Optimal correlation function for Fermi HNC equations

The properties of the fermion hypernetted chain (FHNC) equations due to Fantoni and Rosati are investigated. The FHNC equations are reformulated to make their low-momentum behaviour more transparent, and to facilitate their numerical treatment. It is shown how to derive variational equations for minimizing the ground-state energy in the FHNC approximation, and numerical solutions are given for a model neutron matter with repulsive interactions and for the electron gas. The numerical results indicate that the FHNC equations provide a good description of both short- and long-range correlations if the optimal Jastrow trial functions are used. (Auth.)