  Wavepacket propagation calculations are reported for the interaction of a
Rydberg hydrogen atom ($n=2-8)$ with Cu(111) and Cu(100) surfaces (represented
by a Chulkov potential), in comparison with a Jellium surface. Both copper
surfaces have a projected band gap at the surface in the energy range
degenerate with some or all of the Rydberg energies. The charge transfer of the
Rydberg electron to the surface is found to be enhanced for $n$ values at which
there is a near-degeneracy between the Rydberg energy level and an image state
or a surface state of the surface. The enhancement is facilitated by the strong
overlap of the surface image-state orbital lying outside the surface and the
orbital of the incoming Rydberg atom. These calculations point to the
possibility of using Rydberg-surface collisions as a probe of surface
electronic structure.
