Based on a combined quantum-classical treatment, a complete study of the strong field dynamics of H2+, i.e. including all nuclear and electronic DOF as well as dissociation and ionization, is presented. We find that the ro-vibrational nuclear dynamics enhances dissociation and, at the same time, suppresses ionization, confirming experimental observations by I. Ben-Itzhak et al. [Phys. Rev. Lett. 95, 073002 (2005)]. In addition and counter-intuitively, it is shown that for large initial vibrational excitation ionization takes place favorably at large angles between the laser polarization and molecular axis. A local ionization model delivers a transparent explanation of these findings.
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