Theory of the atomic limit of the Anderson model. I. Perturbation expansions re-examined

A perturbation expansion about the atomic limit of the Anderson model is formulated in the limit of infinite conduction bandwidth. Terms up to second order in Delta are constructed in various temperature regimes; non-logarithmic terms are explicitly given. Particular care is taken to expose the structure of perturbation theory in the valence fluctuation limit. An expression for the Kondo temperature is obtained and compared with numerical results. The structure of the expansion is commented on in the light of scaling theory.