Basic matrix elements for level shifts and widths of hydrogenic levels in ion-surface interactions.

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. @S1050-2947~96!02408-0#