Static and dynamic susceptibility of a mixed-valence impurity

A mixed-valence Anderson impurity with orbital degeneracy and the two active configurations corresponding to ${4f}^0$ and ${4f}^1$ is considered in the $U\to \infty$ limit. The static charge and spin susceptibilities are obtained through the one-$f$-electron propagators and compared with the results within the Brillouin-Wigner scheme. The dynamic susceptibilities are calculated by means of Mori's technique. The charge- and spin-relaxation rates are discussed, as well as bumps due to charge excitations.