Gromov-Hausdorff-like distance function defined in the aspect of Riemannian submanifold theory

In this paper, we discuss how a Gromov-Hausdorff-like distance function over the space of all isometric classes of compact $C^k$-Riemannian manifolds should be defined in the aspect of the Riemannan submanifold theory, where $k\geq 1$. The most important fact in this discussion is as follows. The Hausdorff distance function between two spheres of mutually distinct radii isometrically embedded into the hypebolic space of curvature $c$ converges to zero as $c\to-\infty$. The key in the construction of the Gromov-Hausdorff-like distance function given in this paper is to define the distance of two $C^{k+1}$-isometric embeddings of distinct compact $C^k$-Riemannian manifolds into a higher dimensional Riemannian manifold by using the Hausdorff distance function in the tangent bundle of order $k+1$ equipped with the Sasaki metric. Furthermore, we show that the convergence of a sequence of compact Riemannian manifolds with respect to this distance function coincides with the convergence in the sense of R. S. Hamilton.Comment: 14 page

Influence of shape resonances on the angular dependence of molecular photoionization delays.

Characterizing time delays in molecular photoionization as a function of the ejected electron emission direction relative to the orientation of the molecule and the light polarization axis provides unprecedented insights into the attosecond dynamics induced by extreme ultraviolet or X-ray one-photon absorption, including the role of electronic correlation and continuum resonant states. Here, we report completely resolved experimental and computational angular dependence of single-photon ionization delays in NO molecules across a shape resonance, relying on synchrotron radiation and time-independent ab initio calculations. The angle-dependent time delay variations of few hundreds of attoseconds, resulting from the interference of the resonant and non-resonant contributions to the dynamics of the ejected electron, are well described using a multichannel Fano model where the time delay of the resonant component is angle-independent. Comparing these results with the same resonance computed in e-NO+ scattering highlights the connection of photoionization delays with Wigner scattering time delays

Experimental and theoretical threshold photoelectron spectra of methylene

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Normal and resonant Auger spectroscopy of isocyanic acid, HNCO

In this paper, we investigate HNCO by resonant and nonresonant Auger electron spectroscopy at the K-edges of carbon, nitrogen, and oxygen, employing soft X-ray synchrotron radiation. In comparison with the isosteric but linear CO2 molecule, spectra of the bent HNCO molecule are similar but more complex due to its reduced symmetry, wherein the degeneracy of the π-orbitals is lifted. Resonant Auger electron spectra are presented at different photon energies over the first core-excited 1s → 10a′ resonance. All Auger electron spectra are assigned based on ab initio configuration interaction computations combined with the one-center approximation for Auger intensities and moment theory to consider vibrational motion. The calculated spectra were scaled by a newly introduced energy scaling factor, and generally, good agreement is found between experiment and theory for normal as well as resonant Auger electron spectra. A comparison of resonant Auger spectra with nonresonant Auger structures shows a slight broadening as well as a shift of the former spectra between -8 and -9 eV due to the spectating electron. Since HNCO is a small molecule and contains the four most abundant atoms of organic molecules, the reported Auger electron decay spectra will provide a benchmark for further theoretical approaches in the computation of core electron spectra

Angle-resolved studies of XUV–IR two-photon ionization in the RABBITT scheme

International audienceReconstruction of attosecond beating by interference of two-photon transitions (RABBITT) is an established technique for studying time-delay in photoionization of atoms and molecules. It has been recently extended to angle-resolved studies, accessing diverse fingerprint observables of the attosecond photoemission dynamics within the bound-continuum and continuumcontinuum transitions. In this work, we address the general form of the ISB(,) two-photon photoelectron angular distributions (PADs) associated to the RABBITT sideband signal, as a function of the emission angle , and the delay between the XUV attosecond pulse train and the infrared (IR) dressing field at play in the RABBITT scheme. Relying on the expansion in Legendre polynomials, the PAD is synthesized in terms of a reduced set of coefficients which fully describe both its static (-independent) and dynamic (-dependent) components and enables us to retrieve any observable characterizing the PAD. This unified framework streamlines the comparison between different experimental or theoretical data sets and emphasizes how some observables depend on the experimental conditions. Along with the modelled analysis, we report new results of angle-resolved RABBITT direct ionization of the np valence orbital of Ar(3p 6) and Ne(2p 6), employing electron-ion coincidence momentum spectroscopy at the new Attolab facility. In this case, the nine coefficients synthesizing the PAD are further linked to the magnitude and phase of the transition dipole matrix elements, providing a fundamental test of theoretical predictions. Similarities and differences are found between Ar and Ne in the explored low energy region, up to 20 eV above the ionization threshold, where the electron dynamics is most sensitive to electronic correlation. Further interpretation of these results would benefit from a comparison with advanced many-body theoretical simulations

Synchrotron-based valence shell photoionization of CH radical

International audienceWe report the first experimental observations of X+ 1Σ+←X 2Π and a+ 3Π←X 2Π single-photon ionization transitions of the CH radical performed on the DESIRS beamline at the SOLEIL synchrotron facility. The radical was produced by successive hydrogen-atom abstractions on methane by fluorine atoms in a continuous microwave discharge flow tube. Mass-selected ion yields and photoelectron spectra were recorded as a function of photon energy using a double imaging photoelectron/photoion coincidence spectrometer. The ion yield appears to be strongly affected by vibrational and electronic autoionizations, which allow the observation of high Rydberg states of the neutral species. The photoelectron spectra enable the first direct determinations of the adiabatic ionization potential and the energy of the first triplet state of the cation with respect to its singlet ground state. This work also brings valuable information on the complex electronic structure of the CH radical and its cation and adds new observations to complement our understanding of Rydberg states and autoionization processes

Valence shell threshold photoelectron spectroscopy of the C3Hx (x=0-3)

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