Matrix elements for level shifts and widths of hydrogenic levels in ion-surface interactions

The authors present a derivation of basic one-electron matrix elements involved in the ion-metal surface scattering theory. Their method allows for the convenient generation of matrix elements for high principal quantum numbers of the projectile states and thus provides basic building blocks for the ab-initio description of highly charged ion-surface interactions. The matrix elements related to the energy shifts can be evaluated for an arbitrary one-dimensional potential therefore allowing the inclusion of electronic and nuclear self-image potentials. The authors extend these concepts to wave functions generated from an arbitrary one-dimensional surface potential and show applications to various surface potentials, projectile nuclear charges and hydrogenic levels