Transport and relaxation processes in superfluidHe3close to the transition temperature

We derive the Boltzmann equation describing long-wavelength low-frequency transport and relaxation processes in a superfluid Fermi liquid close to the transition temperature $T_c$. In the superfluid, the quasiparticle number is not conserved and therefore one has to take into account the decay of one quasiparticle into three and the inverse process, as well as the two-quasiparticle scattering process. We calculate the collision term in the Boltzmann equation to first order in the superfluid gap $\Delta$ and show that it is related rather simply to the corresponding normal-state collision term. As applications of the Boltzmann equation, we solve it exactly to calculate the shear viscosity, and the intrinsic spin relaxation rate. The shear viscosity drops as $\Delta \propto {(T_c-T)}^{\frac{1}{2}}$ for temperatures just below $T_c$, and we determine the coefficient of $\Delta$ as a function of the normal-state collision probability. Leggett and Takagi's characteristic spin-relaxation time is shown to be equal to the relaxation time of a normal-state quasiparticle at the Fermi energy at $T_c$. The results provide one with a useful consistency check on experimental measurements which is independent of any assumption about the normal-state collision probability.