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

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 slow 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 slow 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 e²v, owing to these fast-slow interference terms.