Abstract
The quantum regime of highly doubly excited states in two-electron atoms has, so far, been largely inaccessible both to numerical methods as well as to experiments. Recent advances in semiclassical closed orbit theory in combination with a quantum mapping approach have shown a new way into this region of high dynamical complexity. In particular, new scaling laws near the double-ionization threshold as well as the dominant semiclassical contributions to the total photoionization cross section can be identified. We will present this new approach here in all its detail. It is based on representing the photoionization cross section in terms of quantum maps. These quantum maps or quantum propagators are used as a starting point for developing an efficient numerical method for calculating cross sections. Furthermore, by writing the quantum operators in semiclassical approximations, it is possible to interpret the quantum results in terms of classical triple collision orbits and to derive threshold laws near the three-particle breakup point. Semiclassical and numerical quantum results show excellent agreement for a model system, namely collinear helium.
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