  We present numerical renormalization group (NRG) calculations for a
single-impurity Anderson model with a linear coupling to a local phonon mode.
We calculate dynamical response functions, spectral densities, dynamic charge
and spin susceptibilities. Being non-perturbative, the NRG is applicable for
all parameter regimes. Our calculations cover both weak and strong
electron-phonon coupling for zero and finite electron-electron interaction. We
interpret the high- and low-energy features and compare our results to atomic
limit calculations and perturbation theory. In certain restricted parameter
regimes for strong electron-phonon coupling, a soft phonon mode develops
inducing a very narrow resonance at the Fermi level.
