Scaling Laws for the Photoionization Cross Section of Two-Electron Atoms

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 $\sigma \propto |E{|}^{\mu }$ 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-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.

Figure 1

The Fourier spectrum of the fluctuating part of the $eZe$ cross section rescaled according to (12); the circles denote the position ${\tilde{S}}_j$ and (relative) size of $|M_{12}{|}_j^{-1/2}$ for CTCO’s with $\tilde{S}/2\pi <13$. Corresponding trajectories in configuration space are shown for the first 4 peaks. Inset: ${\sigma }_{\mathrm{fl}}$ for $N\le 52$.