Anharmonic decay and the propagation of phonons in an isotopically pure crystal at low temperatures: Application to dark-matter detection

Abstract

We consider the propagation and anharmonic decay of high-energy phonons introduced into a perfect dielectric crystal at low temperatures. The phonon-decay rate is calculated for an fcc model with central forces between nearest neighbors. We give an approximate relation between the parameters entering into this model and the experimentally known properties of real crystals. A discussion is given of the range of wave vectors over which slow transverse phonons are stable against anharmonic decay. These results are relevant to the design of experiments to detect dark matter via the study of the phonons excited in a crystal when a dark-matter particle scatters off a nucleus. We discuss the primary phonon production mechanism and the possibility that there is an anisotropy of the phonon flux that is related to the direction in which the nucleus recoils.