Resonance formation of hydrogenic levels in front of metal surfaces

The electronic self-energy of hydrogenic ions interacting with a jellium metal surface is studied within the fixed-ion approximation. A model framework is introduced that allows for the efficient computation of the complex (non-Hermitian) self-energy matrix in a large space of (bound) hydrogenic states. For the specific case of protons interacting with an aluminum surface, resonance energies and widths of dressed ionic states are obtained by diagonalizing the self-energy matrix. The hybridization properties of the dressed ionic states are analyzed. The self-energy of individual dressed states is found to converge rapidly with increasing dimension of the space of unperturbed hydrogen states. The resonance energies are compared to (1) energies obtained by diagonalizing only the direct couplings among the hydrogen states and (2) the real part of the diabatic (diagonal) self-energy. This comparison demonstrates the pronounced effect that indirect couplings between hydrogen states via conduction band states have on the resonance energies at intermediate and small ion-surface distances. Our results for incident protons are confronted with the results of other (perturbative and nonperturbative) calculations of level shifts and widths in proton-surface interactions. Although we use a simplified electronic potential, we find good agreement with calculations employing more refined potentials.