Abstract
We present selected results from combined analytical and numerical studies of the Anderson-impurity model within the framework of infinite-order perturbation theory with respect to the hybridization. Our approximation goes considerably beyond the well-known non-crossing approximation (NCA): the resummations include skeleton diagrams up to infinite order of the crossing variety, including all 1/N2 contributions (N = degeneracy of the magnetic state). We demonstrate, in a comparison with NCA theory, changes in the threshold behaviour of local propagators, a qualitative improvement of spectral properties and a clear progress in attaining local Fermi-liquid properties. Further applications of the post-NCA theory are pointed out.