Two-photon double-ionization of the H$_2$ molecule in light perpindicular to the internuclear axis: effects of pulse duration

Earlier~[1--3], we solved the time-dependent Schr\"odinger equation to calculate the two-photon double ionization of the hydrogen molecule induced by non-sequential absorption of photons with a central energy of 30~eV in a short laser pulse lasting for about 1.6~femtoseconds. The linear polarization of the radiation was aligned with the internuclear axis. At the equilibrium distance R$_{eq}$, several doubly excited $^1\Sigma_{g,u}$ states, accessible through photon absorption,lie about 30~eV above the $X\,^1\Sigma_g$ ground state. These states are likely responsible for the significant disagreement seen in the literature for previous results on both angle-integrated and angle-differential cross sections. Here we continue to explore the fundamental role of doubly excited states on the two-photon break-up process,now for the even more difficult problem of laser polarization perpendicular to the internuclear axis. Such studies require relatively long laser pulses, thus making the calculations computationally very challenging.\\[4pt] [1] X.~Guan, K.~Bartschat, and B.~Schneider, Phys. Rev. A {\bf 82}, 041404 (2010).\\[0pt] [2] X.~Guan, K.~Bartschat, and B.~Schneider, Phys. Rev. A {\bf 84}, 033403 (2011).\\[0pt] [3] X.~Guan, K.~Bartschat, B.~Schneider and L.~Koesterke, Phys. Rev. A {\bf 88}, 043402(2013)