Search for anisotropy in the Debye-Waller factor of HCP solid (4)He.

Abstract

The properties of hexagonal close packed (hcp) solid (4)He are dominated by large atomic zero point motions. An accurate description of these motions is therefore necessary in order to accurately calculate the properties of the system, such as the Debye-Waller (DW) factors. A recent neutron scattering experiment reported significant anisotropy in the in-plane and out-of-plane DW factors for hcp solid (4)He at low temperatures, where thermal effects are negligible and only zero-point motions are expected to contribute. By contrast, no such anisotropy was observed either in earlier experiments or in path integral Monte Carlo (PIMC) simulations of solid hcp (4)He. However, the earlier experiments and the PIMC simulations were both carried out at higher temperatures where thermal effects could be substantial. We seek to understand the cause of this discrepancy through variational quantum Monte Carlo simulations utilizing an accurate pair potential and a modified trial wavefunction which allows for anisotropy. Near the melting density, we find no anisotropy in an ideal hcp (4)He crystal. A theoretical equation of state is derived from the calculated energies of the ideal crystal over a range of molar volumes from 7.88 to 21.3 cm(3), and is found to be in good qualitative agreement with experimental data.