Effect of pair breaking on branch relaxation in nonequilibrium superconductors

The kinetic (Boltzmann) equation for the quasiparticle distribution function in the presence of electron-phonon and magnetic-impurity scattering is derived and its solution is analyzed. It is shown that the phonon collision integral makes two contributions to the branch imbalance relaxation time. The first is associated with inelastic scattering of quasiparticles within a branch, and the second with pair breaking associated with between-branch relaxation. The latter can be combined with the magnetic-impurities collision integral to yield a single pair-breaking term. Branch-branch relaxation is shown to be proportional to the square root of the product of the in-branch and between-branch relaxation rates.