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broadening of atomic levels near thin metallic films is studied theoretically within the fixed-atom approximation. § First-order level widths are calculated by using a Jennings-type jellium potential to describe the electronic states of the film, and hydrogenic wave functions in parabolic © S tark representation for the atomic orbitals.

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-Hermitian͒ self-energy matrix in a large space of ͑bound͒ 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 ͑1͒ energies obtained by diagonalizing only the direct couplings among the hydrogen states and ͑2͒ the real part of the diabatic ͑diag-onal͒ 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 nonper-turbative͒ 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.

We present extensive studies of basic one-electron matrix elements involved in ion-metal surface scattering theory. Our method allows for the convenient generation of matrix elements for high principal quantum numbers of hydrogenic projectile states and thus provides basic building blocks for the ab initio description of the interaction of highly charged ions with surfaces. The matrix elements related to the energy shifts can be evaluated for an arbitrary one-dimensional potential therefore allowing for flexibility in the choice of modelperturbation potentials. The transfer matrix elements between hydrogenic levels and conduction-band states have been formerly evaluated for the special case of eigenfunctions to the step-function potential. We extend these calculations to wave functions generated from an arbitrary one-dimensional surface potential and show applications to various surface potentials and hydrogenic levels. ͓S1050-2947͑96͒02408-0͔

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