Ground State of Liquid ${\mathrm{He}}^4$

The properties of the ground state of liquid ${\mathrm{He}}^4$ are studied using a variational wave function of the form ${\Pi }_{i<j}f\left(r_{\mathrm{ij}}\right)$. The Lennard-Jones 12-6 potential is used with parameters determined from the gas data by deBoer and Michiels. The configuration space integrals are performed by a Monte Carlo technique for 32 and 108 atoms in a cube with periodic boundary conditions. With $f\left(r\right)=\exp [-{\left(\frac{2.6 \mathrm{\AA }}{r}\right)}^5]$, the ground-state energy is found to be -0.78 × ${10}^{-15\mathrm{}}$ ergs/atom, which is 20% above the experimental value. The liquid structure factor and the two-particle correlation function are in reasonably good agreement with the x-ray and neutron scattering experiments.