Renormalized parameters for impurity models

We show that the low energy behaviour of quite diverse impurity systems can be described by a single renormalized Anderson model, with three parameters, an effective level (epsilon) over tilde (d), an effective hybridization (V) over tilde, and a quasiparticle interaction (U) over tilde. The renormalized parameters are calculated as a function of the bare parameters for a number of impurity models, including those with coupling to phonons and a Falikov-Kimball interaction term. In the model with a coupling to phonons we determine where the interaction of the quasiparticles changes sign as a function of the electron-phonon coupling. In the model with a Falikov-Kimball interaction we show that to a good approximation the low energy behaviour corresponds to that of a bare Anderson model with a shifted impurity level.