Elastic scattering of acoustic phonons on point mass defects

The problem of eigenvalues of the collision operator for a gas of acoustic phonons scattered by point mass defects of small concentration embedded in transversely isotropic media is considered. For this purpose the properties of solution of the Boltzmann-Peierls kinetic equation for spatially homogeneous states are studied. An analytic formula for the Laplace transform of the distribution function is obtained. The singularities of this Laplace transform and the initial distribution function determine the dependence of this distribution function on time. For several hexagonal materials characteristics of the singularity set are calculated. Usually the singularity set consists of a continuous part and four discrete points. However, there exist elastic hexagonal materials (⁴He, Cd, Ta, Zn) for which some of discrete points are absent. For some materials (e.g. Zr) the continuous part is very narrow.