  We determine the wavefunctions of electrons bound to a positively charged
mesoscopic metallic cluster covered by an insulating surface layer. The radius
of the metal core and the thickness of the insulating surface layer are of the
order of a couple of angstroems. We study in particular the electromagnetic
decay of externally located electrons into unoccupied internally located states
which exhibits a resonance behaviour. This resonance structure has the
consequence that the lifetime of the `mesoscopic atoms' may vary by up to 6
orders of magnitude depending on the values of the parameters (from sec to
years).
