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 (He⁴) 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/³ (experiment: 0.022 atoms/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 (He³) 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 He³, for which no experimental result is yet available, is calculated in this approximation.