Dissociative photoionization of the NO molecule studied by photoelectron-photon coincidence technique

Low-energy photoelectron–vacuum ultraviolet (VUV) photon coincidences have been measured using synchrotron radiation excitation in the inner-valence region of the nitric oxide molecule. The capabilities of the coincidence set-up were demonstrated by detecting the 2s−1 → 2p−1 radiative transitions in coincidence with the 2s photoelectron emission in Ne. In NO, the observed coincidence events are attributed to dissociative photoionization with excitation, whereby photoelectron emission is followed by fragmentation of excited NO+ ions into O+ + N* or N+ + O* and VUV emission from an excited neutral fragment. The highest coincidence rate occurs with the opening of ionization channels which are due to correlation satellites of the 3σ photoionization. The decay time of VUV photon emission was also measured, implying that specific excited states of N atoms contribute significantly to observed VUV emission

Emitter-site selective photoelectron circular dichroism of trifluoromethyloxirane

The angle-resolved inner-shell photoionization of R-trifluoromethyloxirane, C3H3F3O, is studied experimentally and theoretically. Thereby, we investigate the photoelectron circular dichroism (PECD) for nearly-symmetric O 1s and F 1s electronic orbitals, which are localized on different molecular sites. The respective dichroic $\beta_{1}$ and angular distribution $\beta_{2}$ parameters are measured at the photoelectron kinetic energies from 1 to 16 eV by using variably polarized synchrotron radiation and velocity map imaging spectroscopy. The present experimental results are in good agreement with the outcome of ab initio electronic structure calculations. We report a sizable chiral asymmetry $\beta_{1}$ of up to about 9% for the K-shell photoionization of oxygen atom. For the individual fluorine atoms, the present calculations predict asymmetries of similar size. However, being averaged over all fluorine atoms, it drops down to about 2%, as also observed in the present experiment. Our study demonstrates a strong emitter- and site-sensitivity of PECD in the one-photon inner-shell ionization of this chiral molecule

Infinitesimals without Logic

We introduce the ring of Fermat reals, an extension of the real field containing nilpotent infinitesimals. The construction takes inspiration from Smooth Infinitesimal Analysis (SIA), but provides a powerful theory of actual infinitesimals without any need of a background in mathematical logic. In particular, on the contrary with respect to SIA, which admits models only in intuitionistic logic, the theory of Fermat reals is consistent with classical logic. We face the problem to decide if the product of powers of nilpotent infinitesimals is zero or not, the identity principle for polynomials, the definition and properties of the total order relation. The construction is highly constructive, and every Fermat real admits a clear and order preserving geometrical representation. Using nilpotent infinitesimals, every smooth functions becomes a polynomial because in Taylor's formulas the rest is now zero. Finally, we present several applications to informal classical calculations used in Physics: now all these calculations become rigorous and, at the same time, formally equal to the informal ones. In particular, an interesting rigorous deduction of the wave equation is given, that clarifies how to formalize the approximations tied with Hook's law using this language of nilpotent infinitesimals.Comment: The first part of the preprint is taken directly form arXiv:0907.1872 The second part is new and contains a list of example

Singular open book structures from real mappings

We prove extensions of Milnor's theorem for germs with nonisolated singularity and use them to find new classes of genuine real analytic mappings $\psi$ with positive dimensional singular locus \Sing \psi \subset \psi^{-1}(0), for which the Milnor fibration exists and yields an open book structure with singular binding.Comment: more remark

Photon-electron coincidence experiments at synchrotron radiation facilities with arbitrary bunch modes

We report the adaptation of an electron–photon coincidence detection scheme to the multibunch hybrid mode of the synchrotron radiation source BESSY II (Helmholtz-Zentrum Berlin). Single-event-based data acquisition and evaluation, combined with the use of relative detection times between the coincident particles, enable the acquisition of proper coincidence signals from a quasi-continuous excitation pattern. The background signal produced by accidental coincidences in the time difference representation is modeled using the non-coincident electron and photon spectra. We validate the method by reproducing previously published results, which were obtained in the single bunch mode, and illustrate its usability for the multibunch hybrid mode by investigating the photoionization of CO2 into CO+2 B satellite states, followed by subsequent photon emission. The radiative lifetime obtained and the electron binding energy are in good agreement with earlier publications. We expect this method to be a useful tool to extend the versatility of coincident particle detection to arbitrary operation modes of synchrotron radiation facilities and other excitation sources without the need for additional experimental adjustments

Groupoids and Wreath Products of Musical Transformations: a Categorical Approach from poly-Klumpenhouwer Networks

Transformational music theory, pioneered by the work of Lewin, shifts the music-theoretical and analytical focus from the "object-oriented" musical content to an operational musical process, in which transformations between musical elements are emphasized. In the original framework of Lewin, the set of transformations often form a group, with a corresponding group action on a given set of musical objects. Klumpenhouwer networks have been introduced based on this framework: they are informally labelled graphs, the labels of the vertices being pitch classes, and the labels of the arrows being transformations that maps the corresponding pitch classes. Klumpenhouwer networks have been recently formalized and generalized in a categorical setting, called poly-Klumpenhouwer networks. This work proposes a new groupoid-based approach to transformational music theory, in which transformations of PK-nets are considered rather than ordinary sets of musical objects. We show how groupoids of musical transformations can be constructed, and an application of their use in post-tonal music analysis with Berg's Four pieces for clarinet and piano, Op. 5/2. In a second part, we show how groupoids are linked to wreath products (which feature prominently in transformational music analysis) through the notion of groupoid bisectionsComment: 16 pages, 9 figures; comments welcom

Lagrange-Fedosov Nonholonomic Manifolds

We outline an unified approach to geometrization of Lagrange mechanics, Finsler geometry and geometric methods of constructing exact solutions with generic off-diagonal terms and nonholonomic variables in gravity theories. Such geometries with induced almost symplectic structure are modelled on nonholonomic manifolds provided with nonintegrable distributions defining nonlinear connections. We introduce the concept of Lagrange-Fedosov spaces and Fedosov nonholonomic manifolds provided with almost symplectic connection adapted to the nonlinear connection structure. We investigate the main properties of generalized Fedosov nonholonomic manifolds and analyze exact solutions defining almost symplectic Einstein spaces.Comment: latex2e, v3, published variant, with new S.V. affiliatio