Singularities in the X-Ray Absorption and Emission of Metals. I. First-Order Parquet Calculation

X-ray emission and absorption spectra in metals may display singularities near the Fermi-level threshold. These singularities, predicted by Mahan, are due to final-state interactions between conduction electrons and the localized disturbance created by the x ray. The effect is treated within a simple model by the methods of perturbation theory. It is shown that even to lowest order one must sum the so-called parquet diagrams, in close analogy with the Abrikosov theory of the Kondo effect. Mahan's prediction is confirmed, and its validity discussed. Various secondary effects which could blur the singularity are analyzed.