Thermodynamics of the Anderson impurity with finite on-site Coulomb interaction

We develop here an analytical approximation to the vertex correction and also to relevant spectral functions which appear within the Non-Crossing Approximation (NCA) for the Anderson impurity model with finite on-site Coulomb interaction U. The computations are greatly reduced by this approach and may be done when the Crystalline Electric Field (CEF) is incorporated. At zero temperature our theory reproduces the Gunnarson-Schönhammer (GS) variational results [1] and for U → ∞ the ZZF approximate scheme [2] evolves, f-state populations and the BIS part of the f-electron spectral function are presented here for typical Ce³⁺ and Yb³⁺ parameters.