Resonant electron transfer at metal surfaces: Theoretical analysis of scaling properties and universal behavior

Abstract

The resonant electron transfer processes that occur when slowly moving atoms and (positive) ions interact with metal surfaces are theoretically analyzed with regard to scaling properties and universal behavior. Within the first-order adiabatic approximation, a simple model is employed that allows a systematic (formal and numerical) study of the dependence of transition matrix elements and transition rates upon the parameters characterizing the ion-metal system. Scaling parameters are introduced, through which scale transformations of the system parameters are defined. The ion-surface distance, in particular, is scaled by means of the ‘‘classical threshold distance,’’ below which, at given electronic energy, resonant electron transfer is classically allowed. When transformed to the scaled representation, transition matrix elements and rates are found to be expressible in terms of ‘‘reduced,’’ universal functions, which are independent of the parameters characterizing the strength of the electronic potentials in the ion-metal system. In the limit of large ionic principal quantum numbers, the behavior of transition matrix elements and rates is largely determined by three universal functions that depend on the scaled ion-surface distance only. Scaling laws connecting transition matrix elements and rates for different ionic principal quantum numbers are established. Resonance neutralization of highly charged ions and resonance ionization of Rydberg atoms are considered as specific cases. Quasiclassical aspects and possible applications of our results as well as extensions of our analysis are briefly discussed.