On General Volume-Preserving Mechanical Systems via Cohomology

We present the general form of equations that generate a volume-preserving flow on a symplectic manifold (M,ω) via the highest Euler-Lagrange cohomology.It is shown that for every volume-preserving flow there are some 2-forms that play a similar role to the Hamiltonian in the Hamilton mechanics and the ordinary canonical equations with Hamiltonian H are included as a special case with a 2-form Hω/(n-1).     

On General Volume-Preserving Mechanical Systems via Cohomology

We present the general form of equations that generate a volume-preserving flow on a symplectic manifold(Μ,ω) via the highest Euler-Lagrange cohomology. It is shown that for every volume-preserving fiow there are some 2-forms that play a similar role to the Hamiltonian in the Hamilton mechanics and the ordinary canonical equations with Hamiltonian H are included as a special case with a 2-form Hω/(n - 1).     

Lattice models with N=2 supersymmetry

We introduce lattice models with explicit N=2 supersymmetry. In these interacting models, the supersymmetry generators Q+/- yield the Hamiltonian H=(Q(+),Q(-)) on any graph. The degrees of freedom can be described as either fermions with hard cores, or as quantum dimers; the Hamiltonian of our simplest model contains a hopping term and a repulsive potential. We analyze these models using conformal field theory, the Bethe ansatz, and cohomology. The simplest model provides a manifestly supersymmetric lattice regulator for the supersymmetric point of the massless (1+1)-dimensional Thirring (Luttinger) model. Generalizations include a quantum monomer-dimer model on a two-leg ladder.     

Unification of perturbation theory, random matrix theory, and semiclassical considerations in the study of parametrically dependent eigenstates

We consider a classically chaotic system that is described by a Hamiltonian H(Q,P;x), where x is a constant parameter. Specifically, we discuss a gas particle inside a cavity, where x controls a deformation of the boundary or the position of a "piston." The quantum eigenstates of the system are |n(x)>. We describe how the parametric kernel P(nmid R:m) = ||(2) evolves as a function of deltax = x-x(0). We explore both the perturbative and the nonperturbative regimes, and discuss the capabilities and the limitations of semiclassical as well as random waves and random-matrix-theory considerations.     

Sharp spectral lines observed in gamma-ray ionized parahydrogen crystals

We have observed sharp infrared spectral lines ( Deltanu approximately 60 MHz FWHM) in gamma-ray ionized para- H2 crystals. The lines are assigned to the Q1(0) transition of H2 near H+3 and H-, which becomes optically active and Stark shifted by the Coulomb fields of the ions. A simple model calculation gives a spectrum which agrees approximately with the observation. The spectrum stays the same over many days, demonstrating the stability of the ionized system. The remarkable sharpness and reproducibility of the line positions indicate uniformity of the local structure surrounding the charges.     

Quantum theory of optical multistability in a two-photon three-level medium

An effective Hamiltonian for the two-level model is derived from the microscopic Hamiltonian of a three-level atom in a configuration, interacting through two-photon transitions with a lightfield. The effective Hamiltonian includes a term describing the optical Stark shift. With this effective Hamiltonian, we study the steady-state equation and the squeezing spectrum from a cavity field mode interacting with an ensemble of three level configuration atoms by a two-photon transition. It is shown that the inclusion of optical Stark shift brings about changes in drift and diffusion coefficients as well as additional nonzero correlations between the stochastic forces. As a result, although qualitative features remain unaltered, quantitative changes both in the transmission characteristics and the squeezing spectrum are significant.     

