Two-photon double ionization of the hydrogen molecule

Cross sections for the removal of both electrons of the hydrogen molecule by two photons are presented at 30 eV photon energy using the time-dependent close-coupling method. Our approach allows detailed information about the dynamics of the ionization process to be extracted, including angular distributions for the outgoing electrons. Analysis of our calculations reveals some similarities to the analogous process of two-photon double ionization of helium, but also uncovers some purely molecular effects. For example, we find that the differential cross sections vary with the kinetic energy released to the outgoing protons if the molecule is parallel to the polarization direction, but do not vary if the molecule is perpendicular to the polarization direction. (Some figures in this article are in colour only in the electronic version) Few-photon multiple ionization processes in light atoms and molecules are currently a timely and exciting field of study in atomic collision physics. The advent of free-electron lasers (FELs) such as at the FLASH facility in Germany, which provide intense photon sources over wide energy ranges, coupled with the latest experimental techniques, such as COLTRIMS spectroscopy, allow maximal extraction of information about the ionization dynamics [1]. Anticipating these exciting experimental advances, much theoretical effort has recently been placed in calculating cross sections for the two-photon double ionization of helium [2–11]. Although even the magnitude of the two-photon double ionization cross section has been under intense debate, it appears that fully converged non-perturbative methods are coming to some agreement [10] near the only available experimental data point [12] for the total cross section. Also, several of these methods allow the calculation of fully differential cross sections for this process [4, 7, 9]. In addition, the role of sequential versus nonsequential ionization for the two-electron escape is currently under scrutiny [10]. There has been also recent progress in the study of the single-photon double ionization of H2, in which experimental measurements of fully differential cross sections [13, 14] have recently been confirmed by the latest theoretical techniques [15–18]. These theoretical and experimental studies have uncovered ionization dynamics unique to molecules, such as dependence of the electron angular distributions on the orientation of the molecule with respect to the polarization direction, and on the kinetic energy released to the protons. These single-photon studies are complemented by intense efforts in examining the strong-field (multiphoton) ionization of molecules (see [19] for a review). Experimental work in this field has recently focused, for example, on short-pulse laser ionization of H2 and control of the Coulomb explosion after multiphoton ionization [20]. These techniques have been used to propose a ‘molecular clock’ [21] which can distinguish recollision processes from non-sequential processes in strongfield ionization. Such work is complemented by calculations of these (one-electron) multi-photon processes in H2 and H2, some of which has been able to include the nuclear vibrational motion in the calculations so that dissociative processes may be investigated in tandem with experiment [22]. In this communication, we demonstrate that the timedependent close-coupling method is capable of combining the first two fields described, in the study of two-photon double ionization of H2. Two-photon ionization is of interest as it probes final-state correlations in the H2 system of a gerade symmetry, unlike single-photon ionization which can only 0953-4075/08/121002+06$30.00 1 © 2008 IOP Publishing Ltd Printed in the UK J. Phys. B: At. Mol. Opt. Phys. 41 (2008) 121002 Fast Track Communication result in final ungerade states. We emphasize that we are not exploring the well-studied strong-field ionization of H2, in which multiphoton ionization by 10 or more photons is common. Rather, we focus on few-photon processes and on the correlated electron dynamics which results when two electrons are instantaneously ejected from H2 by two photons. We present the total and triple differential cross sections (TDCS) for this process at a photon energy of 30 eV. We employ the ‘fixed-nuclei’ approximation, which assumes that both electrons are doubly ionized from the molecule before the nuclei begin to move apart, which is a very good approximation due to the large mass differences between the protons and electrons, and when the electrons are ejected with sufficient energy so that they move quickly away from the nuclei. If the length of the incoming laser pulse is long, it may be necessary to relax the fixed-nuclei approximation, since there is the possibility that the molecule could stretch between absorption of the two photons. However, for now we focus on the short pulse case where both photons are absorbed instantaneously and so our assumption that the nuclei do not move is valid. Thus we focus solely on the electron dynamics of the double ionization into this gerade final state. Since there are no other theoretical or experimental works with which to compare our cross sections, we compare and contrast our results to equivalent two-photon double ionization cross sections for helium. We also examine the TDCS as a function of internuclear separation (which is equivalent to a dependence on the kinetic energy release to the outgoing protons). The time-dependent Schrödinger equation for a twoelectron molecule in a strong time-varying laser field may be written as