At high pressure and low temperature, helium crystallizes into a solid with its atoms arranged in a hexagonal closed packed configuration. Lattices of this type exhibit phonons of E2g symmetry. The frequency of this phonon in solid helium can be measured to a high degree of precision using Raman spectroscopy or neutron scattering, and it depends strongly on the density of the solid. A program based on centroid path integral quantum Monte Carlo simulations has been developed for studying solid helium, with the ultimate goal being a detailed understanding of the effect of zero-point motion and three-body interactions on the E2g phonon frequency. A finite solid, consisting of a closed packed assembly of helium atoms, has been simulated. The inner atoms of the assembly are treated using path integral centroids and the outer atoms are represented by stationary lattice points characterized by Gaussian distribution averages of the helium two body potential developed by Aziz. The program has been used to calculate zero-point motion induced mean square displacements for a helium atom at the center of the assembly. The program can simulate the temperature and density dependence of the atomic zero-point motion in the crystal, information that is key to understanding the effect of zero-point motion on the E2g phonon. In addition to calculating mean squared displacements of the central atom, the forces on the central atom as well as their cartesian components have been calculated. Calculating force components as a function of the position of the central atom can be used to generate elements of the dynamical matrix. Once the elements of the dynamical matrix are fully known, the frequencies of the E2g phonon can be calculated.

Centroid path integral investigation of zero-point motion and its effects in solid helium

2019 Spring National Meeting

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