Phonon Dispersion Relations for hcpHe4at a Molar Volume of 16cm3

The phonon spectrum of hcp ${\mathrm{He}}^4$ has been measured along the three principal symmetry axes by inelastic neutron scattering from a single crystal with a molar volume of 16.00 ${\mathrm{cm}}^3$ at 4.2 K. The results are in fair agreement with the theoretical calculations of Gillis, Koehler, and Werthamer, the maximum discrepancy being about 30%. Considerable phonon damping has been observed for the ${\Delta }_2\left(\mathrm{LO}\right)$ and ${\Sigma }_3\left({\mathrm{TO}}_{\perp }\right)$ branches. A modified axially symmetric force-constant model has been fitted to the dispersion curves and used as an interpolation scheme to calculate the frequency distribution function and other thermodynamic functions.