Renormalized parameters and perturbation theory for an n-channel Anderson model with Hund's rule coupling

We extend the renormalized perturbation theory for the single impurity Anderson model to the n-channel model with a Hund's rule coupling, and show that the exact results for the spin, orbital and charge susceptibilities, as well as the leading low temperature dependence for the resistivity, are obtained by working to second order in the renormalized couplings. A universal relation is obtained between the renormalized parameters, independent of n, in the Kondo regime. An expression for the dynamic spin susceptibility is also derived by taking into account repeated quasiparticle scattering, which is asymptotically exact in the low frequency regime and satisfies the Korringa-Shiba relation. The renormalized parameters, including the renormalized Hund's rule coupling, are deduced from numerical renormalization group calculations for the model for the case n=2. The results confirm explicitly the universal relations between the parameters in the Kondo regime. Using these results we evaluate the spin, orbital and charge susceptibilities, temperature dependence of the low temperature resistivity and dynamic spin susceptibility for the particle-hole symmetric n=2 model.