Extension of the Non-Crossing Approximation for the Anderson Model with   Finite Coulomb Repulsion
  The non-crossing approximation (NCA) is generalized for the Anderson model with finite Coulomb repulsion U. Resummation of infinite number of terms is performed so as to incorporate all leading contributions in the limit of large degeneracy of the local states. With negligible weight of the doubly occupied local states in equilibrium, the extension is achieved through simple modifications of the lowest order formulae. The single-particle excitation spectrum is calculated with almost the same computational effort as in the original NCA. The present scheme reproduces the scaling behavior of the Kondo resonance in the density of states, and gives reasonable description of thermodynamics of the finite-U Anderson model over a wide range of temperature. 
J. Otsuki and Y. Kuramoto