The Relaxation of High Energy Phonons in Anisotropic Distributions in Superfluid 4He

Anisotropic distributions of low energy phonons in momentum space, in superfluid helium, create high energy phonons with energy (epsilon)/k B>10K. It has been shown that phonons with (epsilon)/k B>11K cannot decay by the inverse of the process that creates them, if the low energy phonons are in such a momentum cone of 11°. Here we investigate other possible phonon scattering processes that could annihilate high energy phonons. We find that interactions between two high energy phonons, which can create one low and one high energy phonon, is effective. We calculate the scattering rates for all the four phonon processes as functions of momentum of the high energy phonon, cone angle and the temperature of the low energy phonons. We obtain analytic results from which we can understand the physical reasons for all the functional dependencies. The analytic results are in good agreement with our computer evaluations. We show that a dynamic equilibrium number of high energy phonons can be established in a propagating pulse of phonons and the distribution will be suprathermal.