Theory of inelastic scattering from magnetic impurities

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We use the numerical renormalization group method tocalculate 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, Tₖ, which crosses over to a ω² behavior only at extremely low energies. Our method can be generalized to other quantum impurity models.