Liquid Structure Factor of Ground-StateHe4

Abstract

A nonlinear integral equation for the liquid structure factor of ground-state ${\mathrm{He}}^4$, constructed from various frequency moments of the density-density correlation function, is proposed. This equation is solved for a particularly simple choice of two-body potential, and the results for the self-consistently-determined particle density are compared with experiment. The energy per particle and the sound velocity are also determined at the calculated density. The density, energy, and sound velocity, as well as the structure-factor curve as a function of $k$, all agree quite closely with experimental values. There are no free parameters once the choice of two-body potential has been made.