On Z-gradations of twisted loop Lie algebras of complex simple Lie algebras

We define the twisted loop Lie algebra of a finite dimensional Lie algebra $\mathfrak g$ as the Fr\'echet space of all twisted periodic smooth mappings from $\mathbb R$ to $\mathfrak g$. Here the Lie algebra operation is continuous. We call such Lie algebras Fr\'echet Lie algebras. We introduce the notion of an integrable $\mathbb Z$-gradation of a Fr\'echet Lie algebra, and find all inequivalent integrable $\mathbb Z$-gradations with finite dimensional grading subspaces of twisted loop Lie algebras of complex simple Lie algebras.Comment: 26 page

Low-Energy Photodisintegration of the Deuteron and Big-Bang Nucleosynthesis

The photon analyzing power for the photodisintegration of the deuteron was measured for seven gamma-ray energies between 2.39 and 4.05 MeV using the linearly polarized gamma-ray beam of the High-Intensity Gamma-ray Source at the Duke Free-Electron Laser Laboratory. The data provide a stringent test of theoretical calculations for the inverse reaction, the neutron-proton radiative capture reaction at energies important for Big-Bang Nucleosynthesis. Our data are in excellent agreement with potential model and effective field theory calculations. Therefore, the uncertainty in the baryon density obtained from Big-Bang Nucleosynthesis can be reduced at least by 20%.Comment: 5 pages, 5 figure

Cartan subalgebras in C*-algebras of Hausdorff etale groupoids

The reduced $C^*$-algebra of the interior of the isotropy in any Hausdorff \'etale groupoid $G$ embeds as a $C^*$-subalgebra $M$ of the reduced $C^*$-algebra of $G$. We prove that the set of pure states of $M$ with unique extension is dense, and deduce that any representation of the reduced $C^*$-algebra of $G$ that is injective on $M$ is faithful. We prove that there is a conditional expectation from the reduced $C^*$-algebra of $G$ onto $M$ if and only if the interior of the isotropy in $G$ is closed. Using this, we prove that when the interior of the isotropy is abelian and closed, $M$ is a Cartan subalgebra. We prove that for a large class of groupoids $G$ with abelian isotropy---including all Deaconu--Renault groupoids associated to discrete abelian groups---$M$ is a maximal abelian subalgebra. In the specific case of $k$-graph groupoids, we deduce that $M$ is always maximal abelian, but show by example that it is not always Cartan.Comment: 14 pages. v2: Theorem 3.1 in v1 incorrect (thanks to A. Kumjain for pointing out the error); v2 shows there is a conditional expectation onto $M$ iff the interior of the isotropy is closed. v3: Material (including some theorem statements) rearranged and shortened. Lemma~3.5 of v2 removed. This version published in Integral Equations and Operator Theor

Polarons with a twist

We consider a polaron model where molecular \emph{rotations} are important. Here, the usual hopping between neighboring sites is affected directly by the electron-phonon interaction via a {\em twist-dependent} hopping amplitude. This model may be of relevance for electronic transport in complex molecules and polymers with torsional degrees of freedom, such as DNA, as well as in molecular electronics experiments where molecular twist motion is significant. We use a tight-binding representation and find that very different polaronic properties are already exhibited by a two-site model -- these are due to the nonlinearity of the restoring force of the twist excitations, and of the electron-phonon interaction in the model. In the adiabatic regime, where electrons move in a {\em low}-frequency field of twisting-phonons, the effective splitting of the energy levels increases with coupling strength. The bandwidth in a long chain shows a power-law suppression with coupling, unlike the typical exponential dependence due to linear phonons.Comment: revtex4 source and one eps figur

Cross-section measurements of the 86Kr(γ, n) reaction to probe the s-process branching at 85Kr

For the first time, cross-section measurements were carried out for the 86Kr(γ, n) reaction in order to probe the s-process branching point nucleus 85Kr. The branching point nuclei in the s-process path are of importance in testing and constraining the nucleosynthesis models. Cross-section measurement for the photoneutron reaction on the neighbouring stable isotope is carried out to deduce the aforesaid neutron capture cross-section, as has been adopted in the present case of 85Kr branching point. The cross-section results from the 86Kr(γ, n) reaction were compared with the statistical model calculations using TALYS code

