Selfconsistent hybridization expansions for static properties of the Anderson impurity model

By means of a projector-operator formalism we derive an approximation based on a self consistent hybridization expansion to study the ground state properties of the Anderson Impurity model. We applied the approximation to the general case of finite Coulomb repulsion $U$, extending previous work with the same formalism in the infinite-$U$ case. The treatment provides a very accurate calculation of the ground state energy and their related zero temperature properties in the case in which $U$ is large enough, but still finite, as compared with the rest of energy scales involved in the model. The results for the valence of the impurity are compared with exact results that we obtain from equations derived using the Bethe ansatz and with a perturbative approach. The magnetization and magnetic susceptibility is also compared with Bethe ansatz results. In order to do this comparison, we also show how to regularize the Bethe ansatz integral equations necessary to calculate the impurity valence, for arbitrary values of the parameters.