Study of the lattice dynamics of hexagonal close-packed He-3 and He-4 using inelastic x-ray scattering

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