Scaling laws for the photo-ionisation cross section of two-electron atoms

Abstract

The cross sections for single-electron photo-ionisation in two-electron atoms show fluctuations which decrease in amplitude when approaching the double-ionisation threshold. Based on semiclassical closed orbit theory, we show that the algebraic decay of the fluctuations can be characterised in terms of a threshold law $σ\propto |E|^μ$ as $E \to 0_-$ with exponent $μ$ obtained as a combination of stability exponents of the triple-collision singularity. It differs from Wannier's exponent dominating double ionisation processes. The details of the fluctuations are linked to a set of infinitely unstable classical orbits starting and ending in the non-regularisable triple collision. The findings are compared with quantum calculations for a model system, namely collinear helium.

4 pages, 1 figure