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, $K\propto J^4\mathrm{/}{E}^2$. The exchange constant J is renormalized due to the Kondo effect, yielding an additional weak dependence of K on the energies of the colliding electrons. At small energy transfers, the $1\mathrm{/}{E}^2$ divergence is cut off; the cut-off 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.