SCREENING OF A STATIC CHARGE BY A DEGENERATE ELECTRON-GAS

It is shown, by very simple arguments, that the well-known formula for the long-wavelength static dielectric function of a homogeneous electron gas, established by Nozieres (1964), is valid only with accuracy O(1). The resulting consequences on the screening of the static charge and the long-wavelength sum rules for the dielectric function are discussed. The consequences are relatively modest.