Anderson impurity model: Vertex corrections within the finite U non-crossing approximation

We revise the simplest possible approximations to solve numerically the vertex equations for the single impurity Anderson model (SIAM) within the finite U   non-crossing approximation (UNCA), considering the self-energies at lowest order in the 1/N1/N diagrammatic expansion. We introduce an approximation to the vertex corrections that includes the double energy dependence and compare it with an approximation (NCAf22v) that neglects a second energy argument. Finally, we analyse the influence of the different approximations on the estimated Kondo scale for simple electronic models.