  We calculate the conductance spectra of a Co atom adsorbed on Cu(111),
considering the Co $3d$ orbitals within a correlated multiple configurations
model interacting through the substrate band with the Co $4s$ orbital, which is
treated in a mean-field like approximation. By symmetry, only the $d_{z^2}$
orbital couples with the $s$ orbital through the Cu bands, and the interference
between both conduction channels introduces a zero-bias anomaly in the
conductance spectra. We find that, while the Kondo resonance is mainly
determined by the interaction of the Co $d$ orbitals with the bulk states of
the Cu(111) surface, a proper description of the contribution given by the
coupling with the localized surface states to the Anderson widths is crucial to
describe the interference line shape. We find that the coupling of the Co $4s$
orbital with the Shockley surface states is responsible of two main features
observed in the measured conductance spectra, the dip shape around the Fermi
energy and the resonance structure at the surface state low band edge.
