Ionization of a Model Atom: Exact Results and Connection with Experiment

We prove that a model atom having one bound state will be fully ionized by a time periodic potential of arbitrary strength $r$ and frequency $\omega$. The survival probability is for small $r$ given by $e^{-\Gamma t}$ for times of order $\Gamma^{-1} \sim r^{-2n}$, where $n$ is the number of ``photons'' required for ionization, with enhanced stability at resonances. For late times the decay is like $t^{-3}$. Results are for a 1d system with a delta function potential of strength $-g(1 + \eta (t))$ but comparison with experiments on the microwave ionization of excited hydrogen atoms and with recent analytical work indicate that many features are universal.