  When surface state electrons scatter at perturbations, such as magnetic or
nonmagnetic adatoms or clusters on surfaces, an electronic resonance, localized
at the adatom site, can develop below the bottom of the surface state band for
both spin channels. In the case of adatoms, these states have been found very
recently in scanning tunneling spectroscopy experiments\cite{limot,olsson} for
the Cu(111) and Ag(111) surfaces. Motivated by these experiments, we carried
out a systematic theoretical investigation of the electronic structure of these
surface states in the presence of magnetic and non-magnetic atoms on Cu(111).
We found that Ca and all 3$d$ adatoms lead to a split-off state at the bottom
of the surface band which is, however, not seen for the $sp$ elements Ga and
Ge. The situation is completely reversed if the impurities are embedded in the
surface: Ga and Ge are able to produce a split-off state whereas the 3$d$
impurities do not. The resonance arises from the s-state of the impurities and
is explained in terms of strength and interaction nature (attraction or
repulsion) of the perturbing potential.
