Ground State of Liquid Helium-4 and Helium-3

Abstract

A variational calculation of the ground-state energy of liquid helium-3 and liquid helium-4 is made using, respectively, Jastrow- and Slater-Jastrow-type trial wave functions. In the boson (${\mathrm{He}}^4$) case, the quantum average, analogous to a statistical average over a fictitious canonical ensemble, is computed by a molecular-dynamics method for a system of 864 atoms. The following quantities are obtained: ground-state energy: -5.95°K/atom (experiment: -7.14°K/atom); equilibrium density (0.020±0.002) atoms/${\mathrm{\AA }}^3$ (experiment: 0.022 atoms/${\mathrm{\AA }}^3$); liquid-structure factor; fraction of particles condensed in the zero-momentum state: 0.105±0.005. This is in good agreement with previous computations. In the fermion (${\mathrm{He}}^3$) case, the energy expectation value is calculated approximately by use, up to second order, of a cluster expansion of the effect of the antisymmetrization, developed by Wu and Feenberg. The ground-state energy obtained is -1.35°K/atom (experiment: -2.52°K/atom). The liquid-structure factor of liquid ${\mathrm{He}}^3$, for which no experimental result is yet available, is calculated in this approximation.