Alignment dependence in the breakup of the H$_2$ molecule by xuv laser pulses

We present predictions of angular distributions for two-photon double ionization of the hydrogen molecule by a short laser pulse with a central photon energy of 30~eV. Using the fixed-nuclei approximation, the laser-driven electronic wave packets are obtained by solving the time-dependent Schr\"odinger equation in two-center elliptical coordinates with the inter\-nuclear distance fixed at 1.4~bohr. In addition to the parallel and perpendicular geometries, we explore the dependence of the angular distribution on the relative orientation of the molecular axis and the linear polarization vector of the laser field. The individual contributions from the $^1\Sigma_{\rm g}$ and $^1\Delta_{\rm g}$ channels are found to be very sensitive to both the orientation angle and the direction of the reference electron that is observed at a fixed angle with a preset energy. The resulting interference effect between the different ionization channels is analyzed in detail.