Using the rigid-ion model, we have calculated the lifetime of longitudinal-acoustic phonons in Ca${\mathrm{F}}_2$ with frequency $\nu$ between 2.5 and 5.5 THz at low crystal temperatures. Neutron scattering data and temperature-dependence data of the second-order elastic constants have been used to determine the parameters of the theory. The results show a marked anisotropy and a small deviation from the long-wavelength approximation. The overall agreement with recent experiments is good but suggests a more careful analysis of the raw experimental data.

• Received 18 March 1982

DOI:https://doi.org/10.1103/PhysRevB.26.2208