  We have considered the relaxation of transverse thermal and high-frequency
phonons for the Landau-Rumer mechanism in the semiconductor cubic crystals.
Using the known values of these elastic moduli, the parameters determining the
transverse phonon relaxation rates for the Landau-Rumer mechanism have been
evaluated for the crystals under consideration. It is shown that the dependence
of the relaxation rate on the wave vector of thermal and high-frequency phonons
strongly differs from the classical Landau-Rumer relationship both in the
isotropic medium and in the cubic crystals studied. In contrast to the
isotropic medium, for Ge, Si, InSb, and GaSb crystals in the [100] direction,
this dependence has an essentially non-monotonic character with two maxima, the
second of which is in the range of high-frequency phonons. This anomaly in the
[100] direction is most pronounced for InSb and GaSb crystals. The features of
the relaxation rate are found to result from the angular dependence of the
probability of anharmonic scattering and from the anisotropy of elastic
properties.
