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Two-electron effects pervading the formation of highly excited neutral atoms in the break-up of strongly driven H$_{2}$

We present the first theoretical treatment of the formation of highly excited neutral H atoms (H$^{*}$) for strongly driven H$_{2}$. This process, with one electron ionizing and one captured in a Rydberg state, was recently reported in an experimental study in Phys. Rev. Lett {\bf 102} 113002 (2009). We show that two mechanisms underlie this process: a non-sequential one resembling non-sequential double ionization, and a sequential one resembling double ionization through enhanced ionization. We also predict a new feature, asymmetric energy sharing between H$^{*}$ and H$^{+}$ with increasing intensity. This feature is a striking demonstration of the influence the electron has on the nuclear motion.