Optimized correlations inspired by perturbation theory

We study the accuracy of analytical wave-function-based many-body methods derived by energy minimization of a Jastrow-Feenberg ansatz for electrons (the "Fermi hypernetted chain/Euler Lagrange" approach). Approximations to avoid the complexity of the fermion problem are chosen to parallel successful boson theories and to be computationally efficient. For the three-dimensional homogeneous electron gas, we calculate the correlation energy, the pair distribution function, and the static structure function in comparison with simulation results. We also present a variant of theory which is interpreted as an approximate, self-consistent sum of ladder and ring diagrams of perturbation theory. The theory performs particularly well in the highly dilute density regime.