SO(r+2, r) pure spinors

Chevalley gave a comprehensive treatment of pure spinors for Clifford algebras whose quadratic form has maximal index. We here show how the notion of pure spinor can be extended to the real Clifford algebras associated with quadratic forms with r+2 positive and r negative eigenvalues.     

Exact bound states for the potentialV(r)=r 2+βr −4+λr −6 using partial algebraization technique

For the potential considered new sets of ground state and first few excited states are obtained. Also the defect of the wave function suggested by Kaushal and Parashar [Phys. Lett. A170 (1992) 335] and Gaurdiala and Ros [J. Phys. A25 (1992) 1351] has been shown.     

Stereodynamics of the reactions Ne+H2+/Ne+D2+/Ne+T2

The vector correlations between products and reagents for the reactions Ne+H + 2 , Ne+D + 2 , and Ne+T + 2 are calculated by means of the quasi-classical trajectory method on a new potential energy surface constructed by Lü et al. [J. Chem. Phys. 2010 132, 014303]. The polarization-dependent differential cross-sections (2π/σ)(dσ 00 /dω t ), (2π/σ)(dσ 20 /dω t ), (2π/σ)(dσ 22+ /dω t ), and (2π/σ)(dσ 21 /dω t ), and the distributions of P (θ r ), P (φ r ), and P (θ r ,φ r ) are calculated. The isotopic effect, which is associated with the difference in mass factor among the three reactions, is revealed.     

Exchange interaction and spin dynamics in pentanuclear clusters, Cu3Ln2(ClCH2COO)12(H2O)8 (Ln = Nd3+, Sm3+, Pr3+)

New compounds, [Cu₃Ln₂(ClCH₂COO)₁₂(H₂O)₈]·2H₂O with Ln = Nd³⁺ (I), Sm³⁺ (II), Pr³⁺ (III), built up of pentanuclear clusters were synthesized and studied by means of X-ray analysis and electron paramagnetic resonance (EPR). X-ray data show that all compounds are isostructural and the pentanuclear clusteres may be considered as a linear system with alternating Cu(II) and Ln(III) ions: Cu(2)-L¹-Ln-L²-Cu(1)-L²-Ln-L²-Cu(2) with L¹ and L² being bridging fragments and Cu(1) and Cu(2) being structurally nonequivalent copper complexes. EPR studies demonstrate that in the temperature range of 100–293 K the signals due to only one type of the copper complexes are observed in the spectra of I–III. AtT<100 K the spectral temperature dependence is nontrivial. AtT<30 K new signals are detected in the spectra of I and II. The temperature dependence of the EPR spectra is interpreted under the assumption that the parameter of the exchange interaction Cu(2)-Ln considerably exceeds the parameter of the interaction Cu(1)-Ln. EPR spectra are calculated for the fragments of five paramagnetic centers in the frames of the model taking into account the nonequivalence of two copper complexes, short longitudinal and transverse paramagnetic relaxation times of the rare-earth ions at room temperature and the change of the relaxation rates when the temperature decreases. The results of the calculations show that it is possible to obtain information about the interactions in the system on the basis of the analysis of the temperature dependence of the EPR spectra of the central copper complex. The parameter of the isotropic part of the exchange interaction between copper and neodymium ions (for the interaction Cu(2)-Nd) is estimated as about 15 cm⁻¹. A considerable rearrangement of the spin states when the temperature changes is found for all complexes.     

EPR and optical-absorption studies of Cu2+-doped Zn(NH2(CH2)3NHOH)2Ni(CN)4 single crystals

Electron paramagnetic resonance of Cu²⁺-doped catena-trans-bis(N-(2-hydroxyethyl)-ethylenediamine) zinc(II)-tetra-μ-cyanonicelate(II) [Zn(NH₂(CH₂)₃NHOH)₂Ni(CN)₄] single crystals and powder are examined at room temperature. The spectra show the substitution of the Zn²⁺ ion with the Cu²⁺ ion. The crystal field around the Cu²⁺ ion is nearly axial. There is a single paramagnetic site withg _xx=2.073,g _yy=2.060,g _zz=2.248,A _xx=40.5 G,A _yy=50.8 G,A _zz=172.0 G. The ground-state wave function is an admixture of d _x ²−y ² and d _z ² states. The optical-absorption studies show two bands at 320 nm (31250 cm⁻¹) and 614 nm (16286 cm⁻¹) which confirm the axial symmetry. The crystal field parameters and the wave function are determined.     

