Showing papers on "Quadrupole published in 1994"

23Na NMR Spectroscopy of Solids: Interpretation of Quadrupole Interaction Parameters and Chemical Shifts

Abstract: Quadrupole coupling constants (QCC), asymmetry parameters of the electric field gradients (η), and isotropic chemical shifts (δ cs ) of sodium-23 were determined by computer simulation of the central transition line shapes of the 23 Na MAS NMR spectra of a series of crystalline sodium compounds in which sodium has exclusively oxygen atoms as nearest neighbors. The relations between the crystal structure and the above parameters were discussed qualitatively for typical examples. The bond-valence method is applied to derive empirical models for the calculation of a «shift parameter» (A) and of oxygen atomic charges (model I) from which QCC and η were calculated by a simple point charge model

Vibrational Raman optical activity calculations using London atomic orbitals

Abstract: Ab initio calculations of Raman differential intensities are presented at the self-consistent field (SCF) level of theory. The electric dipole–electric dipole, electric dipole–magnetic dipole and electric dipole–electric quadrupole polarizability tensors are calculated at the frequency of the incident light, using SCF linear response theory. London atomic orbitals are employed, imposing gauge origin invariance on the calculations. Calculations have been carried out in the harmonic approximation for CFHDT and methyloxirane.

Fourier analysis of redshift-space distortions and the determination of Ω

Abstract: The peculiar velocities of galaxies distort the pattern of galaxy clustering in redshift space, making the redshift-space power spectrum anisotropic. In the linear regime of gravitational instability models, the strength of this distortion depends only on the ratio β≡f(Ω)/b≃Ω 0.6 /b, where Ω is the cosmological density parameter, and b is the bias parameter. We derive a linear-theory estimator for β, based on the harmonic moments of the redshift-space power spectrum. Using N-body simulations, we examine the impact of non-linear gravitational clustering on the power-spectrum anisotropy and on our β-estimator. Non-linear effects can be important out to wavelengths λ∼50 h −1 Mpc or larger; in most cases, they lower the quadrupole moment of the power spectrum, and thereby depress the estimate of β below the true value

Hydrodynamics of Binary Coalescence.I. Polytropes with Stiff Equations of State

Abstract: We have performed a series of three-dimensional hydrodynamic calculations of binary coalescence using the smoothed particle hydrodynamics (SPH) method. The initial conditions are exact polytropic equilibrium configurations with $\gam > 5/3$, on the verge of dynamical instability. We calculate the emission of gravitational radiation in the quadrupole approximation. The fully nonlinear development of the instability is followed until a new equilibrium configuration is reached. We find that the properties of this final configuration depend sensitively on both the compressibility and mass ratio. An {\em axisymmetric} merged configuration is always produced when $\gam\lo2.3$. As a consequence, the emission of gravitational radiation shuts off abruptly right after the onset of dynamical instability. In contrast, {\em triaxial\/} merged configurations are obtained when $\gam\go2.3$, and the system continues to emit gravitational waves after the final coalescence. Systems with mass ratios $q e1$ typically become dynamically unstable before the onset of mass transfer. Stable mass transfer from one neutron star to another in a close binary is therefore probably ruled out. The maximum amplitude $h_{max}$ and peak luminosity $L_{max}$ of the gravitational waves emitted during the final coalescence are nearly independent of $\gam$, but depend very sensitively on the mass ratio $q$.

Structure, internal mobility and spectrum of the ammonia dimer: calculation of the vibration-rotation-tunneling states

Abstract: We have obtained a potential for (NH3)2 by calculating the six‐dimensional vibra‐ tion–rotation‐tunneling (VRT) states from a model potential with some variable parameters, and adjusting some calculated transition frequencies to the observed far‐infrared spectrum. The equilibrium geometry is strongly bent away from a linear hydrogen bonded structure. Equivalent minima with the proton donor and acceptor interchanged are separated by a barrier of only 7 cm−1. The barriers to rotation of the monomers about their C3 axes are much higher. The VRT levels from this potential agree to about 0.25 cm−1 with all far‐infrared frequencies of (NH3)2 observed for K=0, ‖K‖=1, and ‖K‖=2 and for all the symmetry species: Ai=ortho–ortho, Ei=para–para, and G=ortho–para. Moreover, the dipole moments and the nuclear quadrupole splittings agree well with the values that are observed for the G states. The potential has been explicitly transformed to the center‐of‐mass coordinates of (ND3)2 and used to study the effects of the deuteration on the VRT states. The observed decrease of the dipole moment and the (small) changes in the nuclear quadrupole splittings are well reproduced. It follows from our calculations that the ammonia dimer is highly nonrigid and that vibrational averaging effects are essential. Seemingly contradictory effects of this averaging on its properties are the consequence of the different hindered rotor behavior of ortho and para monomers.

