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.

https://science.sciencemag.org/content/sci/320/5878/920.full.pdf

Ultrafast Probing of Core Hole Localization in N2

The core-level photoelectron spectra of N2 molecules are observed at high energy resolution, resolving the 1σg and 1σu components as well as the vibrational components in the extended energy region from the threshold up to 1 keV. The σg/σu cross section ratios display modulation as a function of photoelectron momentum due to the two-centre interference, analogous to the classical Young’s double-slit experiment, as predicted by Cohen and Fano a long time ago. The Cohen–Fano interference modulations display different phases depending on the vibrational excitations in the core-ionized state. Extensive ab initio calculations have been performed within the Hartree–Fock and random phase approximations in prolate spheroidal coordinates. The dependence of photoionization amplitudes on the vibrational states was taken into account using the Born–Oppenheimer approximation. The ab initio results are in reasonable agreement with the experimental data. The theoretical analysis allows the modulation to be connected with the onset of transitions to the states of increasing orbital angular momentum which occurs at increasing photon energies. Deviation from the Cohen–Fano formula is found for both the experimental and the ab initio results and is attributed to electron scattering by the neighbouring atom. A new formula for the interference modulation is derived within the framework of the multiple scattering technique. It differs from the classical Cohen–Fano formula by the addition of twice the scattering phase of the photoelectron by the neighbouring atom. We demonstrate that

Young's double-slit experiment using core-level photoemission from N2: revisiting Cohen–Fano's two-centre interference phenomenon

Young's double-slit experiment using core-level photoemission from N2

We used cold target recoil ion momentum spectroscopy (COLTRIMS) to investigate the decay of Ne2 after K-shell photoionization. The breakup into Ne1+/Ne2+ shows interatomic Coulombic decay (ICD) occurring after a preceding atomic Auger decay. The molecular frame angular distributions of the photoelectron and the ICD electron show distinct, asymmetric features, which imply localization of the K-vacancy created at one of the two atomic sites of the Ne2 and an emission of the ICD electron from a localized site. The experimental results are supported by calculations in the frozen core Hartree–Fock approach.

https://iopscience.iop.org/article/10.1088/0953-4075/41/10/101002/pdf

Localization of inner-shell photoelectron emission and interatomic Coulombic decay in Ne2

The ratios of photoionization cross sections of the 1σg and 1σu shells of the N2 molecule for the vibrational transitions to the v' = 0 and v' = 1 core-ionized states in the photon energy region between 440 and 550 eV have been measured. The calculations in the random phase approximation well reproduce the experimental data. The variation of the ratio with photon energy is attributed to the interference modulation that is caused by coherent photoemission from the two atoms, as an analogue of the Young's double-slit experiment. The calculations extended up to 1.8 keV allow connecting the modulation with the onset of transitions to the states of increasing orbital angular momentum which occurs at increasing photon energies and demonstrate that the main contribution to these modulations comes from the σ continuum states.

Interference modulation in the vibrationally resolved photoionization of the 1σgand 1σucore levels of the N2molecule

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.

F. Tahara

Papers

Vibrationally resolved photoionization of the 1σg and 1σu shells of N2 molecule

Non-Franck-Condon behavior in the C 1s photoelectron spectrum of the methane molecule