Electron energy relaxation in the presence of magnetic impurities

We study inelastic electron-electron scattering mediated by the exchange interaction of electrons with magnetic impurities and find the kernel of the corresponding two-particle collision integral. In a wide region of parameters, the kernel K is proportional to the inverse square of the transferred energy, K proportional to J4/E2. The exchange constant J is renormalized due to the Kondo effect. At small energy transfers, the 1/E2 divergence is cut off; the cutoff energy is determined by the dynamics of the impurity spins. The obtained results may provide a quantitative explanation of the experiments of Pothier et al. [Phys. Rev. Lett. 79, 3490 (1997)] on anomalously strong energy relaxation in short metallic wires.