Deep-Hole Excitations in Solids. I. Fast-Electron-Plasmon Effects

Abstract

The theory of plasmon satellites in experiments where ion cores are excited is developed in a manner which complements the work of one of the authors, which showed how the interaction of electrons with plasmons could be treated to all orders in perturbation theory in a certain approximation. Here the fast-electron-plasmon coupling is treated by perturbation theory. The details of the calculation of the fast-electron admittance function mentioned earlier are given, and, in addition, the interference terms or vertex corrections between fast and electrons are treated by lowest-order perturbation theory. As prototypes, the theories of appearance-potential spectroscopy and electron energy loss with core excitation are considered. For the latter, because of slow-charge conservation, all plasmon effects, including these interference terms, associated with the core excitation are negligible. However, appearance-potential spectroscopy, because of nonconservation of slow charge, has plasmon satellites associated with the core excitation which are reduced in strength by a fractional amount of the order of $\frac{{e}^{2}}{\ensuremath{\hbar}v}$, owing to these fast-slow interference terms.