First High-Resolution Infrared Observation of the Symmetry-Forbidden nu(5) Band of (10)B(2)H(6)

Spectra of (10)B monoisotopic diborane, B(2)H(6), have been recorded at high resolution (2-3 x 10(-3) cm(-1)) by means of Fourier transform spectroscopy in the region 700-1300 cm(-1). A thorough analysis of the nu(18) a-type, nu(14) c-type, and nu(5) symmetry-forbidden band has been performed. Of particular interest are the results concerning the nu(5) symmetry-forbidden band, which is observed only because it borrows intensity through an a-type Coriolis interaction with the very strong nu(18) infrared band located approximately 350 cm(-1) higher in wavenumber. The nu(5) band has been observed around 833 cm(-1) and consists of a well-resolved Q branch accompanied by weaker P- and R-branch lines. Very anomalous line intensities are seen, with the low K(a) transitions being vanishingly weak, and Raman-like selection rules observed. The determination of the upper state Hamiltonian constants proved to be difficult since the corresponding energy levels of each of the bands are strongly perturbed by nearby dark states. To account for these strong localized resonances, it was necessary to introduce the relevant interacting terms in the Hamiltonian. As a result the upper state energy levels were calculated satisfactorily, and precise vibrational energies and rotational and coupling constants were determined. In particular the following band centers were derived: nu(0) (nu(5)) = 832.8496(70) cm(-1), nu(0) (nu(14)) = 977.57843(70) cm(-1), and nu(0) (nu(18)) = 1178.6346(40) cm(-1). (Type A standard uncertainties (1varsigma) are given in parentheses.) Copyright 2000 Academic Press.     

A solid-state N magic-angle spinning NMR study of some amino acids

Experimental strategies for the acquisition of high-quality 14N magic-angle spinning (MAS) NMR spectra of the simple amino acids, which exhibit 14N quadrupole coupling constants (C(Q)) on the order of 1.2 MHz, are devised. These are the first useful 14N MAS spectra reported for nitrogen compounds having a C(Q)(14N) value in excess of 1 MHz. The complete manifolds of spinning sidebands (ssbs), i.e., about 300 ssbs for a spinning frequency of 6.0 kHz, have been observed in the 14N MAS NMR spectra of a series of amino acids. In their crystal structure these amino acids all exhibit the zwitterionic form and thus the 14N MAS NMR spectra represent those of a rotating -NH(3)(+) group and not of an amino (-NH(2)) group. Computer simulations combined with fitting of simulated to the experimental ssb intensities result in the determination of precise values for the 14N quadrupole coupling (C(Q)) and its associated asymmetry parameter (eta(Q)) for the nitrogen sites in these molecules. For some of the amino acids the 14N MAS NMR spectra exhibit overlap between the manifolds of ssbs from two different nitrogen sites in accordance with their crystal structures. Computer analysis of these spectra results in two different sets of (C(Q), eta(Q)) values which mainly differ in the magnitudes for eta(Q).     

BF自由基X~1Σ~+和a~3Π态光谱常数和分子常数研究

采用内收缩多参考组态相互作用方法和相关一致基aug-cc-pV6Z,对BF自由基X~1∑~+和a~3Π态的势能曲线进行了研究.计算是在0.095-133 nm的核间距内进行的.为获得更准确的结果,计算中还考虑了Davidson修正、相对论修正及核价相关修正对势能曲线的影响.相对论修正采用的方法是二阶DouglasKroll哈密顿近似,修正计算是在cc-pV5Z基组水平上进行的.核价相关修正使用的是cc-pCV5Z基组.利用得到的势能曲线,拟合出了各种修正下BF自由基X~1∑~+和a~3Ⅱ态的光谱常数De,Re,ωe,ωeχe,ωeye,Be和αe、并与实验结果进行了比较.结果表明:考虑Davidson修正、相对论修正和核价相关修正后得到的光谱常数最接近实验结果.利用修正后的势能曲线,通过求解径向振转Schr6dinger方程,找到了转动量子数J=0时这两个电子态的全部振动态,并计算了每一电子态前20个振动态的振动能级、惯性转动常数和离心畸变常数,其值与已有的实验结果较为一致.本文得到的光谱常数和分子常数达到了很高的精度,能为进一步的光谱实验提供可靠的参考.     

