Study of the lattice dynamics of hexagonal close-packed³He and⁴He using inelastic x-ray scattering

Abstract

We present the first measurement of the coherent dynamic structure factor S(Q,) of solid 3He. At a density of 13.25(10) cm3 mol-1, we observed longitudinal phonons, using high-resolution inelastic x-ray scattering at momentum transfers 6 nm-1 < |Q| < 23 nm-1. Their dispersion relation was determined along the c-axis in single crystals of hcp 3He, and the spectra were described with a single-phonon model. For comparison, hcp 4He at the same density was studied with the same technique. The comparison, including all available 4He data from neutron scattering experiments, results in a phonon frequency ratio 3/4 of 1.11(5). Special attention is given to the scattering contribution due to multi-phonon excitations.