Mean-trajectory approximation for charge- and energy-transfer processes at surfaces

We discuss electronic energy and charge-transfer processes at surfaces in terms of curve-crossing models. We suggest that at low kinetic energies the trajectory approximation should be replaced by a mean-trajectory approximation (MTA), in which the nuclear motion gets feedback from and adjusts to the curve-crossing dynamics. We discuss two derivations of MTA by using an eikonal approximation and a path-integral method. The effects of phonon or electron-hole pair excitations on the charge-transfer process are also incorporated.