect should be taken into consideration. We also propose an approximation (the mixed-state Born approximation) which shows the potential to include both the final-state effect and the dynamic effect. BG’s model is discussed in detail, and its relation with real systems made clear. The final-state Born approximation is derived from the structure of perturbation theory—a new derivation for the approximation.