A solid-state 14N magic-angle spinning NMR study of some amino acids

Experimental strategies for the acquisition of high-quality 14N magic-angle spinning (MAS) NMR spectra of the simple amino acids, which exhibit 14N quadrupole coupling constants (C(Q)) on the order of 1.2 MHz, are devised. These are the first useful 14N MAS spectra reported for nitrogen compounds having a C(Q)(14N) value in excess of 1 MHz. The complete manifolds of spinning sidebands (ssbs), i.e., about 300 ssbs for a spinning frequency of 6.0 kHz, have been observed in the 14N MAS NMR spectra of a series of amino acids. In their crystal structure these amino acids all exhibit the zwitterionic form and thus the 14N MAS NMR spectra represent those of a rotating -NH(3)(+) group and not of an amino (-NH(2)) group. Computer simulations combined with fitting of simulated to the experimental ssb intensities result in the determination of precise values for the 14N quadrupole coupling (C(Q)) and its associated asymmetry parameter (eta(Q)) for the nitrogen sites in these molecules. For some of the amino acids the 14N MAS NMR spectra exhibit overlap between the manifolds of ssbs from two different nitrogen sites in accordance with their crystal structures. Computer analysis of these spectra results in two different sets of (C(Q), eta(Q)) values which mainly differ in the magnitudes for eta(Q).     

Asymmetric Berry-phase interference patterns in a single-molecule magnet

A Mn(4) single-molecule magnet displays asymmetric Berry-phase interference patterns in the transverse-field (H(T)) dependence of the magnetization tunneling probability when a longitudinal field (H(L)) is present, contrary to symmetric patterns observed for H(L)=0. Reversal of H(L) results in a reflection of the transverse-field asymmetry about H(T)=0, as expected on the basis of the time-reversal invariance of the spin-orbit Hamiltonian which is responsible for the tunneling oscillations. A fascinating motion of Berry-phase minima within the transverse-field magnitude-direction phase space results from a competition between noncollinear magnetoanisotropy tensors at the two distinct Mn sites.     

Investigation of the conjectured nucleon deformation at low momentum transfer

We report new precise H(e,e(')p)pi(0) measurements at the Delta(1232) resonance at Q(2)=0.127 (GeV/c)(2) obtained at the MIT-Bates out-of-plane scattering facility which are particularly sensitive to the transverse electric amplitude (E2) of the gamma(*)N-->Delta transition. The new data have been analyzed together with those of earlier measurements to yield precise quadrupole to dipole amplitude ratios: Re(E(3/2)(1+)/M(3/2)(1+))=(-2.3+/-0.3(stat+syst)+/-0.6(model))% and Re(S(3/2)(1+)/M(3/2)(1+))=(-6.1+/-0.2(stat+syst)+/-0.5(model))% for M(3/2)(1+)=(41.4+/-0.3(stat+syst)+/-0.4(model))(10(-3)/m(pi(+))). The derived amplitudes give credence to the conjecture of deformation in hadrons favoring, at low Q2, the dominance of mesonic effects.     

Satellite transitions in natural abundance solid-state (33)S MAS NMR of alums--sign change with zero-crossing of C(Q) in a variable temperature study

Experiences obtained from recent improvements in the performance of solid-state (14)N MAS NMR spectroscopy have been used in a natural abundance (33)S MAS NMR investigation of the satellite transitions for this interesting spin I=3/2 isotope. This study reports the first observation of manifolds of spinning sidebands for these transitions in (33)S MAS NMR as observed for the two alums XAl(SO(4))(2) x 12H(2)O with X=NH(4) and K. For the NH(4)-alum a variable temperature (33)S MAS NMR study, employing the satellite transitions, shows that the (33)S quadrupole coupling constant (C(Q)) exhibits a linear temperature dependence (in the range -35 degrees C to 70 degrees C) with a temperature gradient of 3.1 kHz/ degrees C and undergoes a sign change with zero-crossing for C(Q) at 4 degrees C (277 K). For the isostructural K-alum a quite similar increase in the magnitude of C(Q) with increasing temperature is observed, and with a temperature gradient of 2.3 kHz/ degrees C. Finally, for optimization purposes, a study on the effect of the applied pulse widths at constant rf field strength on the intensity and variation in second-order quadrupolar lineshape for the central (1/2<-->-1/2) transition of the K-alum has been performed.     

