Extracting inter-nuclear distances in the oxygen molecule interacting with an XFEL-pulse: a fundamental system for understanding Coulomb explosion imaging

We investigate the interaction of O$_{2}$ with an X-ray Free Electron laser (XFEL) pulse of short duration. We consider a photon energy of 570 eV, which allows for the formation of molecular states with up to two core holes. We compute the sum of the final kinetic energies, i.e. the kinetic energy release (KER) of the atomic fragments for different fragmentation channels. We demonstrate that with the knowledge of the potential energy curves the equilibrium inter-nuclear distance of O$_{2}$ is best extracted from the O$^{+}$+O$^{+}$ channel and not from higher-charged channels such as O$^{2+}$+O$^{2+}$. This challenges our current understanding of Coulomb explosion imaging, where from just applying quasi-classical dynamics one expects that the equilibrium inter-nuclear distance of molecules is best extracted from higher-charged fragmentation channels. On the other hand, we show that the KER of the O$^{+}$+O$^{+}$ channel is inconsistent with the one obtained by just calculating the Coulomb repulsion of the atomic fragments resulting from molecular dissociation.