In this paper, we present ab initio two-electron model calculations of laser-induced single and double ionization of the hydrogen molecule in a linearly polarized laser field with static nuclei located along the polarization axis. Within the model, the center-of-mass motion of the two electrons is restricted along the polarization axis of the field, while the relative electron motion is unrestricted. The results of numerical simulations allow us to identify and characterize the mechanisms leading to single and double ionization in an intense few-cycle laser pulse. The role of the rescattering mechanism on the ionization processes is analyzed in particular.
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