Exact results for ionization of a model atom

Summary form only given.We investigate some fundamental aspects of the process underlying electron production via atomic ionization by external fields. Using a combination of exact analytic and controlled numerical methods we obtain in Costin et al., (2000) rigorous qualitative and quantitative results for a model atom having one bound state with energy hbar/spl omega//sub 0/. In particular we prove that this system will be fully ionized by a time periodic field r/spl eta/(t) of arbitrary frequency /spl omega/ and arbitrary strength r for almost all shapes of /spl eta/(t). (There are however exceptional /spl eta/(t) for which full ionization fails). In the case of a harmonic /spl eta/(t)=sin(/spl omega/t) the survival probability of the bound state for small r is given by e/sup -1/, for times of order /spl Gamma//sup -1,/ with /spl Gamma//spl sim/r/sup 2n/, where n is the minimum number of "photons" required for ionization (with large modification at resonances). For late times the survival probability is oscillatory with an envelope that decays like t/sup -3/. The onset of the power law, replacing the exponential regime, occurs earlier when r is large. This can lead to a decrease in ionization rates when the strength of the ionizing field is increased and corresponds to what is called stabilization, a phenomenon which has been observed experimentally. These and other comparisons with analytical works and experiments indicate that the main features of the, ionization behavior we obtain are in fact quite universal. These include the large dynamic Stark shifts for strong fields and above ionization threshold peaks, with period hbar/spl omega/, in the kinetic energy of the ejected electrons.