Infrared catastrophe in two-quasiparticle collision integral

Relaxation of a non-equilibrium state in a disordered metal with a spin-dependent electron energy distribution is considered. The collision integral due to the electron-electron interaction is computed within the approximation of a two-quasiparticle scattering. We show that the spin-flip scattering processes with a small energy transfer may lead to the divergence of the collision integral for a quasi one-dimensional wire. This divergence is present only for a spin-dependent electron energy distribution which corresponds to the total electron spin magnetization $\mathcal M=0$ and only for non-zero interaction in the triplet channel. In this case a non-perturbative treatment of the electron-electron interaction is needed to provide an effective infrared cut-off.