Dielectric Constant of a Dense Electron Gas Containing a Fixed Point Charge

An expression for the dielectric constant of a dense electron gas containing a positive point charge $\mathrm{Ze}$ with a neutralizing positive background is obtained by employing the diagram technique of quantum field theory. The present derivation leads to some more terms in addition to those obtained in the self-consistent-field approximation. Besides, our derivation rigorously takes into account the Pauli exclusion principle. The simplest evaluation of the dielectric constant is made in the region where collective effect dominates, and the results are compared with those obtained in the self-consistent-field approximation.