High-frequency and -field EPR and FDMRS study of the [Fe(H2O)6]2+ ion in ferrous fluorosilicate

The complex [Fe(H2O)6]SiF6 is one of the most stable and best characterized high-spin Fe(II) salts and as such, is a paradigm for the study of this important transition metal ion. We describe high-frequency and -field electron paramagnetic resonance studies of both pure [Fe(H2O)6]SiF6 and [Zn(H2O)6]SiF6 doped with 8% of Fe(II). In addition, frequency domain magnetic resonance spectroscopy was applied to these samples. High signal-to-noise, high resolution spectra were recorded which allowed an accurate determination of spin Hamiltonian parameters for Fe(II) in each of these two, related, environments. For pure [Fe(H2O)6]SiF6, the following parameters were obtained: D=+11.95(1) cm(-1), E=0.658(4) cm(-1), g=[2.099(4),2.151(5),1.997(3)], along with fourth-order zero-field splitting parameters: B4(0)=17(1)×10(-4) cm(-1) and B4(4)=18(4)×10(-4) cm(-1), which are rarely obtainable by any technique. For the doped complex, D=+13.42(1) cm(-1), E=0.05(1) cm(-1), g=[2.25(1),2.22(1),2.23(1)]. These parameters are in good agreement with those obtained using other techniques. Ligand-field theory was used to analyze the electronic absorption data for [Fe(H2O)6]SiF6 and suggests that the ground state is 5A1, which allows successful use of a spin Hamiltonian model. Density functional theory and unrestricted Hartree-Fock calculations were performed which, in the case of latter, reproduced the spin Hamiltonian parameters very well for the doped complex.     

Nuclear Structure and Electromagnetic Transitions Investigation in Er Isotopes within Framework of Interacting Boson Model

Interacting Boson Model-2 (IBM-2) is used to determine the Hamiltonian for Er nuclei. Fit values of parameters are used to construct the Hamiltonian, energy levels and electromagnetic transitions (B(E2), B(M1)) multipole mixing ratios (δ(E2/M1)) for some even-even Er nuclei and monopole transition probability are estimated. New ideas are used for counting bosons number at N = 64 and results are compared with previous works.     

Using a cross-coil to reduce RF heating by an order of magnitude in triple-resonance multinuclear MAS at high fields

Four different coil designs for use with MAS in triple-resonance multi-nuclear experiments at high fields are compared, using a combination of finite element analysis (FEA) software and NMR experiments, with respect to RF field strength per unit power and relative sample heating, as governed by mean E/B(1) within the sample region. A commercial FEA package, Microwave Studio 5.1 by Computer Simulation Technology (CST) is shown to obtain remarkably accurate agreement with the experiments in Q(L), L, B, E, and mode frequencies in all cases. A simplified treatment of RF heating in NMR MAS samples is derived and shown to agree with the NMR experimental results within about 10% for two representative stator designs. The coil types studied include: (1) a variable-pitch solenoid outside a ceramic coilform, (2) a conventional solenoid very closely spaced to the MAS rotor, (3) a scroll coil, and (4) a segmented saddle cross coil (XC) for (1)H with an additional solenoid over it for the two lower-frequency channels. The XC/solenoid is shown to offer substantial advantages in reduced decoupler heating, improved S/N, and improved compatibility with multinuclear tuning and high-power decoupling. This seems largely because the division of labor between two orthogonal coils allows them each, and their associated circuitry, to be separately optimized for their respective regimes.     

