Abstract
Within the framework of a time-dependent Anderson-Newns model, charge exchange between an atomic particle and a surface with a finite band of electronic states is considered. Asymptotically exact solutions of the model for different time dependences of hopping matrix elements between the atomic and band states are derived. It is shown that for a finite energy band, the resulting charge state of the atomic particle can be a non-monotonic function of its energy only when the time dependence of the coupling has an adiabatically part.
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