Phonon Spectrum of hcpHe4

The phonon dispersion relation of the quantum crystal hcp ${\mathrm{He}}^4$ has been studied for wave vectors along the [$10\overline{1}0$] and [0001] symmetry directions. Of the 10 branches of the spectrum along these directions, we have observed phonon groups from all but two, the $\mathrm{T}{\mathrm{O}}_{\perp }\left[10\mathrm{}\overline{1}0\right]$ and LO [0001]. The LO and LA [$10\overline{1}0$] branches are only partially complete. The experimental results have been compared with a calculation for the spectrum by Gillis, Koehler, and Werthamer; the agreement is found to be reasonable. The excitations are found to be well defined, except for the LO [$10\overline{1}0$] branch, where we observe a wave-vector-dependent relaxation. The single crystals of helium used for the experiment were held at 1.03 ± 0.09°K and had a molar volume of 21.1 ± 0.1 ${\mathrm{cm}}^3$.