Gravitational radiation from coalescing binary neutron stars.

Abstract: We calculate the gravitational radiation produced by the merger and coalescence of inspiraling binary neutron stars using 3-dimensional numerical simulations. The stars are modeled as polytropes and start out in the point-mass limit at wide separation. The hydrodynamic integration is performed using smooth particle hydrodynamics (SPH) with Newtonian gravity, and the gravitational radiation is calculated using the quadrupole approximation. We have run several simulations, varying both the neutron star radius and the equation of state. The resulting gravitational wave energy spectra $dE/df$ are rich in information about the hydrodynamics of merger and coalescence. In particular, our results demonstrate that detailed information on both $GM/Rc^2$ and the equation of state can in principle be extracted from the spectrum.

Resonance ejection ion trap mass spectrometry and nonlinear field contributions. The effect of scan direction on mass resolution

Abstract: Mass resolution obtained with the commonly employed stretched quadrupole ion trap geometry is shown to be dependent upon scan direction when resonance ejection is used as the mass analysis method. Data are also presented showing that the energy absorption profile for ions subjected to resonance excitation broadens with the amplitude of ion oscillation and shifts to higher frequencies, an observation consistent with behavior predicted for ion motion in a quadrupole electric field with relatively small higher-order field components. The observed effect of scan direction on mass resolution is therefore reasoned to arise from an effect analogous to Doppler focusing or defocusing, depending on scan direction relative to the direction of the ion frequency shift with oscillatory amplitude. 15 refs., 7 figs.

Monopole-quadrupole static axisymmetric solutions of Einstein field equations

Abstract: An infinite family of exact solutions of the Einstein vacuum equations for the static case with axial symmetry is presented in an explicit form Each solution of this family contains two arbitrary parametersM andQ that represent the mass and quadrupole moment of the source In addition, each solution can be interpreted physically as the pure relativistic quadrupole correction to the Schwarzschild solution at a given multipole order

Sum Rules and Fundamental Spectra of Magnetic X-Ray Dichroism in Crystal Field Symmetry.

Abstract: The sumrules for X-ray absorption and photoemission [Thole et al ., Phys. Rev. Lett. 68 (1992) 1943; 70 (1993) 2499] which relate the integrated signals of the magnetic circular and linear dichroism to the orbital magnetic moment and quadrupole moment are generalized to point group symmetry. The polarization dependence of the spectra is obtained by separating the geometry from the physical properties. The number of fundamental spectra is equal to the number of total symmetric representations of the recoupled moment in the point group. Cylindrical symmetry is particularly simple because it has the natural basis lm. The presented results can be useful for measurements of magnetic materials that contain transition metal, rare earth or actinide ions using linearly and circularly polarized X-rays.

An eigenvalue theory of circular birefringence and dichroism in a non-magnetic chiral medium

Abstract: By means of known constitutive relations for the D and H fields, which include both electric quadrupole and magnetic dipole terms, an eigenvalue theory is developed for electromagnetic wave propagation in an absorbing chiral medium. The theory allows the polarization eigenvectors to be determined, which the medium supports, and also their refractive indices and absorption coefficients. Uniaxial and cubic crystals, as well as an ideal gas, are treated in this way, and expressions are derived for their circular birefringence and dichroism in terms of property tensors of the medium. These expressions are shown to be independent of the arbitrary origin to which the multipole moments are referred. The theory is also applicable to artificial chiral materials which are "optically active" in the microwave regime.

