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Physical Review A

Direct versus sequential double ionization in atomic systems

P. Lambropoulos, Lampros A. A. Nikolopoulos, M. G. Makris, A. Mihelič

Published Nov 19, 2008• 34 citations
Publisher

Abstract

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 $54.4\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, 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.

DOI
10.1103/physreva.78.055402

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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 investigate the two-photon double ionization of beryllium atom induced by ultrashort pulses. We use a time-dependent formalism to evaluate the ionization amplitudes and generalized cross sections for the ejection of the 2s22{s}^{2}2s2 valence shell electrons in the presence of a fully occupied 1s21{s}^{2}1s2 frozen core shell. The relative contributions of the two-photon direct and sequential process are systematically explored by varying both pulse duration and central frequency. The energy and angular differential ionization yields reveal the signatures of both mechanisms, as well as the role of electron correlation in both the single and double ionization continua. In contrast with previous results on the helium atom, the presence of an electronic core strongly affects the final state leading to back-to-back electron emission even in the a priori less correlated two-photon sequential mechanism. In particular, a dominant pathway via excitation ionization through the Be+(2p){\mathrm{Be}}^{+}(2p)Be+(2p) determines the profiles and pulse-duration dependencies of the energy and angle differential yields.
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.
Above 54.4eV54.4\phantom{\rule{0.3em}{0ex}}\mathrm{eV}54.4eV, two-photon double ionization of helium is dominated by a sequential absorption process, producing characteristic behavior in the single and triple differential cross sections. We show that the signature of this process is visible in the nuclear recoil cross section, integrated over all energy sharings of the ejected electrons, even below the threshold for the sequential process. Since nuclear recoil momentum imaging does not require coincident photoelectron measurement, the predicted images present a viable target for future experiments with new short-pulse vacuum ultraviolet (vuv) and soft x-ray sources.
We analyze in this paper the process of double-electron ejection through two-photon absorption from the fundamental state of helium. We focus on the case of photon energies close to 2 a.u., which marks the threshold between direct and sequential double-ionization regimes. We demonstrate the crucial role of two-photon excitation-plus-ionization process of ${\mathit{nlk}}^{\ensuremath{'}}{l}^{\ensuremath{'}}$ Rydberg series. We show that the latter channel must be taken into account in the theory in order to properly describe two-electron ejection. A simple expression is derived for the electron energy spectrum, leading to better insights into the physics underlying two-photon absorption close to the sequential threshold.
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.
We investigate the two-photon double ionization of atomic magnesium induced by ultrashort pulses. Though the initial and final state symmetries are comparable to the same process in helium, in stark contrast the range of photon energies for which nonsequential ionization is the only open pathway is narrow (less than 1 eV) in magnesium. Thus several sequential ionization pathways feature heavily in these processes. Nonetheless, it is found that for pulse durations between 0.25 and 2.0 fs, the joint angular dependence of the ejected electrons can depend sensitively on pulse length, varying between the strictly back-to-back ejection characteristic of nonsequential ionization to other distributions. The significance of excited-state correlating configurations in representing the initial state of magnesium is discussed in the light of their consequences for the resulting angular distributions at photon energies where sequential ionization can access intermediate states that lie nearby in energy, particularly for longer pulses.