Static response and local field factor of the electron gas

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 2q_F. 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 q ≲ 2q_F. We give a simple formula to reproduce G(q) at relevant values of the wave vector.