Final-state and other approximations in x-ray spectra

Abstract
The final-state rule (due to von Barth and Grossman and to Mahan) for the calculation of x-ray absorption and emission spectra of a metal is considered. Limiting forms of the exact Mahan, Nozières, and de Dominicis theory, valid far from threshold, are derived and compared to this rule. It is shown for a simple model that the use of "orthogonalized final-state" orbitals provides more accurate results.