Inelastic-Neutron Scattering from bccHe4

Inelastic neutron scattering experiments were carried out on large single crystals of the quantum solid bcc ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. The crystals were oriented in the [011] zone and had volumes larger than 5 ${\mathrm{cm}}^3$. Both transverse and longitudinal excitations were studied with propagation vectors along the [100], [111], and [011] principal symmetry directions. Dispersion relations along these three symmetry directions are presented and discussed within the context of the results of recent theories for this highly anharmonic solid. The data, which present clear evidence for strong phonon relaxation, are also compared with theoretical linewidth estimates. The elastic constants calculated from these data are $\frac{c_{11}}{\rho }=1.77\mathrm{}\pm 0.32$, $\frac{c_{12}}{\rho }=1.58\mathrm{}\pm 0.35$, and $\frac{c_{44}}{\rho }=1.07\mathrm{}\pm 0.10$ in units of ${10}^5$ ${\mathrm{m}}^2$/${\sec }^2$, in good agreement with the results obtained from ultrasonic and thermodynamic measurements. When the amplitude of the scattering vector $\left|\overrightarrow{\mathrm{Q}}\right|$ approaches $1.6a^{*}=2.44\mathrm{}$ ${\mathrm{\AA }}^{-1\mathrm{}}$, where $a^{*}$ is the reciprocal-lattice vector of length 1.525 ${\mathrm{\AA }}^{-1\mathrm{}}$, some extra intensity is observed near an energy of 1.4 meV. Evidence that this intensity is indeed real and anomalous, some four times as much as expected from single-phonon scattering, is presented. The physical origin of this extra scattering is not presently known.