Ground State of Solid Helium-4 and -3

Abstract

A variational calculation of the curve of ground-state energy versus density for solid helium-3 and solid helium-4 at absolute zero is presented, using a two-parameter "localized" Jastrow \ifmmode\times\else\texttimes\fi{} Gaussian trial wave function. The energy expectation value is calculated by a Monte Carlo method taking advantage of the formal analogy between the quantum-variational integral and a classical canonical-ensemble configuration integral. Results are in good agreement with experiment. The solid-liquid phase transition for both ${\mathrm{He}}_{3}$ and ${\mathrm{He}}_{4}$ is predicted to take place at densities close to the experimental ones. The Monte Carlo method has also been used to test the validity of a variational calculation on a truncated cluster expansion of the energy expectation value due to Nosanow.