We describe new exact results for a model of ionization of a bound state, induced by an oscillating potential. In particular we have obtained exact expressions, in the form of readily computable rapidly convergent sums, for the energy distribution of the emitted particles as a function of time, frequency and strength of the oscillating potential. Going beyond perturbation theory, these show resonances in the energy distribution which look like single or multi-photon absorption, similar to those observed in laser induced electron emission from solids or atoms. This is particularly so when the strength of the oscillating potential is small compared to the binding energy but is still visible for large fields, and even for time-periods of a few oscillations. We have also obtained the space-time structure of the wave function. Our model exhibits a form of stabilization; the ionization probability is not monotone in the strength of the oscillating potential.
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