  The electronic properties of a semi-infinite metal surface without a bulk gap
are studied by a formalism able to account for the continuous spectrum of the
system. The density of states at the surface is calculated within the $GW$
approximation of many-body perturbation theory. We demonstrate the presence of
an unoccupied surface resonance peaked at the position of the first image
state. The resonance encompasses the whole Rydberg series of image states and
cannot be resolved into individual peaks. Its origin is the shift in spectral
weight when many-body correlation effects are taken into account.
