Four- and three-phonon scattering in isotropic superfluid helium Available to Purchase

We analyze the important role of four-phonon processes (4pp) in isotropic phonon systems of superfluid helium. The matrix elements and the rate of four-phonon processes are calculated. Special consideration is given to the 4pp in the momentum range where three-phonon processes are allowed. In this momentum range, we show that the 4pp scattering rate, at small angles, is equal to the scattering rate due to three-phonon processes. Then we show that the coefficient of first viscosity of superfluid helium is caused by two processes: the first is due to the transverse relaxation caused by many three-phonon processes, and the second is due to four-phonon processes. The relaxation time that governs the viscosity is obtained from the sum of the rates due to these two processes. The temperature dependence of the attenuation coefficient of a pulse of high-energy phonons in He II, due to scattering with thermal phonons, is also calculated. The theoretical results are compared with experimental data and found to be in good agreement.