  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, $\sigma_{\rm
inel}(\omega)$. We find an almost linear frequency dependence of $\sigma_{\rm
inel}(\omega)$ below the Kondo temperature, $T_K$, which crosses over to a
$\sim \omega^2$ behavior only at extremely low energies. Our method can be
generalized to other quantum impurity models.
