Abstract
We present an analytic approach to the solution of the time-dependent Newns-Anderson model of charge transfer during atom-surface scattering. For sufficiently slow atomic velocities we show, using a WKB technique, that the time evolution of the electronic state of the atom is determined by the instantaneous quasiparticle energies of the coupled atom plus surface system. Surface electronic structure and level-crossing effects are thus incorporated into the theory in a natural way. The results of the analysis compare quite favorably with numerical solutions and recently discovered exact solutions.
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