Local field factor and effective potentials in liquid metals

The authors recently evaluated the local field factor, G(q) of the electron gas by accurate fixed-node diffusion Monte Carlo (DMC) simulations. Here, the G(q) obtained from a simple fit to the DMC results and from several approximations available in the literature is used to derive the effective pair potential φ(r) in simple metals within second-order perturbation theory. Using a local electron-ion pseudopotential, it is found that φ is determined mostly by the behavior of G(q) at q ≤ ca. 2q_F, where the DMC data are well reproduced by the local field within local density approximation, GL_DA(q) = A(q /q_F)² with A related to the compressibility of the uniform electron gas.