Fermi hypernetted-chain calculations of the electron-gas correlations

Abstract

We have performed reliable variational calculations of the electron-gas correlations over a density range of ${r}_{s}=1\ensuremath{-}100$. The Jastrow trial function is chosen to minimize the ground-state energy in the Fermi hypernetted-chain (FHNC) approximation by solving the corresponding Euler-Lagrange equation for the pair-correlation function. The present method does not require any parametrizations or adjustments, and yet the calculated quantities show the expected behavior. In addition to the correlation energies, pair-correlation functions, and liquid structure functions, we have evaluated the one-body momentum distribution in the electron fluid by employing a modern FHNC-type summation procedure for the one-particle density matrix. An estimate of ${r}_{s}\ensuremath{\simeq}120$ is obtained for the crystallization density by relating the disappearance of the quasiparticle pole to the solidification. On the other hand, the possibility of a phase transition to the spin-polarized phase is also considered by comparing the ground-state energies of the two phases. We obtain an estimate of ${r}_{s}\ensuremath{\approx}13$ for the upper bound of the transition density. Comparisons with variational Monte Carlo results show that the FHNC approximation indeed is very reliable in the case of the electron gas.