Variational calculation for electron correlations at metallic densities

An exact hierarchy of integral equations involving $n$-particle distribution functions is obtained within the context of Slater-Jastrow many-body wave function. The "convolution approximation" is used to truncate this hierarchy. This results in a new integral equation for the static structure function. The equation is solved numerically to obtain the pair correlation functions and the ground-state energies of the homogeneous electron gas for a range of densities. The results obtained, throughout the metallic range, are in reasonable agreement with those obtained by successful nonvariational methods, and are better than those of earlier variational calculations.