Electron Interaction in Solids. Collective Approach to the Dielectric Constant

A quantum theory of the dielectric constant for solids of both low and high polarizability is developed from first principles. In the latter case, the approach used is collective in that the long-range part of the electron interaction is described by the plasmon field. The conditions under which the local field corrections of Lorentz may be neglected are clearly defined. Both the static and frequency-dependent dielectric constant are derived. It is shown that the interaction between electrons may be described in terms of the dielectric constant of the solid provided the electrons in question form a small minority group which can be isolated from the much larger majority electron group. The theory is applied to a calculation of the frequency-dependent longitudinal conductivity and the optical properties of the solid.