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.

Angular distributions of photoelectrons from both C and O K-shells of the fixed-in-space CO molecule have been measured using the angle-resolved photoelectron-photoion coincidence technique. The measurements have been performed at several photon energies from the ionization thresholds up to about 30 eV above them, where the σ* shape resonances occur. Experimental results are compared with the multiple-scattering calculations of Dill et al (1976 J. Chem. Phys. 65 3158) and with our new calculations in the relaxed-core Hartree-Fock approximation. Our calculations are in a better agreement with the experimental data though numerical discrepancies remain. The experimental angular distributions are fitted by the expansion in Legendre polynomials containing up to ten terms and the extracted parameters are compared with the corresponding theoretical values.

Using the experimental angular distributions of photoelectrons from the K-shells of an oriented CO molecule reported in a companion paper, we have performed a so-called complete experiment and determined 18 dynamical parameters (ten moduli of transition moments and eight phase differences) for the O K-shell, and 16 dynamical parameters (nine moduli of transition moments and seven phase differences) for the C K-shell, and compared them with the results of our calculations in the relaxed-core Hartree-Fock (RCHF) approximation. The agreement between theory and experiment is only qualitative, therefore the model has to be improved by including electron correlations. From the analysis of experimental data we proved that the σ * shape resonance is due to not only the f-wave, as was widely believed earlier, but is due to approximately equal contributions of three partial waves with 1 l 3 for the C K-shell, and four partial waves with 0 l 3 for the O K-shell, with a rather substantial contribution of other partial waves with l 5. From the analysis of the transition moments determined from the experiment it follows that several Cooper minima are likely to exist in partial photoionization cross sections, in particular, in the C 1sσ → εsσ and in the O 1sσ → εdσ transitions.

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Theoretical and experimental study of vibrationally resolved partial photoionization cross sections and angular asymmetry parameter β for the 1σg and 1σu shells of N2 molecule in the region of the σ* shape resonance is reported. The measurements were made at the synchrotron radiation facility SPring-8 in Japan. The calculations in the random phase approximation have been performed using the relaxed core Hartree–Fock wavefunctions with the fractional charge of the ion core equal to 0.7. With its help, the role of interchannel coupling between the closely spaced 1σg and 1σu shells was studied. The experiment demonstrates the existence of a correlational maximum in the 1σu shell photoionization cross section induced by the σ* shape resonance in the 1σg shell. This maximum reveals itself even more clearly in the angular asymmetry parameter β for the v′ = 0 and v′ = 1 vibrational states of the ion. The calculation in the random phase approximation gives a consistent interpretation of the experimental data.

It is demonstrated theoretically in the random phase approximation (RPA) that due to the intershell many-electron correlations the sigma(*) shape resonance in the photoionization of K shells of the N2 molecule appears not only in the 1sigma(g)-->varepsilonsigma(u) channel as it was believed earlier on the basis of single particle calculations, but in both 1sigma(g)-->varepsilonsigma(u) and 1sigma(u)-->varepsilonsigma(g) channels. As a confirmation of this phenomenon we show that the experimental angular distributions of photoelectrons ejected from fixed-in-space N2 molecules can be reproduced theoretically only after taking into account many-electron correlations.

Partial and total photoionization cross sections of N 2 molecule are calculated using the generalization of the random-phase approximation ͑RPA͒ which earlier has been successfully applied to the description of the atomic photoionization processes. According to this method, at first the Hartree-Fock ͑HF͒ ground-state wave functions are calculated in prolate spheroidal coordinates using the fixed-nuclei approximation. With their help the zero order basis set of single particle Hartree-Fock wave functions containing both discrete excited states and continuous spectrum is calculated in the field of a frozen core of a singly charged ion. The calculations are performed for all four valence shells of N 2 molecule, 3 g , 1 u , 2 u , and 2 g , with the intershell correlations fully taken into account within the RPA method. It is demonstrated that different intershell correlations, especially between three outer shells, play an important role in photoionization process. Examples of the influence of intershell correlations on several transitions are presented. Partial and total photoionization cross sections of N 2 molecule obtained by this method in the photon energy range from ionization threshold up to 70 eV are in a good agreement with the existing experimental data and with the recent RPA calculations ͓Cacelli et al., Phys. Rev. A 57, 1895 ͑1998͔͒.

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