ELECTRON-INTERACTION EFFECTS ON SOFT X-RAY EMISSION SPECTRUM OF METALS .I. FORMALISM AND FIRST-ORDER THEORY

The soft x-ray emission spectrum of metals is studied using a diagrammatic many-body perturbation theory to account for the interactions between electrons. On the basis of a one-electron model, the emission spectrum gives a direct measure of the Fermi energy and is simply related to the conduction-electron density of states. In actual metals, however, the spectra are strongly modified by electron interactions, and these relations are no longer valid. A low-energy tail is introduced in place of a sharp emission threshold, and a satellite band appears which is associated with plasmon excitation in the metal. The first-order theory described here shows that certain interference terms play an important role in determining the emission intensity. For sodium, a satellite band is obtained with maximum intensity between 1% and 2% of the parent band, in agreement with observations by Rooke. The low-energy tail has a similar strength in the region of the satellite. The first-order theory, however, breaks down in the region of the parent band spectrum. © 1969 The American Physical Society.