Theory of Inelastic Scattering from Magnetic Impurities

We use the numerical renormalization group method to calculate the single-particle matrix elements T of the many-body T matrix of the conduction electrons scattered by a magnetic impurity at T=0 temperature. Since T determines both the total and the elastic, spin-diagonal scattering cross sections, we are able to compute the full energy, spin, and magnetic field dependence of the inelastic scattering cross section σ_inel(ω). We find an almost linear frequency dependence of σ_inel(ω) below the Kondo temperature T_K, which crosses over to a ω² behavior only at extremely low energies. Our method can be generalized to other quantum impurity models.