Lattice Excitations of theHe4Quantum Solids

Abstract

Extensive inelastic-neutron-scattering experiments have been carried out on single crystals of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ in the bcc and low-density hcp phases. The results of our present and previous measurements have established the over-all characteristics of the scattering function $S(Q,\omega )$ for a wide range of energy and momentum transfers. The general features of the scattering function can be described as showing well-defined, sharp, elementary excitations at energy transfers $\hslash \omega <1.0\mathrm{}$ meV, and single-particle excitations for scattering vectors $\mathrm{}\left|Q\right|>3.0\mathrm{}$ ${\mathrm{\AA }}^{-1\mathrm{}}$ and $\hslash \omega >5.0\mathrm{}$ meV. The changes in the structure of the scattering function to accommodate these two different excitations occur in an ill-defined "transition" region, wherein the spectral response of the sharp excitation gradually becomes more distorted and merges with the multiexcitation response at the higher energies. In the low-energy regime, the scattering cross section for sharp excitations observed in the [$0\overline{1}1$] zone for the bcc phase is found to be unusual in that the effective Debye-Waller factor constructed from the data via the Ambegaokar, Conway, and Baym sum rule displays oscillations. The data for the lowest transverse branch $T_1$, however, do not show oscillations. In our previous work, this anomalous cross section appeared to be associated with an energy transfer of ∼ 1.4 meV, and a concomittant distortion in the Gaussian-like spectral response. The present results show that this is not the case. The unexpected behavior of the cross section was observed for sharp, symmetric excitations whose energy distribution has no extraordinary contribution near 1.4 meV. The measurements in the hcp phase show that these anomalous features of the scattering function are similar in both phases. The high-resolution measurements on the sharp excitations at small wave vector were used to construct a self-consistent set of elastic constants. These elastic constants are considerably more accurate than those from previous measurements. They suggest that the dispersion of the $T_1$ mode in the [011] direction need not be anomalous, in contrast to recent theoretical results. Finally, at high energy and momentum transfers, single-particle excitations are observed in both phases. Their dispersion relation is isotropic, and is the same in both phases within the accuracy of the measurements. The profiles of these excitations are very similar to those recently observed by Woods and Cowley in the superfluid phase.