  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 $\sigma \propto |E|^{\mu}$ as $E \to 0_-$ with exponent
$\mu$ 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.
