Screening of a Foreign Charge by an Electron Gas

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Abstract
The random-phase approximation of the displaced density of an electron gas due to the presence of a foreign charge assumes a rather large error when the mean density of the gas is commensurate with that of conduction electrons in a metal. The assumption of a linear response is not quite valid. A modified formula, entailing little additional mathematical labor but treating the low-density problem more realistically, is proposed for the case of a negative foreign charge. For an arbitrary foreign-charge distribution, two expressions, each of which contains as special cases both the random-phase and the nonlinear Fermi-Thomas approximations. are examined. One of these comes quite close to reproducting the exact quantum-mechanical results in the hypothetical test case of a gas of noninteracting electrons.

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