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.
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