Ground State of Liquid Helium-4 and Helium-3

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 (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^/atom (experiment: -7. 14^/atom) ; equilibrium density (0. 0200. 002) atoms/^3 (experiment: 0. 022 atoms/^3) ; liquid-structure factor; fraction of particles condensed in the zero-momentum state: 0. 1050. 005. This is in good agreement with previous computations. In the fermion (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^/atom (experiment: -2. 52^/atom). The liquid-structure factor of liquid He^3, for which no experimental result is yet available, is calculated in this approximation.