Sensitivity enhancement in natural-abundance solid-state 33S MAS NMR spectroscopy employing adiabatic inversion pulses to the satellite transitions

The WURST (wideband uniform rate smooth truncation) and hyperbolic secant (HS) pulse elements have each been employed as pairs of inversion pulses to induce population transfer (PT) between the four energy levels in natural abundance solid-state (33)S (spin I=3/2) MAS NMR, thereby leading to a significant gain in intensity for the central transition (CT). The pair of inversion pulses are applied to the satellite transitions for a series of inorganic sulfates, the sulfate ions in the two cementitious materials ettringite and thaumasite, and the two tetrathiometallates (NH(4))(2)WS(4) and (NH(4))(2)MoS(4). These materials all exhibit (33)S quadrupole coupling constants (C(Q)) in the range 0.1-1.0 MHz, with precise C(Q) values being determined from analysis of the PT enhanced (33)S MAS NMR spectra. The enhancement factors for the WURST and HS elements are quite similar and are all in the range 1.74-2.25 for the studied samples, in excellent agreement with earlier reports on HS enhancement factors (1.6-2.4) observed for other spin I=3/2 nuclei with similar C(Q) values (0.3-1.2 MHz). Thus, a time saving in instrument time by a factor up to five has been achieved in natural abundance (33)S MAS NMR, a time saving which is extremely welcome for this important low-gamma nucleus.     

Stark spectrum of barium in highly excited Rydberg states

We present observations of Stark spectra of barium in highly excited Rydberg states in the energy region around n = 35. The one-photon excitation concerns the π transition. The observed Stark spectra at electric fields ranging from 0 to 60 V·cm-1 are well explained by the diagonalization of the Hamiltonian incorporating the core effects. From the Stark maps, the anti-crossings between energy levels are identified experimentally and theoretically. The time of flight spectra at the specified Stark states are recorded, where the deceleration and acceleration of barium atoms are observed. This is very consistent with the prediction derived from the Stark maps from the point of view of energy conservation.     

Characterization of molecular motion in the solid state by carbon-13 spin-lattice relaxation times

Relaxation calculations for rapidly spinning samples show that spin-lattice relaxation time (T(1Z)) anisotropy varies with the angle between the rotor spinning axis and the external field. When the rate of molecular motion is in the extreme narrowing limit, the measurement of T(1Z) anisotropies for two different values of the spinning angle allows the determination of two linear combinations of the three static spectral densities, J(0)(0), J(1)(0), and J(2)(0). These functions are sensitive to molecular geometry and the rate and trajectory of motion. The utility of these linear combinations in the investigation of molecular dynamics in solids has been demonstrated with natural abundance (13)C NMR experiments on ferrocene. In an isolated (13)C-(1,2)H group, the dipole-dipole interaction has the same orientational dependence as the quadrupole interaction. Thus, the spectral densities that are responsible for dipolar relaxation of (13)C are the same as those responsible for deuteron quadrupolar relaxation. For ferrocene-d(10), deuteron T(1Z) and T(1Q) anisotropies and the relaxation time of the (13)C magic angle spinning peak provide sufficient information to determine the orientation dependence of all three individual spectral densities.     

Inhibition of copper corrosion by bis-(1,1′-benzotriazoly)-α,ω-diamide compounds in aerated sulfuric acid solution

Three kinds of novel corrosion inhibitors, bis-(1,1′-benzotriazoly)-α,ω-succinyldiamide (BSU), bis-(1,1′-benzotriazoly)-α,ω-adipoyldiamide (BAD), and bis-(1,1′-benzotriazoly)-α,ω-azelayldiamide (BAZ) were synthesized and certified by IR and ¹H NMR. Their corrosion inhibition effects for copper in 0.5 M H₂SO₄ were evaluated by weight-loss method. It shows that among the three compounds, only BSU behaves better compared with BTA. The inhibition efficiency (IE) increased with increasing BSU concentration to 85.2% at the 5 × 10⁻⁴ M level. Polarization studies showed that BSU suppressed both anodic and cathodic corrosion reactions. The minimum energy conformation of these compounds was obtained by MM2 force field program. The two benzotriazoly moieties in BSU molecule are more parallel than in other compounds. This is benefit to increase the inhibition effects of BSU.