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Journal of Physics B Atomic Molecular and Optical Physics

Five-photon double ionization of helium

Ye Li, Michael Stuart Pindzola, James P. Colgan

Published Feb 4, 2016• 2 citations
Publisher

Abstract

Abstract A time-dependent close-coupling method is used to calculate the five-photon double ionization of He. It is found that the generalized cross section used in the past for two-photon double ionization of He cannot be extended to five-photon double ionization of He. Therefore only five-photon double ionization probabilities that depend on specific radiation field pulses can be calculated.

DOI
10.1088/0953-4075/49/5/055401

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Abstract A time-dependent close-coupling method is used to calculate the five-photon double ionization of He. It is found that the generalized cross section used in the past for two-photon double ionization of He cannot be extended to five-photon double ionization of He. Therefore only five-photon double ionization probabilities that depend on specific radiation field pulses can be calculated.
We present accurate cross sections for two-photon double ionization of helium at photon energies above and below the threshold for sequential double ionization. Above this threshold (54.4eV)(54.4\phantom{\rule{0.3em}{0ex}}\mathrm{eV})(54.4eV), sequential ionization competes with nonsequential ionization. Remarkably, even below 54.4eV54.4\phantom{\rule{0.3em}{0ex}}\mathrm{eV}54.4eV, sequential ionization leaves a clear signature in the magnitude and shape of both the total and energy-sharing cross sections---even though at these energies it is only a virtual process.
In view of recent papers on two-photon double ionization of helium, pertaining to a perceived anomaly in the behavior of the sequential process and its influence on the direct process, as well as the dependence of both on the laser pulse duration, we show that upon the proper formulation, the sequential is well defined and free of divergence, and that the dependence on pulse duration is considerably more intricate. We also argue that the apparent sharp rise of the cross section for the direct process, around 54.4eV54.4\phantom{\rule{0.3em}{0ex}}\mathrm{eV}54.4eV, is due to the unintended inclusion of the sequential process, which in any case is not properly describable in terms of a single cross section.
We report on the experimental estimation of a lower bound of helium. Our experiment differs from a previous one described by Hasegawa et al. [Phys. Rev. A 71, 023407 (2005)]. The photons that correspond to the 27th harmonic of a Ti:sapphire laser have an energy of 41.8eV41.8\phantom{\rule{0.3em}{0ex}}\mathrm{eV}41.8eV. The extraction of the cross section rests on a theoretical model, based on the rate equations, that fully includes the contribution from the sequential channels and the macroscopic effects. Some of the experimental parameters are very difficult to measure accurately. For those parameters, we deliberately consider values compatible with their experimental determinations and that lead systematically to an underestimation of the two-photon double ionization cross section. Our estimation of this lower bound is higher than a bunch of various theoretical results. It stays, however, too close to these latter ones to draw any definite conclusion about their validity, even though it clearly indicates that the actual value of the double ionization cross section is higher than expected.
Calculations of the two-photon ionization of metastable levels of helium and the first three s levels of cesium are presented. The calculations are carried out to second order in a perturbation expansion and are valid for low laser intensities. The behavior of the ionization cross section at high photon frequencies ω is studied, and it is found that the N-photon ionization cross section behaves as σ(N) ∝ ω−(2N+1/2). This analytic asymptotic behavior is verified numerically in the case of two-photon ionization.
Double ionization is studied by direct numerical integration of the time-dependent Schrödinger equation for a model two-electron system in the field of an electromagnetic wave in the case when the photon energy exceeds the energy required for the removal of both electrons of the atom. The probabilities of single-electron and double ionization are obtained as functions of the radiation intensity. The energy spectra and double pulse distributions of photoelectrons are analyzed. It is shown that single-photon ionization plays a significant role only in the limiting cases of weak and strong fields. The obtained results are used in an analysis of the contributions from different channels to the double-ionization process (in particular, for clarifying the role of the electron-electron interaction). The results of numerical calculations are compared with the analytic model of the phenomenon.