We propose a model to treat the local motion of atoms in solid ${}^4\mathrm{He}$ as a local mode. In this model, the solid is assumed to be described by the self-consistent harmonic approximation, combined with an array of local modes. We show that in the bcc phase the atomic local motion is highly directional and correlated, while in the hcp phase there is no such correlation. The correlated motion in the bcc phase leads to a strong hybridization of the local modes with the $T_1\mathrm{}\left(110\right)\mathrm{}$ phonon branch, which becomes much softer than that obtained through a self-consistent harmonic calculation, in agreement with experiment. In addition, we predict a high-energy excitation branch that is important for self-diffusion. Both the hybridization and the presence of a high-energy branch are a consequence of the correlation, and appear only in the bcc phase. We suggest that the local modes can play the role in mass transport usually attributed to point defects (vacancies). Our approach offers a more overall consistent picture than obtained using vacancies as the predominant point defect. In particular, we show that our approach resolves the long-standing controversy regarding the contribution of point defects to the specific heat of solid ${}^4\mathrm{He}.$

• Received 30 December 1998

DOI:https://doi.org/10.1103/PhysRevB.60.1019