Evidence of triple collision dynamics in partial photo-ionization cross sections of helium

Abstract

Experimental results on partial photo-ionisation cross sections of helium are analysed in the light of recent advances in the semiclassical theory of two-electron atoms. Byun et al [1] predict that the total photo-ionisation cross section below the double-ionisation threshold can, semiclassically, be described in terms of contributions associated with classical orbits starting and ending in the triple collision. The necessary modifications of the semiclassical theory for partial cross sections is developed here. It is argued that partial cross sections are also dominated by the triple collision dynamics. The expected semiclassical contributions can be identified in the Fourier transformation of the experimental data. This clearly demonstrates for the first time the validity of the basic assumptions made in [1]. Our findings explain furthermore in a natural way the self-similar structures observed in cross section signals for different channel numbers.

Photoionization of two-electron atoms via highly doubly excited states: Numerical and semiclassical results

“…In particular, for source points R < R 0 , one obtains for R > R 0 , (20) in terms of the local scattering operators s and r and the local scattering solutions ± ; note, q ≡ (r 1 ,r 2 ) here.…”

“…Likewise, the quantum scattering maps s, r featuring in Eq. (20) can asymptotically be written as sums over trajectories starting and ending on the dividing surface , that is, at R = R = R 0 [43,44]. The dominant semiclassical contributions to the photoionization cross section are thus due to trajectories starting and ending in the phase-space region R R 0 .…”

“…Recent experimental progress in detector technology and synchrotron sources has made it possible to get fully resolved single-ionization spectra up to N ≈ 15 both for partial [17][18][19][20] and total [21,22] photoionization cross sections. Here, the quantum number N refers to the hydrogen-like state of the remaining ion with energy I N = − Z 2 2N 2 and Z is the charge of the nucleus.…”

“…[33] for total cross sections and in Ref. [20] for partial cross sections. In particular, it can be demonstrated that the fluctuations in the total and partial cross sections due to overlapping resonances decays algebraically with an exponent determined by the triple collision singularity different from Wannier's exponent.…”

Periodic orbits and binary collisions in the classical three-body Coulomb problem

“…Thanks to these tools, the dynamics near triple collision and the structure of stable and unstable manifolds were elucidated to some extent. In fact, a quantum manifestation of triple collision was demonstrated [15,16]. But we still know less about periodic orbits in two-dimensional dynamics, which are needed for semiclassical analysis.…”