Ground-State Properties of Solid Helium-4 and -3

Abstract

Previous Monte Carlo computations of ground-state properties of solid helium using a correlated trial wave function are extended in several directions. A generalized wave function which includes a simple model for "phonon" correlations is tested; no significant lowering of ground-state energies is obtained. Detailed results for bcc ${\mathrm{He}}^{3}$ and hcp ${\mathrm{He}}^{4}$ are tabulated in the low-density region. The extension of the variational computations to considerably higher densities (10 ${\mathrm{cm}}^{3}$/mole) stresses the need for inclusion of short-range correlations over a wide density range and clearly reveals the inadequacy of the commonly used Lennard-Jones 12-6 potential with the de Boer parameters. Various other recently proposed interaction potentials are investigated in conjunction with known three-body forces. Reasonable agreement with experimental energies, pressures, and compressibilities follows from the use of a potential due to Beck. The relation between the melting properties of helium and two "hard-core" models is discussed and the possibility of Bose-Einstein condensation in the solid is investigated in conjunction with a theorem due to Reatto.