The cross sections for single-electron photoionization in two-electron atoms show fluctuations which decrease in amplitude when approaching the double-ionization threshold. Based on semiclassical closed orbit theory, we show that the algebraic decay of the fluctuations can be characterized in terms of a threshold law sigma proportional to |E|(mu) as E --> 0(-) with exponent mu obtained as a combination of stability exponents of the triple-collision singularity. It differs from Wannier's exponent dominating double-ionization processes. The details of the fluctuations are linked to a set of infinitely unstable classical orbits starting and ending in the nonregularizable triple collision. The findings are compared with quantum calculations for a model system, namely, collinear helium.

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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