Electron Interaction in Solids. Characteristic Energy Loss Spectrum

The characteristic energy loss spectrum of solids is analyzed with the aid of the dielectric formulation of the many-body problem developed by the authors. It is shown that a measurement of the angular distribution of inelastically scattered fast electrons is a direct measurement of the imaginary part of the inverse dielectric constant of the solid, at the frequency and momentum of the energy transfer to the electrons in the solid. The calculations of the dielectric constant by means of first-order perturbation theory and within the random phase approximation are discussed with regard to their implications for the characteristic energy loss spectrum. It is shown that plasmons provide the dominant excitation mode at low momentum transfer for the free electron gas and for most solids; an explicit calculation is given of the role of screening in reducing the role of the independent electron excitations in this region. A comparison is made between characteristic energy loss experiments and other techniques for exploring the energy level structure of solids, including the non-relativistic Compton effect, optical transmission and reflection experiments, and x-ray emission and absorption studies. An analogous formulation of the optical properties of solids is given, which shows that in general the transverse and longitudinal dielectric constants will not be equal. They are equal within the random phase approximation, so that a careful comparison of optical data with characteristic energy loss data permits a direct verification of the validity of the random phase approximation. Such a comparison likewise yields information on the magnitude of the screening of individual electron transitions and permits the unambiguous identification of plasmon excitations. Finally it is shown that to the extent that the random phase approximation is valid, the results of a characteristic energy loss experiment may be used for a direct experimental determination of the ground-state energy of the electrons in a solid.