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We have evaluated the density-density static response of the electron gas at zero temperature and in the metallic regime by diffusion Monte Carlo. The computed local field factor G (q) smoothly interpolates between the asymptotic small and large q behavior, with a crossover around 2q₅. In fact, G (q) appears to be almost completely given by its asymptotes, being accurately reproduced by the local density approximation to density functional theory for q2q₅. We give a simple formula to reproduce G (q) at relevant values of the wave vector.
Moroni et al. (Mon,) studied this question.