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The ionisation of two simple systems in intense electromagnetic fields is studied by numerical integration of the time-dependent Schrodinger equation. The first system has a single bound state. The second system has two bound states and resonant two-photon ionisation can be studied. It is found that, for both systems, ionisation is very rapid with high fields and a perturbation theory description is not valid. In addition, a constant transition rate is not observed at short times. In the two-photon case conventional resonant behaviour is not observed at either high or low fields.
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Elizabeth J. Austin (1979) studied this question.
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