Computation of Phonon Spectral Functions and Ground-State Energy of Solid Helium. I. bcc Phase

Abstract

Computations incorporating the three-phonon interaction process are presented of phonon spectral functions, yielding frequency and lifetime dispersion curves, for the bcc solid phase of both ${\mathrm{He}}^{3}$ and ${\mathrm{He}}^{4}$. Comparison of the compressibilities obtained from ground-state energy and elastic constants as functions of molar volume quantify the effects of certain analytical approximations. A model calculation shows the sensitivity of elastic anisotropy and long-wavelength dispersions to the precise form of the three-phonon vertex.