Asymptotic Form of Charge Screening in an Electron Gas of Arbitrary Degeneracy

Expressions for the long-range screening field around a localized point charge in an electron gas of arbitrary degeneracy have been obtained by evaluating the Dirac density integral for a scattered plane wave and appropriate expansions of the Fermi-Dirac function. The results present a more comprehensive account of the variation of long-range screening with distance and electron-gas degeneracy than has yet been given. It is found that corrections to simple standard forms like the Friedel oscillations and the Brooks-Herring screened Coulomb are quite complex and more significant than generally believed. In the alkali and noble metals these corrections can reverse the sign, and change by a sizable factor the magnitude, of the interaction given by the Friedel expression at the first-neighbor distance.