Static local-field correction from Monte Carlo studies of the homogeneous electron gas

From the fixed-node diffusion Monte Carlo (DMC) results obtained by Ortiz and Ballone [Phys. Rev. B 50, 1391 (1994)], we develop semianalytic expressions of the static local-field correction (LFC) for the dielectric function describing exchange and correlation effects in a homogeneous electron gas. These expressions, correcting some errors of earlier papers, are derived following the Vashista-Singwi [Phys. Rev. B 6, 875 (1972)] and Utsumi-Ichimaru [Phys. Rev. B 22, 5203 (1980)] schemes. Both satisfy physical requirements as the "compressibility sum rule" for an interacting fermion system. The behavior of these LFC functions is discussed and compared with the well-known LFC's given in the literature. More tractable density-dependent expressions are given in order to allow easy calculations of physical properties without losing accuracy relative to DMC numerical results.