Although valence electrons are clearly delocalized in molecular bonding frameworks, chemists and physicists have long debated the question of whether the core vacancy created in a homonuclear diatomic molecule by absorption of a single x-ray photon is localized on one atom or delocalized over both. We have been able to clarify this question with an experiment that uses Auger electron angular emission patterns from molecular nitrogen after inner-shell ionization as an ultrafast probe of hole localization. The experiment, along with the accompanying theory, shows that observation of symmetry breaking (localization) or preservation (delocalization) depends on how the quantum entangled Bell state created by Auger decay is detected by the measurement.

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We examine the origin of recently observed variations with internuclear distance (R) of the fully differential cross sections for double ionization of aligned H2 by absorption of a single photon. Using the results of fully converged numerical solutions of the Schrödinger equation, we show that these variations arise primarily from pronounced differences in the R dependence of the parallel and perpendicular components of the ionization amplitude. We also predict that R dependences should be readily observable in the asymmetry parameter for photodouble ionization, even in experimental measurements that are not differential in the energy sharings between ejected photoelectrons.