On the Yangian Y $$(\mathfrak{g}\mathfrak{l}_{m|n} )$$ and its quantum Berezinian

Jonathan Brundan and Alexander Kleshchev recently introduced a new family of presentations for the Yangian Y of the general linear Lie algebra . In this article, we extend some of their ideas to consider the Yangian Y of the Lie superalgebra . In particular, we give a new proof of the result by Nazarov that the quantum Berezinian is central. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

Laplace-Beltrami operator on symmetric space X ≡ SOo(2, 3)/SO(2) × SO(3) of rank 2 and the related 2-body one dimensional quantum systems

The explicit form of the Laplace-Beltrami operator Δ_LB on symmetric space X  SO₀(2,3)/SO(2) xSO(3) of rank 2 is given. Using the representation of SO₀(2,3) the eigenfunctions of δ_LB, i.e. plane waves on X are constructed. The integral representation of the zonal spherical functions of the group SO_o(2, 3) is presented and the related 2-body one-dimensional quantum systems are considered.     

R-matrix formulation of the quantum inhomogeneous groups ISO q,r (N) and ISp q,r (N)

The quantum commutationsRTT=TTR and the orthogonal (symplectic) conditions for the inhomogeneous multiparametricq-groups of theB _n ,C _n ,D _n type are found in terms of theR-matrix ofB _n+1 ,C _n+1 ,D _n+1 .A consistent Hopf structure on these inhomogeneousq-groups is constructed by means of a projection fromB _n+1 ,C _n+1 ,D _n+1 .Real forms are discussed; in particular, we obtain theq-groups ISO _q,r (n+1,n–1), including the quantum Poincaré group. The inhomogeneusq-groups do not contain dilatations when the parameters satisfy certain conditions. For example, we find a dilatation-freeq-Poincaré group depending on one real parameterq.     

On the mechanism of the (n, 2n) reaction with 14MeV projectiles on127I and209Bi

The angular and spectral distributions of coincident neutrons from the reactions¹²⁷I(n, 2n)¹²⁶I and²⁰⁹Bi(n, 2n)²⁰⁸Bi have been measured with two time-of-flight detectors at the incident energy 14.1 MeV. Neutron emission has been studied for reaction anglesθ _lab between 10° and 150° (relative angles from 60° to 270°). Energy spectra, angular distributions and coincidence yields are compared with statistical model calculations including preequilibrium decay modes, and nuclear level density and spin cut off parameters are derived.     

Determination of the subthreshold state contribution in 13C(alpha,n)16O,the main neutron-source reaction for the s process

The reaction rate of the stellar reaction 13C(alpha,n)16O, which is currently considered to be the main neutron source for the slow (s) process at low energies, has been rederived using the direct alpha-transfer reaction 13C(6Li,d)17O leading to the subthreshold state at 6.356 MeV in 17O. The contribution of the subthreshold state is found to be much smaller than the currently accepted predictions for the main neutron source of the s process, indicating less of a role of this reaction as the neutron source for the s-process scenario in low-mass stars at the asymptotic giant branch.     

Energy, fine structure, and hyperfine structure of the core-excited states 1s2s2pnp 5P (n = 2–5) and 1s2p2mp 5S (m = 2–5) for Li- ion

The relativistic energies, the oscillator strength, and the lifetimes of high-lying core-excited states 1s2s2pnp ⁵P (n=2–5) and 1s2p²mp ⁵S^o (m=2–5) of Li^- ion are calculated with the saddle-point variational method and restricted variation method. The fine structure and the hyperfine structure of the core-excited states for this system are also explored. The results are compared with other theoretical and experimental data in the literature.     

On the accuracy of classical, semiclassical and quantum methods in collision line broadening calculations: Comparative analysis for C2H2-Ar, He systems

Accuracies of classical, semiclassical and quantum methods are comprehensively examined in calculations of impact line widths of C₂H₂ molecules perturbed by Ar and He. The field of comparative study covers both infrared absorption and Raman scattering lines of acetylene having rotational quantum number J=0-30 at temperatures 173 and 296 K. Calculations have been made by fully classical method and by three basic least approximate semiclassical methods, namely, Neilsen-Gordon (NG) method, peaking approximation (PA) and Smith-Giraud-Cooper (SGC) method. Most accurate ab initio potential energy surfaces (PES) of Yang et al. (1996) [21] and Mozsynski et al. (1995) [22] have been applied to model C₂H₂-Ar and C₂H₂-He interactions. The comparison has been made also with available experimental data and with the results of rigorous fully quantum-mechanical calculations within close coupling and coupled states approaches in identical conditions. Semiclassical methods are proved to be not so much accurate as it is generally believed since all they gave in the cases considered seriously underestimated results. The fundamental issue of the adequacy of simplified trajectories in collision broadening calculations is finally reasonably solved. In cases of C₂H₂-Ar and C₂H₂-He systems the use of the “exact” isotropic trajectories (i.e. driven only by the isotropic part of PES) is the main reason of failing of NG, PA and SGC methods. Thus the neglecting of back-influence of the RT exchange on the classical path is a principal defect of semiclassical methods. Finally, the application of simplified trajectories is recognized as inadequate and risky in broadening calculations for molecules having relatively small rotational constants when accurate ab initio PES are applied.     