The exact bound-state ansaetze as zero-order approximations in perturbation theory II. An illustration:V(r)=r 2+fr 2/(1+gr 2)

Challenging Gallas double-well interactions are shown tractable by the quasi Rayleigh Schroedinger perturbation theory of paper I, and a good precision is obtained in the first-order numerical test. The related technicalities are clarified: The existence of the suitable zero-order solutions withf 0 andg 0 is proved and a few closed formulas for corrections are given and discussed.     

Line strength measurements of carbonyl sulfide (OCS) in the 2v3, v1+2v2+v3, and 4v2+v3 bands

To support planetary studies of the Venus atmosphere, we measured line strengths of the 2v₃, v₁+2v₂+v₃, and 4v₂+v₃ bands of the primary isotopologue of carbonyl sulfide (¹⁶O¹²C³²S), whose band centers are located at 4101.387, 3937.427, and 4141.212 cm⁻¹, respectively. For this, infrared absorption spectra in normal carbonyl sulfide (OCS) sample gas were recorded at an unapodized resolution of 0.0033 cm⁻¹ at ambient room temperatures using a Bruker Fourier transform spectrometer (FTS) at the Jet Propulsion Laboratory. The FTS instrumental line shape (ILS) function was investigated, which revealed no significant instrumental line broadening or distortions. Various custom-made short cells and a multi-pass White cell were employed to achieve optical densities sufficient to observe the strong 2v₃ and the weaker bands in the region. Gas sample impurities and the isotopic abundances were determined from mass spectrum analysis. Line strengths were retrieved spectrum by spectrum using a non-linear curve fitting algorithm adopting a standard Voigt line profile, from which Herman–Wallis factors were derived for the three bands. The band strengths of 2v₃, v₁+2v₂+v₃, and 4v₂+v₃ of ¹⁶O¹²C³²S (normalized at 100% of isotopologue) are observed to be 6.315(13)×10⁻¹⁹, 1.570(2)×10⁻²⁰, and 7.949(20)×10⁻²¹ cm⁻¹/molecule cm⁻², respectively, at 296 K. These results are compared with earlier measurements and the HITRAN 2004 database.     

Experimental determination of the potential energy curves of the I(3/2u) and I(3/2g) states of Kr+ 2

The I(3/2u) and I(3/2g) states of Kr⁺ ₂ have been investigated by pulsed-field-ionization zero-kinetic-energy (PFI-ZEKE) photoelectron spectroscopy following (2 + 1′) resonance-enhanced multiphoton excitation via the 0⁺ _g Rydberg state located below the Kr?([4p]⁵5p[1/2]₀) + Kr(¹S₀) dissociation limit of Kr₂. From the positions of a large number of vibrational bands in the spectra of the ⁸⁴Kr₂ and ⁸⁴Kr-⁸⁶Kr isotopomers, the adiabatic ionization potentials (IP(I(3/2u)) = 112672.4 ± 0.8cm^?1, IP(I(3/2g)) = 111 395.0 ± 1.4cm^?1), the dissociation energies (D ⁺ ₀(I(3/2u)) = 368.8 ± 2.0cm^?1, D ⁺ ₀(I(3/2g)) = 1646.2 ± 2.3cm^?1) and vibrational constants for both ionic states have been determined. Potential energy curves have been extracted which perfectly reproduce all experimental observations and are accurate over a wide range of energies and internuclear distances. The equilibrium internuclear distances (R ⁺ _e(I(3/2u)) = 4.11 ± 0.04 Å, R ⁺ _e(I(3/2g)) = 3.35 ± 0.10 Å) have been derived by comparing the intensity distribution in the PFI-ZEKE photoelectron spectra to calculated Franck-Condon factors. The dissociation energy of the I(3/2g) state and the equilibrium internuclear distance of the I(3/2u) state differ markedly from previously reported values.     

