RESONANCE FORMATION OF HYDROGENIC LEVELS IN FRONT OF METAL-SURFACES

The electronic self-energy of hydrogenic ions interacting with a jelli um metal surface is studied within the fixed-ion approximation. A mode l framework is introduced that allows for the efficient computation of the complex (non-Hermitian) self-energy matrix in a large space of (b ound) hydrogenic states. For the specific case of protons interacting with an aluminum surface, resonance energies and widths of dressed ion ic states are obtained by diagonalizing the self-energy matrix. The hy bridization properties pf the dressed ionic states are analyzed. The s elf-energy of individual dressed states is found to converge rapidly w ith increasing dimension of the space of unperturbed hydrogen states. The resonance energies are compared to (1) energies obtained by diagon alizing only the direct couplings among the hydrogen states and (2) th e real part of the diabatic (diagonal) self-energy. This comparison de monstrates the pronounced effect that indirect couplings between hydro gen states via conduction band states have on the resonance-energies a t intermediate and small ion-surface distances. Our results for incide nt protons are confronted with the results of other (perturbative and nonperturbative) calculations of level shifts and widths in proton-sur face interactions. Although we use a simplified electronic potential, we find good agreement with calculations employing more refined potent ials.