Flow-Equation method for a superconductor with magnetic correlations

The flow equation method has been used to calculate the energy of single impurity in a superconductor for the Anderson model with $U \neq 0$. We showed that the energy of the impurity depends only of the $\Delta^{2}_{R}$ (renormalized order parameter) which depends on the renormalized Hubbard repulsion$U^R$. For a strong Hubbard repulsion $U^R = U$ and $\Delta^R = \Delta ^I$ the effect of the $s-d$ interactions are nonrelevant, a result which is expected for this model.