Interplay between Electronic and Nuclear Motion in the Photodouble Ionization of H$_{2}$

Photodouble ionization of molecular hydrogen results in a ``Coulomb explosion,'' as the two protons rapidly separate in opposite directions. The internuclear distance, $R$, between the two nuclei at the instant of photodouble ionization can be accessed through the kinetic energies of the emitted protons. A systematic analysis of the variation with $R$ of the fully differential cross section (FDCS) for this process is presented for a geometry where the 4-body interaction is completely probed. Dramatic variations in the FDCS with different $R$ are observed for geometries where the molecule is at approximately 20$^{\circ}$ to the polarization axis. Excellent agreement is found between experiment and Time-Dependent Close-Coupling theory after convolution of the latter over the relevant solid angles. We show that the observed variations are purely due to the $\varepsilon_{\Sigma}$ component of the polarization vector $\varepsilon$ along the molecular axis and a physical interpretation is proposed by analogy with single ionization of H$_{2}^{+}$, where similar variations in the angular distributions of the outgoing electron are found as a function of $R$.