Cross-sections for the formation of isomeric pair Ge through (n, 2n), (n, p) and (n, α) reactions measured over 13.73 MeV to 14.77 MeV and calculated from near threshold to 20 MeV neutron energies

The cross-sections for formation of isomeric pair, ⁷⁵Ge^m(σ_m) and ⁷⁵Ge^g(σ_g), through ⁷⁶Ge(n, 2n), ⁷⁵As(n, p) and ⁷⁸Se(n, α) reactions were measured at 13.73 MeV, 14.42 MeV and 14.77 MeV neutrons and also estimated using EMPIRE-II and TALYS codes over neutron energies from near threshold to 20 MeV. For each (n, 2n), (n, p) and (n, α) reaction, the cross-section initially increases with neutron energy, but starts decreasing as the neutron energy exceeds the respective threshold of (n, 3n), (n, pn) and (n, αn) reactions. The higher values of σ_m relative to σ_g reveal that the transitions of the excited ⁷⁵Ge from higher energy levels to metastable state (7⁺/2) are favored as compared to unstable ground state (1⁻/2). The present values of cross sections for formation of ⁷⁵Ge^m,g through (n, 2n) and (n, α) reactions are lower, and that of (n, p) reaction are higher compared to most of the corresponding literature cross-sections.     

Research on the prompt neutron multiplicity of fission fragments for 235U(n,f)

According to some experimental and evaluated data, the total excitation energy partitioning way between both of the fission fragments was given with a semi-empirical method. With the calculated energy partitioning way, the prompt neutron multiplicity as a function of fragment mass, (-v)(A), for neutron-induced fission of 235U at En=0.0253 eV, 3 MeV, and 5 MeV was calculated. The results are checked with the total average prompt neutron multiplicities (-v) and compared with the experimental and evaluated data.     

A study of the 6Be system by use of the reaction 3He(3He,p)5Li(g.s.) between 17 and 30 MeV with a polarized target

The differential cross section of the reaction ³He(³He, p)⁵Li(g.s.) has been measured at 26 MeV and the analyzing power A_γ in the energy range 17–30 MeV with the use of a polarized ³He target. The data are compared with existing microscopic multi-channel calculations to the ⁶Be system. The influence of the J^π = 4⁺ channels turned out to be too strong. The deviations from the antisymmetry to 90° c.m. of the analyzing power angular distribution _γ(θ) are discussed with respect to the purely direct transfer model for identical particles in the entrance channel.     

High-temperature superconductivity in bismuth-copper oxides of the type Bi m M n Cu p O x (M=Mg,Ca, Sr,Ba, Bi)

Several oxides of the Bi _m M _n Cu _p O _x family (m=2, 3;n=2, 3, 4;p=1, 2, 3 and M=alkaline earth or Bi), possessing structures similar to the Aurivillius family of oxides, show highT _c superconductivity. Contribution No. 514 from the Solid State and Structural Chemistry Unit.     

Measurements of angular distributions for the 6Li(n,t)4 he reaction in the MeV region

Angular distributions have been measured for the ⁶Li(n, t)⁴ He reaction using pulse height spectra in ⁶LiI(Eu).     

Measurement of the proton spin structure function g1(x,Q2) for Q2 from 0.15 to 1.6 GeV2 with CLAS

Double-polarization asymmetries for inclusive ep scattering were measured at Jefferson Lab using 2.6 and 4.3 GeV longitudinally polarized electrons incident on a longitudinally polarized NH3 target in the CLAS detector. The polarized structure function g(1)(x,Q2) was extracted throughout the nucleon resonance region and into the deep inelastic regime, for Q(2)=0.15-1.64 GeV2. The contributions to the first moment Gamma(1)(Q2)= integral g(1)(x,Q2) dx were determined up to Q(2)=1.2 GeV2. Using a parametrization for g(1) in the unmeasured low x regions, the complete first moment was estimated over this Q2 region. A rapid change in Gamma(1) is observed for Q2<1 GeV2, with a sign change near Q(2)=0.3 GeV2, indicating dominant contributions from the resonance region. At Q(2)=1.2 GeV2 our data are below the perturbative QCD evolved scaling value.