The electron-furfural scattering dynamics for 63 energetically open electronic states

We report on integral-, momentum transfer-and differential cross sections for elastic and electronically inelastic electron collisions with furfural (C5H4O2). The calculations were performed with two different theoretical methodologies, the Schwinger multichannel method with pseudopotentials (SMCPP) and the independent atom method with screening corrected additivity rule (IAM-SCAR) that now incorporates a further interference (I) term. The SMCPP with N energetically open electronic states (N-open) at either the static-exchange (N-open ch-SE) or the static-exchange-plus-polarisation (N-open ch-SEP) approximation was employed to calculate the scattering amplitudes at impact energies lying between 5 eV and 50 eV, using a channel coupling scheme that ranges from the 1ch-SEP up to the 63ch-SE level of approximation depending on the energy considered. For elastic scattering, we found very good overall agreement at higher energies among our SMCPP cross sections, our IAM-SCAR+I cross sections and the experimental data for furan (a molecule that differs from furfural only by the substitution of a hydrogen atom in furan with an aldehyde functional group). This is a good indication that our elastic cross sections are converged with respect to the multichannel coupling effect for most of the investigated intermediate energies. However, although the present application represents the most sophisticated calculation performed with the SMCPP method thus far, the inelastic cross sections, even for the low lying energy states, are still not completely converged for intermediate and higher energies. We discuss possible reasons leading to this discrepancy and point out what further steps need to be undertaken in order to improve the agreement between the calculated and measured cross sections. (C) 2016 AIP Publishing LLC.

Deep observation of the NGC1275 region with MAGIC: search of diffuse gamma-ray emission from cosmic rays in the Perseus cluster

Clusters of galaxies are expected to be reservoirs of cosmic rays (CRs) that should produce diffuse γ-ray emission due to their hadronic interactions with the intra-cluster medium. The nearby Perseus cool-core cluster, identified as the most promising target to search for such an emission, has been observed with the MAGIC telescopes at very-high energies (VHE, E ≥ 100 GeV) for a total of 253 hr from 2009 to 2014. The active nuclei of NGC 1275, the central dominant galaxy of the cluster, and IC 310, lying at about 0.6º from the centre, have been detected as point-like VHE γ-ray emitters during the first phase of this campaign. We report an updated measurement of the NGC 1275 spectrum, which is described well by a power law with a photon index Γ = 3.6 ± 0.2_(stat) ± 0.2_(syst) between 90 GeV and 1200 GeV. We do not detect any diffuse γ-ray emission from the cluster and so set stringent constraints on its CR population. To bracket the uncertainties over the CR spatial and spectral distributions, we adopt different spatial templates and power-law spectral indexes α. For α = 2.2, the CR-to-thermal pressure within the cluster virial radius is constrained to be ≤ 1 − 2%, except if CRs can propagate out of the cluster core, generating a flatter radial distribution and releasing the CR-to-thermal pressure constraint to ≤ 20%. Assuming that the observed radio mini-halo of Perseus is generated by secondary electrons from CR hadronic interactions, we can derive lower limits on the central magnetic field, B_(0), that depend on the CR distribution. For α = 2.2, B_(0) ≥ 5 − 8 µG, which is below the ∼25 µG inferred from Faraday rotation measurements, whereas for α ≤ 2.1, the hadronic interpretation of the diffuse radio emission contrasts with our γ-ray flux upper limits independently of the magnetic field strength.

Measurement of picosecond lifetimes in neutron-rich Xe isotopes

Background: Lifetimes of nuclear excited states in fission fragments have been studied in the past following isotope separation, thus giving access mainly to the fragments' daughters and only to long-lived isomeric states in the primary fragments. For the first time now, short-lived excited states in the primary fragments, produced in neutron-induced prompt fission of U-235 and Pu-241, were studied within the EXILL&FATIMA campaign at the intense neutron-beam facility of the Institute Laue-Langevin in Grenoble. Purpose: We aim to investigate the quadrupole collective properties of neutron-rich even-even Xe-138,Xe-140,Xe-142 isotopes lying between the double shell closure N = 82 and Z = 50 and a deformed region with octupole collectivity. Method: The gamma rays emitted from the excited fragments were detected with a mixed array consisting of 8 HPGe EXOGAM Clover detectors (EXILL) and 16 LaBr3(Ce) fast scintillators (FATIMA). The detector system has the unique ability to select the interesting fragment making use of the high resolution of the HPGe detectors and determine subnanosecond lifetimes using the fast scintillators. For the analysis the generalized centroid difference method was used. Results: We show that quadrupole collectivity increases smoothly with increasing neutron number above the closed N = 82 neutron shell. Our measurements are complemented by state-of-the-art theory calculations based on shell-model descriptions. Conclusions: The observed smooth increase in quadrupole collectivity is similar to the evolution seen in the measured masses of the xenon isotopic chain and is well reproduced by theory. This behavior is in contrast to higher Z even-even nuclei where abrupt change in deformation occurs around N = 90.

Multivariate orthogonal polynomials and integrable systems

Multivariate orthogonal polynomials in D real dimensions are considered from the perspective of the Cholesky factorization of a moment matrix. The approach allows for the construction of corresponding multivariate orthogonal polynomials, associated second kind functions, Jacobi type matrices and associated three term relations and also Christoffel-Darboux formulae. The multivariate orthogonal polynomials, their second kind functions and the corresponding Christoffel-Darboux kernels are shown to be quasi-determinants as well as Schur complements of bordered truncations of the moment matrix; quasi-tau functions are introduced. It is proven that the second kind functions are multivariate Cauchy transforms of the multivariate orthogonal polynomials. Discrete and continuous deformations of the measure lead to Toda type integrable hierarchy, being the corresponding flows described through Lax and Zakharov-Shabat equations; bilinear equations are found. Varying size matrix nonlinear partial difference and differential equations of the 2D Toda lattice type are shown to be solved by matrix coefficients of the multivariate orthogonal polynomials. The discrete flows, which are shown to be connected with a Gauss-Borel factorization of the Jacobi type matrices and its quasi-determinants, lead to expressions for the multivariate orthogonal polynomials and their second kind functions in terms of shifted quasi-tau matrices, which generalize to the multidimensional realm, those that relate the Baker and adjoint Baker functions to ratios of Miwa shifted tau-functions in the 1D scenario. In this context, the multivariate extension of the elementary Darboux transformation is given in terms of quasi-determinants of matrices built up by the evaluation, at a poised set of nodes lying in an appropriate hyperplane in R^D, of the multivariate orthogonal polynomials. The multivariate Christoffel formula for the iteration of m elementary Darboux transformations is given as a quasi-determinant. It is shown, using congruences in the space of semi-infinite matrices, that the discrete and continuous flows are intimately connected and determine nonlinear partial difference-differential equations that involve only one site in the integrable lattice behaving as a Kadomstev-Petviashvili type system. Finally, a brief discussion of measures with a particular linear isometry invariance and some of its consequences for the corresponding multivariate polynomials is given. In particular, it is shown that the Toda times that preserve the invariance condition lay in a secant variety of the Veronese variety of the fixed point set of the linear isometry.