Galilean-Invariant (2+1)-Dimensional Models with a Chern–Simons-Like Term andD=2 Noncommutative Geometry

We consider a newD=2 nonrelativistic classical mechanics model providing via the Noether theorem the (2+1)-Galilean symmetry algebra with two central charges: massmand the coupling constantkof a Chern–Simons-like term. In this way we provide the dynamical interpretation of the second central charge of the (2+1)-dimensional Galilean algebra. We discuss also the interpretation ofkas describing the noncommutativity ofD=2 space coordinates. The model is quantized in two ways: using the Ostrogradski–Dirac formalism for higher order Lagrangians with constraints and the Faddeev–Jackiw method which describes constrained systems and produces nonstandard symplectic structures. We show that our model describes the superposition of a free motion in noncommutativeD=2 spaces as well as the “internal” oscillator modes. We add a suitably chosen class of velocity-dependent two-particle interactions, which is described by local potentials inD=2 noncommutative space. We treat, in detail, the particular case of a harmonic oscillator and describe its quantization. It appears that the indefinite metric due to the third order time derivative term in the field equations, even in the presence of interactions, can be eliminated by the imposition of a subsidiary condition.     

Synthesis and characterization of HgBa2Can−1CunO2n+2+δ (n = 1, 2, and 3)

We have successfully prepared the first three members of the mercury-based superconducting compounds Hg--- Ba₂Ca_n−1Cu_nO_2n+2+δ, namely Hg---1201, Hg---1212 and Hg---1223 with high purity and very good quality. T he influence of the synthesis parameters is studied in detail. Using the sealed quartz tube method, very simple procedures are found to ensure a 100% reproducibility of nearly 100% pure Hg---1201 and 85–90% Hg---1212 and Hg---1223. Oxygen annealing of the sample Hg---1201 at 300°C for 18 h results in an enhancement of its critical temperature up to 97 K. The symmetry of the first and second members is tetragonal with lattice parameters

Full-size image (2K)

, respectively. X-ray diffraction lines of Hg---1223 can be indexed in a tetragonal cell with

Full-size image (1K)

as well as in an orthorhombic cell with lattice parameters

Full-size image (1K)

.     

Weak nonleptonic decays of 3/2+ isobars in SU(3)

Weak transitions of decuplet isobars are expanded in terms of eigen-amplitudes of the direct channel in the framework of SU(3). Starting with the most general weak Hamiltonian and assuming intermediate states to be non-exotic, we obtain ΔI=1/2 rule for Ω⁻ decays. Invoking of the CP invariance forbids all thepv weak processesD(10)→D(10) +P(8). Decays of the charmed multiplets are also discussed in these dynamical considerations. We obtain triplet dominance of charm changing weak Hamiltonian for Ω*⁺⁺ ₃ decays.     

Influence of the reagent vibration on the stereo-dynamics of the reactions D- + H2 and H- + D2

Employing the quasi-classical trajectory method and the potential energy surface of Panda and Sathyamurhy [Panda A N and Sathyamurthy N 2004 J. Chem. Phys. 121 9343], the effect of the reagent vibration on vector correlation of the ion-molecule reactions D^- + H₂ and H^- + D₂ is studied at a collision energy of 35.7 kcal/mol. Four generalized polarization-dependent differential cross sections (2π/σ)(dσ₀₀/dω_t),(2π/σ)(dσ₂₀/dω_t),(2π/σ)(dσ₂₂/dω_t), and (2π/σ)(dσ₂₀/dω_t) are presented in the centre-of-mass reference frame, separately. At the same time, the effects on the product angular distributions P(θ_r), P(φ_r) and P(θ_r,φ_r) of the title reactions are also analysed. The calculated results show that the scattering tendencies of the product HD, the alignment and the orientation of j' sensitively depend on reagent molecule vibration.     

