Rydberg states of the hydrogen atom near a metal surface

We consider n = 20 Rydberg states of the hydrogen atom interacting with a nearby metal surface over an atom-surface distance range of 105 nm-530 nm. We show that the traditional quadratic approximation to the potential is insufficient to follow the true potential and one needs to include higher order terms to obtain accurate energies for these Rydberg states. We include terms up to eighth order in the electron-proton distance in the potential and demonstrate by means of basis set calculations that the resulting spectra differ significantly from those obtained in the quadratic approximation. We observe an energy spread of the n = 20 manifold which is roughly twice that given by the quadratic approximation. Observed level repulsions are attributed to z-parity symmetry breaking. We compare our results with those from degenerate perturbation theory.