  A new type of perturbation expansion in the mixing $V$ of localized orbitals
with a conduction-electron band in the $U\to\infty$ Anderson model is
presented. It is built on Feynman diagrams obeying standard rules. The local
correlations of the unperturbed system (the atomic limit) are included exactly,
no auxiliary particles are introduced. As a test, an infinite-order ladder-type
resummation is analytically treated in the Kondo regime, recovering the correct
energy scale. An extension to the Anderson-lattice model is obtained via an
effective-site approximation through a cumulant expansion in $V$ on the
lattice. Relation to treatments in infinite spatial dimensions are indicated.
