Notes on the theory of atom/molecule-surface scattering

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Abstract
The aim of this lecture is to discuss in as pedagogic a fashion as possible and from the point of view of theory some aspects of collision phenomena at surfaces. These phenomena can be very complicated. In particular collisions that result in chemical reaction – e.g., dissociation of molecules – are complex in the sense that the adiabatic approximation, where the electrons are assumed to adapt instantaneously to the motion of the nuclei, is invariably suspect and often manifestly irrelevant. The theoretical problem posed by such collisions is therefore rather intractable and only very simple model systems can be treated [1]. I restrict myself of mechanical collisions characterized by a single potential energy surface V(rp, {ri}), where rp, {ri} are the coordinates of the particle, P, and the lattice nuclei, respectively. V is the electronic ground-state energy with the nuclear coordinates held fixed. This restriction simplifies the problem, which, however, remains far from trivial. We are still left with a many-body-problem involving a potentially infinite number of particles that has been solved only numerically and in the classical limit. If we want more than this, we have to pick away at the problem as best we can using intuition and taking guidance from experiment.