Dense electron-gas response at any degeneracy

Abstract
An exact expression for the linear response function of the dense electron gas valid at any temperature is worked out in the ring (RPA) approximation. The T=0 and T=∞ limits reproduce the already known results. It is used to explain the longitudinal oscillations and the screening around a test charge. The latter is either Thomas–Fermi‐like or Friedel‐like according to the values of the parameters.