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 $U\mathrm{\ne }0$. We showed that the energy of the impurity depends only of the ${\mathrm{\Delta }}_R^2$ (renormalized order parameter) which depends on the renormalized Hubbard repulsion$U^R$. For a strong Hubbard repulsion $U^R=U$ and $\Delta^R = \Delta ^I$theeffectofthe$s-d$ interactions are nonrelevant, a result which is expected for this model.