Y2O3:Yb3+,Tm3+纳米材料的可见及紫外上转换发光

通过燃烧法制备了Yb³⁺-Tm³⁺共掺的Y₂O₃纳米粉体,并对样品在980 nm激光照射下的上转换发光特性进行了研究.实验发现,样品在可见光区域能够产生强烈的蓝色发光(476 nm和487 nm)和较弱的红色发光(约650 nm),而且同时观察到了两个紫外发光峰¹I₆→³H₆ (~297 nm)和^{1关键词： 2O₃:Yb3+')" href="#">Y₂O₃:Yb3+ 3+}')" href="#">Tm³⁺ 上转换光谱 敏化 紫外发光     

Magnetic and electric properties of layered perovskites Nd2−2xSr1+2xMn2O7 (x=0.3–0.5)

Magnetic and electric properties of layered perovskites Nd_2−2xSr_1+2xMn₂O₇ (x=0.3, 0.4 and 0.5) are sensitive to the doping content x. The sample with x=0.5 is antiferromagnetic (AFM) and insulating. On decreasing x, the AFM ordering is suppressed and a canted AFM or weak ferromagnetic (FM) ordering appears, and the resistivity decreases. The sample with x=0.4 still shows insulating behavior, but a metal–insulator transition is observed for x=0.3. By suggesting the presence of a competition between AFM super-exchange interaction and FM double-exchange interaction, the doping dependence of magnetic and electric properties can be understood.     

Grafting and Poisson Structure in (2+1)-Gravity with Vanishing Cosmological Constant

We relate the geometrical construction of (2+1)-spacetimes via grafting to phase space and Poisson structure in the Chern-Simons formulation of (2+1)-dimensional gravity with vanishing cosmological constant on manifolds of topology , where S _g is an orientable two-surface of genus g>1. We show how grafting along simple closed geodesics λ is implemented in the Chern-Simons formalism and derive explicit expressions for its action on the holonomies of general closed curves on S _g .We prove that this action is generated via the Poisson bracket by a gauge invariant observable associated to the holonomy of λ. We deduce a symmetry relation between the Poisson brackets of observables associated to the Lorentz and translational components of the holonomies of general closed curves on S _g and discuss its physical interpretation. Finally, we relate the action of grafting on the phase space to the action of Dehn twists and show that grafting can be viewed as a Dehn twist with a formal parameter θ satisfying θ² = 0.     

Theoretical calculation of of B-like ions： photoionization cross sections N^2＋, O^3＋ and F^4＋

There can be found some notable discrepancies with regard to the resonance structures when R-matrix calculations from the Opacity Project and other sources are compared with recent absolute experimental measurements of Bizau et al [Astron.Astrophts.439 387(2005)] for B-like ions N2+,O3+ and F4+.We performed close-coupling calculations based on the R-matrix formalism for the photoionizations of ions mentioned above both for the ground states and first excited states in the near threshold regions.The present results are compared with experimental ones given by Bizau et al and earlier theoretical ones.Excellent agreement is obtained between our theoretical results and the experimental photoionization cross sections.The present calculations show a significant improvement over the previous theoretical results.     

