Theory of the Phonon Contribution to the Attenuation of Second Sound in 3He–4He Mixtures

We have extended Saam's theory of the attenuation of second sound in ³He-⁴He mixtures to finite frequencies and have included both phonon-phonon interactions and phonon-roton interactions. The theory accounts qualitatively both for the peak in the attenuation of second sound around 0.5K found by Greywall and for the frequency dependence of the attenuation. We obtain a good quantitative fit to the data of Greywall taken at 20 bar when we include the five phonon process. For the data at 0 bar the agreement is good up to 0.3K; above this temperature the agreement is considerably poorer. We ascribe this discrepancy to the three phonon process which is an allowed process at zero bar.