Theory of inelastic scattering from magnetic impurities

Abstract

We use the numerical renormalization group method tocalculate the single particle matrix elements $\cal T$ of the many body $T$-matrix of the conduction electrons scattered by a magnetic impurity at T=0 temperature. Since $\cal T$ 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, $σ_{\rm inel}(ω)$. We find an almost linear frequency dependence of $σ_{\rm inel}(ω)$ below the Kondo temperature, $T_K$, which crosses over to a $\sim ω^2$ behavior only at extremely low energies. Our method can be generalized to other quantum impurity models.