Modified calutron negative ion source operation and future plans

Negative ion generation has advanced rapidly by employing the concept of surface ionization. The modified calutron has proven to be a successful tool to explore these concepts and provide solutions to the many problems which must be evaluated. Many features of the SITEX (Surface Ionization with Transverse Extraction) ion source are ideally suited to this exploration. Some of these features are; a ribbon-like plasma, electron control by transverse magnetic fields and the ability to separate the Cs oven parameters from those which control the positive ion generation

Dynamical description of the breakup of one-neutron halo nuclei 11Be and 19C

We investigate the breakup of the one-neutron halo nuclei 11Be and 19C within a dynamical model of the continuum excitation of the projectile. The time evolution of the projectile in coordinate space is described by solving the three-dimensional time dependent Schroedinger equation, treating the projectile-target (both Coulomb and nuclear) interaction as a time dependent external perturbation. The pure Coulomb breakup dominates the relative energy spectra of the fragments in the peak region, while the nuclear breakup is important at higher relative energies. The coherent sum of the two contributions provides a good overall description of the experimental spectra. Cross sections of the first order perturbation theory are derived as a limit of our dynamical model. The dynamical effects are found to be of the order of 10-15% for the beam energies in the range of 60 - 80 MeV/nucleon. A comparison of our results with those of a post form distorted wave Born approximation shows that the magnitudes of the higher order effects are dependent on the theoretical model.Comment: 15 pages, ReVTeX, 5 figures, typos corrected, accepted for publication in Physical Review

Coupling effects in the elastic scattering of 6^{6}He on 12^{12}C

To study the effect of the weak binding energy on the interaction potential between a light exotic nucleus and a target, elastic scattering of 6He at 38.3 MeV/nucleon on a 12C target was measured at Grand Accélérateur National d'Ions Lourds (GANIL). The 6He beam was produced by fragmentation. The detection of the scattered particles was performed by the GANIL spectrometer. The energy resolution was good enough to separate elastic from inelastic scattering contributions. The measured elastic data have been analyzed within the optical model, with the real part of the optical potential calculated in the double-folding model using a realistic density-dependent nucleon-nucleon interaction and the imaginary part taken in the conventional Woods-Saxon (WS) form. A failure of the "bare" real folded potential to reproduce the measured angular distribution over the whole angular range suggests quite a strong coupling of the higher-order breakup channels to the elastic channel. To estimate the strength of the breakup effects, a complex surface potential with a repulsive real part (designed to simulate the polarization effects caused by the projectile breakup) was added to the real folded and imaginary WS potentials. A realistic estimate of the polarization potential caused by the breakup of the weakly bound 6He was made based on a parallel study of 6He+12C and 6Li+12C optical potentials at about the same energies

Developmental pathways to autism: a review of prospective studies of infants at risk

Autism Spectrum Disorders (ASDs) are neurodevelopmental disorders characterized by impairments in social interaction and communication, and the presence of restrictive and repetitive behaviors. Symptoms of ASD likely emerge from a complex interaction between pre-existing neurodevelopmental vulnerabilities and the child's environment, modified by compensatory skills and protective factors. Prospective studies of infants at high familial risk for ASD (who have an older sibling with a diagnosis) are beginning to characterize these developmental pathways to the emergence of clinical symptoms. Here, we review the range of behavioral and neurocognitive markers for later ASD that have been identified in high-risk infants in the first years of life. We discuss theoretical implications of emerging patterns, and identify key directions for future work, including potential resolutions to several methodological challenges for the field. Mapping how ASD unfolds from birth is critical to our understanding of the developmental mechanisms underlying this disorder. A more nuanced understanding of developmental pathways to ASD will help us not only to identify children who need early intervention, but also to improve the range of interventions available to them