The dielectric constant of an interacting electron gas

A simple method is proposed for finding the local-field correction to the dielectric constant of a system of interacting electrons. In this method, the local distortion of the mean induced density near an individual electron owing to exchange-correlation effects is automatically taken into account by determining the self-consistent potential at the given space-time point under the extra condition that one of the electrons of the system lies at that point. The stated method for accounting for exchange-correlation effects is initially developed within the framework of the single-particle approximation, and then is generalized to the case of analyzing the complete many-electron problem. By using it one can easily reproduce most of the currently known results on the dielectric constant, including those derived by the powerful methods of many-body theory. This study analyzes the contemporary state of the theory of the dielectric constant of an interacting electron gas and briefly presents an application of this theory for describing the physical properties of simple metals.