用于白光LED的单一基质白光荧光粉Ca2SiO3Cl2:Eu2+，Mn2+的发光性质

用高温固相法合成了Eu²⁺，Mn²⁺共激活的Ca₂SiO₃Cl₂高亮度白色发光材料，并对其发光性质进行了研究. 该荧光粉在近紫外光激发下发出强的白色荧光，Eu^{2+中心形成峰值为419 nm和498 nm的特征宽带，通过Eu2+中心向Mn2+中心的能量传递导致了峰值为578 nm的发射，三个谱带叠加从而在单一基质中得到了白光. 激发光谱均分布在250—415 nm的波长范围，红绿蓝三个发射带的激发谱峰值分别位于385 nm，412 nm，370 nm和396 nm处，可以被InGaN管芯产生的紫外辐射有效激发. Ca₂SiO₃Cl₂:Eu2+，Mn2+是一种很有前途的单一基质白光LED荧光粉.}     

Dynamical supersymmetry of the magnetic monopole and the 1/r 2-potential

We examine the recently discovered dynamical OSp(1, 1) supersymmetry of the Pauli Hamiltonian for a spin 1/2 particle with gyromagnetic ratio 2, in the presence of a Dirac magnetic monopole. Using this symmetry and algebraic methods only, we construct the spectrum and obtain the wave functions. At all but the lowest angular momenta, the states transform under a single irreducible representation of OSp(1, 1). On the lowest angular momentum states, it is impossible to define self-adjoint supercharges, and the states transform under an irreducible representation of SO(2, 1) only. The Hamiltonian is not self-adjoint in thes-wave sector, but admits a one parameter family of self-adjoint extensions. The full SO(2, 1) algebra can be realized only for two specific values of the parameter.The Pauli Hamiltonian is generalized to accommodate a ²/r ² potential. The new Hamiltonian exhibits a dynamical OSp(2, 1) supersymmetry. The spectrum and the wave functions are obtained. The states at all but the lowest angular momenta transform under the sum of two irreducible representations of OSp(2, 1). These two representations are distinguished by the chirality of their ground state. On the lowest angular momentum states, the OSp(2, 1) group is still realized, since the supercharges can all be rendered self-adjoint simultaneously, but the states only transform according to a single irreducible representation of OSp(2, 1). The chirality of the ground state for this representation is related to the signs of andeg. The Hamiltonian is not self-adjoint in thes-wave sector when ||<3/2. Only one of its self-adjoint extensions supports the OSp(2, 1) supersymmetry, and yields the wave functions obtained from the group theoretic approach. The supersymmetry is always spontaneously broken as there exists no normalizable zero energy states.The massless Dirac Hamiltonian in the presence of a magnetic monopole and a/r potential is related to a generator of an OSp(2, 1) superalgebra which also contains the Pauli Hamiltonian. This symmetry is used to generate the complete spectrum of the Dirac Hamiltonian.This work is supported in part through funds provided by the U.S. Department of Energy (DOE) under contract DE-AC02-76ER03069, and by the Natural Science and Engineering Research Council (NSERC) of Canada     

Theoretical study of stereodynamics for the reaction O(3P) +D2 (v=0, j=0) to OD+D and isotope effect

Quasi-classical trajectory (QCT) calculations have been performed to study the product polarization behaviours in the reaction O(³P) + D₂ (v= 0, j= 0)→OD + D. By running trajectories on the ³A′ and ³A″ potential energy surfaces (PESs), vector correlations such as the distributions of the polarization-dependent differential cross sections (PDDCSs), the angular distributions of P(θ_r) and P(ø_r) are presented. Isotope effect is discussed in this work by a comprehensive comparison with the reaction O(³P) + H₂ (v= 0, j= 0) → H + H. Common characteristics as well as differences are discussed in product alignment and orientation for the two reactions. The isotope mass effect differs on the two potential energy surfaces: the isotope mass effect has stronger influence on P(θ_r) and PDDCSs of the ³A′ PES while the opposite on P(ø_r) of the ³A″ potential energy surface.     

On the energy levels for the screened Coulomb potentialV(r)=−Z/r+Gλ/(1+λr)

The energy eigenvalues of various eigenstates for the potentialV(r)=?Z/r+Gλ/(1+λr) are accurately evaluated within the framework of the hypervirial-Padé scheme. An approximate formula for energy levels is also obtained with the use of the Ecker-Weizel approximation. The results of the present calculations are compared with those of a dispersion calculation.