We have carried out calculations of the triple-differential cross section for one-photon double ionization of molecular hydrogen for a central photon energy of $75$~eV, using a fully {it ab initio}, nonperturbative approach to solve the time-dependen
t Schro equation in prolate spheroidal coordinates. The spatial coordinates $xi$ and $eta$ are discretized in a finite-element discrete-variable representation. The wave packet of the laser-driven two-electron system is propagated in time through an effective short iterative Lanczos method to simulate the double ionization of the hydrogen molecule. For both symmetric and asymmetric energy sharing, the present results agree to a satisfactory level with most earlier predictions for the absolute magnitude and the shape of the angular distributions. A notable exception, however, concerns the predictions of the recent time-independent calculations based on the exterior complex scaling method in prolate spheroidal coordinates [Phys.~Rev.~A~{bf 82}, 023423 (2010)]. Extensive tests of the numerical implementation were performed, including the effect of truncating the Neumann expansion for the dielectronic interaction on the description of the initial bound state and the predicted cross sections. We observe that the dominant escape mode of the two photoelectrons dramatically depends upon the energy sharing. In the parallel geometry, when the ejected electrons are collected along the direction of the laser polarization axis, back-to-back escape is the dominant channel for strongly asymmetric energy sharing, while it is completely forbidden if the two electrons share the excess energy equally.
Triple-differential cross sections for two-photon double ionization of molecular hydrogen are presented for a central photon energy of 30 eV. The calculations are based on a fully {it ab initio}, nonperturbative, approach to the time-dependent Schroe
dinger equation in prolate spheroidal coordinates, discretized by a finite-element discrete-variable-representation. The wave function is propagated in time for a few femtoseconds using the short, iterative Lanczos method to study the correlated response of the two photoelectrons to short, intense laser radiation. The current results often lie in between those of Colgan {it et al} [J. Phys. B {bf 41} (2008) 121002] and Morales {it et al} [J. Phys. B {bf 41} (2009) 134013]. However, we argue that these individual predictions should not be compared directly to each other, but preferably to experimental data generated under well-defined conditions.
We present a fully {it ab initio}, non-perturbative, time-dependent approach to describe single and double ionization of helium by proton and antiproton impact. A flexible and accurate finite-element discrete-variable-representation is applied to dis
cretize the problem on the radial grid in spherical coordinates. Good agreement with the most recent experimental data for absolute angle-integrated cross sections is obtained over a wide range of incident projectile energies between 3 keV and 6 MeV. Furthermore, angle-differential cross sections for two-electron ejection are predicted for a proton impact energy of 6 MeV. Finally, the time evaluation of the ionization process is portrayed by displaying the electron density as a function of the projectile location.
