Triple-differential cross sections for two-photon double ionization of the aligned hydrogen molecule at the equilibrium distance are presented for a central photon energy of 30 eV. The temporal response of the laser-driven molecule is investigated by solving the time-dependent Schr\"odinger equation in full dimensionality using two-center elliptical coordinates and a finite-element discrete-variable-representation approach. The molecular orientation is found to have a strong effect on the emission modes of the two correlated photoelectrons. This molecular effect is most noticeable when the molecular axis and the laser polarization vector are oriented parallel to each other. For intermediate cases between the parallel and perpendicular geometries, the dominant emission modes for two-electron ejection oscillate between those for the two extreme cases. The contributions from different ionization channels are also analyzed in detail. Depending on the emission direction of the reference electron, the interference contributions from the various channels can be constructive or destructive at small alignment angles, while they always contribute constructively to the triple-differential cross sections near the perpendicular geometry.
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