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We have studied one and two monolayers of barium on Ni(111) and of mercury on Cu(100). Using resonant photoemission, we have found core excited electrons become delocalized with increasing barium coverage. Similarly, upon formation of the mercury bilayer (as determined by low-energy electron diffraction and by atom-beam scattering), there is a substantial increase in the screening of the photohole. A transition of the electronic structure akin to a metal-nonmetal (metal-insulator) transition is apparent in these final-state effects. The band structure for Hg is similar to the band structure expected for a free-standing film with a free-electron sd band. The delocalization of the core excited electrons resembles the exciton unbinding that occurs at the metal-nonmetal Mott transition.