\[fig4\], we have plotted the resonance arising from such a potential on both the impurity site (IS) and nearest neighbor site (NN), for various values of the gap size in the local patch around the impurity, as for the Ni case. There are two obvious difficulties. The first is the well-known problem discussed above, that the intensity on the IS is substantially smaller than on the NN site, in contradiction to experiment. The second problem relates to the behavior of the resonance in different types of local patches. The resonance is suppressed somewhat in the large-gap regions corresponding to Fig. \[fig4\](e-f), but is still clearly visible. In fact, it is clear that the gap modulation $\delta \Delta$ has simply detuned the resonance and acts, via its coupling through the $T$-matrix equations to the diagonal channel, as a renormalization of the impurity potential. The clear splitting of the resonance and shift of the peak with increasing $\delta \Delta$ is obvious in panels (b,d,f). The inability of the conventional screened Coulomb model for Zn to explain the real disappearance of the resonances in the large-gap regions with this scenario was emphasized recently by Kirćan,[@kircan] who studied a similar model.

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