On the collinear and quasi-collinear spontaneous decay of long-wavelength acoustic phonons

For quasi-collinear decay processes of non-dispersive acoustic phonons via cubic anharmonicity, the lowest-order perturbation theory leads to results that depend sensitively on the curvatures of the slowness surface and are partly divergent. The existence of these divergences does not seem to have been realised in previous calculations. The influence of the dispersion is discussed.