S. K. Semenov

Ultrafast Probing of Core Hole Localization in N2

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.

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

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

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

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.

Complete photoionization experiment in the region of the 2σg → σu shape resonance of the N2 molecule

Angular distributions of photoelectrons (ADPs) from the 2σg shell of a fixed-in-space N2 molecule have been measured for left- and right-elliptically polarized, as well as for linearly polarized, light. From these data a set of dipole matrix elements and phase shift differences characterizing the process has been determined taking into account the acceptance angles of both electron and ion detectors, i.e. the complete experiment has been performed. Good agreement between the experimental and the relevant theoretical values calculated in the random phase approximation is obtained. Based on the results of the complete experiment, three-dimensional ADPs and ions are predicted for different light polarizations.

Hartree-Fock deformed jellium model for metallicclusters

We have developed the Hartree-Fock jellium model for deformed metal clusters, which treats the quantized electron motion in the field of the spheroidal ionic jellium background in the Hartree-Fock approximation. Using this model, we have calculated single electron energy levels as a function of the cluster deformation parameter for a series of sodium clusters with the number of atoms N in a cluster ranging from 4 to 40. We have established that the cluster deformations corresponding to the minimum total energy of the oblate and prolate clusters are in a reasonable agreement with the experimental data and predictions of other theoretical models.

A simple atomic model for hydrogen confined inside a prolate-shaped C60 fullerene cage

We present a new theoretical method for the calculation of the electronic structure of the hydrogen atom confined inside a prolate-shaped C60 fullerene cage. The method is based on solving the one-electron Schr?dinger equation written in the prolate-spheroidal-coordinate system and using the quasi-atom concept for modelling the effects of the deformed endohedral environment. The energy levels of H@C60 are qualitatively studied as a function of the deformation parameter ?. Avoided crossing points between levels of the same symmetry are revealed.

State-dependent gerade/ungerade intensity ratios in the Auger spectrum of N2

We have applied both high-resolution photoelectron and Auger spectroscopy to study the N 1s core ionization of N2. From the respective spectra we are able to show that the Auger decay involves delocalized description of core-hole states. Specifically, the Auger spectra of the N 1sσg,u core holes to the quasi-stable final states X1Σ+g and D1Σ+u are presented. They exhibit the gerade/ungerade splitting as well as vibrational progressions. The 1sσg/1sσu Auger intensity ratios are, in agreement with ab initio calculations, 2.1 and 0.8 for the X and the D states respectively. The large value for the X state can qualitatively be related to the gerade or ungerade symmetry of the Auger electron.

Photoelectron and ICD electron angular distributions from fixed-in-space neon dimers

We report on molecular frame angular distributions of 2s photoelectrons and electrons emitted by interatomic Coulombic decay from neon dimers. We found that the measured angular distribution of the photoelectron strongly depends on the environment of the cluster. The experimental results are in excellent agreement with frozen core Hartree–Fock calculations. The ICD electrons show slight variations in their angular distribution for different kinetic energies.

Theoretical study of vibrationally resolved photoionization for the C K-shell of the CO molecule

Partial photoionization cross sections and the angular asymmetry parameter β for the C K-shell of the CO molecule have been calculated in the relaxed core Hartree–Fock approximation. In contrast with all previous calculations, we introduced the relaxed core potential with a fractional charge of the ion which was fitted from the condition to get an agreement with the experimental position of the σ ∗ shape resonance for the K-shell cross section. We found the optimal value of the fractional charge to be 0.5. After performing calculations within the Born–Oppenheimer approximation for several fixed internuclear distances R, we averaged the R-dependent dipole amplitudes over R with the vibrational wavefunctions of the initial and final states. Transitions from the ground vibrational level to several vibrationally excited states of the residual molecular ion have been studied within this approximation. A good agreement was found with the recently published vibrationally resolved experimental data.

Alignment following Au L3 photoionization by synchrotron radiation

The alignment of Au+ ions following L3 photoionization has been studied using a high-resolution x-ray spectrometer. We observed a small anisotropy for the angular dependence of Au Lι and Lα emissions. The alignment parameter derived from the experimental results is compared with theoretical calculations by Hartree–Fock approximation and random phase approximation with exchange. The contribution to the alignment of quadrupole interaction is discussed.