Four- and three-phonon scattering in isotropic superfluid helium

Abstract

We analyse 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 from 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. PACS: 47.37.+q Hydrodynamic aspects of superfluidity; quantum fluids.

Creation of high-energy phonons in superfluidH4eand the dependence of their angular distribution on heater size

“…There is also a much slower scattering by the fourphonon process, 4pp. 20,21 This process does conserve phonon number as two phonons scatter to give two new phonons, again, with energy and momentum conserved. It is the 4pp scattering which creates the high-energy phonons while the 3pp scattering maintains the quasiequilibrium between the low-energy phonons.…”