Theory of quantum solids: Effect of lattice symmetry and anisotropy in the pair-correlation function

Abstract

The theory of quantum solids by Lowy and Woo employs a Hartree-Jastrow wave function in which the Hartree product, thus the wave function, is given its proper exchange symmetry. Coupled integral equations were derived for the one- and two-particle distribution functions, which enter into the energy expression. On account of mathematical and computational complications, the two-particle distribution function was not obtained from actually solving the integral equations. Instead, it was approximated by a product of two one-particle distribution functions with the pair-correlation function for the liquid. The latter lacks the proper lattice symmetry, and is not anisotropic. In this paper, we take into account the effects of both lattice symmetry and anisotropy on the pair-correlation function, solve the coupled integral equations to higher orders, and recalculate the energy curves. It is shown that lattice symmetry in the pair-correlation function lowers the liquid-to-solid transition density by about 2%, while anisotropy raises it by about 7%.