Magnetic quadrupole formation of elliptical sheet electron beams for high-power microwave devices

Abstract: Sheet electron beams are attractive for high-power microwave sources due to their ability to transport high current, at reduced current density, through thin clearance apertures and in close proximity to walls or RF structures. This paper reports on the theoretical investigation of magnetic quadrupole formation of elliptical sheet electron beams for use in high-power microwave devices. The beam envelope equations for an initially round beam passing through a physical non-symmetric quadrupole pair in the presence of space-charge, finite beam emittance, and under the effects of third-order field components and longitudinal velocity variations are presented. The presence of space-charge compensates for over-focusing in the thin beam-dimension and allows for the formation of highly elliptic sheet electron beams. As an example, the results of our study were applied to an existing Pierce gun source with a beam radius of 0.6 cm, beam energy of 10 keV and current density of 2.0 A/cm/sup 2/. We find that an elliptical beam with major radius r/sub a/=3.61 cm, minor radius r/sub b/=0.16 cm and ellipticity (r/sub a//r/sub b/) of 22.5 can be produced with only modest quadrupole gradients of 64 G/cm and 18 G/cm. Quadrupole formation of elliptical sheet-beams may be particularly suited for experimental research applications since existing round-beam electron guns may be used and changes in beam ellipticity may be made without breaking the vacuum system. >

Nuclear quadrupole interaction of highly polarized gas phase 131Xe with a glass surface

Abstract: We report nuclear magnetic resonance (NMR) experiments on 131Xe (I=3/2) gas‐phase atoms which exhibit nuclear quadrupole interaction with the surface of the sample cell. Nuclear quadrupole coupling constants and quadrupole relaxation rates are obtained from the time‐domain signal of the freely precessing nuclear magnetization in weak magnetic fields. The nuclear spin species is polarized by spin‐exchange collisions with optically pumped ground‐state spins of Rb gas atoms. The Rb atoms also present in the sample are used as a magnetometer to probe the free‐induction decay of the nuclear‐spin ensemble. The temperature dependence of both the effective quadrupole splittings and the relaxation rates are explained by a model for the surface interactions of a Xe atom adsorbed on the glass surface. The desorption is thermally activated with an activation energy of EA=0.12 eV. The surface diffusion of an adsorbed atom is characterized by an activation energy ED for thermally activated hopping between neighboring s...

Polarizability of helium and the negative hydrogen ion

Abstract: The authors have carried out precision calculations of the dipole and quadrupole polarizabilities of helium and the negative hydrogen ion and their non-adiabatic extensions. These quantities are obtained from second-order perturbation sums involving energy denominators raised to the power k=1, 2 or 3. The summation over intermediate states is carried out using Hylleraas two-particle wavefunctions of the appropriate symmetry and angular momentum. The measured mass of the nucleus is retained. The convergence is excellent for the helium case and somewhat poorer for H$.

1H -14N Nuclear Quadrupole Double Resonance with Multiple Frequency Sweeps

Abstract: A new highly sensitive 1 H- 14 N nuclear quadrupole double resonance technique is presented which is based on magnetic field cycling and on the application of multiple frequency sweeps of an r.f, magnetic field. The sensitivity and the resolution of the new technique are estimated. Some experimental results obtained by the new technique are presented

Computer simulation of vapor–liquid equilibria of linear quadrupolar fluids. Departures from the principle of corresponding states

Abstract: Vapor–liquid equilibria of different quadrupolar linear Kihara fluids have been studied, by using the Gibbs ensemble Monte Carlo technique. Coexistence curves for fluids with elongations L*=L/σ=0.3, 0.6, and 0.8 and different quadrupoles are given. We analyze the effect of quadrupole moment on critical properties. Quadrupole moment increases the critical temperature, pressure, and density. The magnitude of the increase depends on both anisotropy and quadrupole moment. A new way of reducing the quadrupole is proposed, so that the variation of critical properties due to the quadrupole follows a universal behavior. Quadrupole provokes deviations from the principle of corresponding states. A broadening of the coexistence curve is observed due to the quadrupole. The quadrupole moment increases the slope of the vapor pressure curve vs temperature inverse. Simulation data are used to describe vapor–liquid equilibria of carbon dioxide. Good agreement between simulation and experiment is achieved.

Structure of LiNO3 : point charge model and sign of the 7Li quadrupole coupling constant

Abstract: The crystal structure of LiNO 3 is determined by single-crystal X-ray diffraction. The structure is isomorphous with that of calcite; lithium is coordinated by oxygen in a trigonally-elongated octahedron. A positive sign of the 7 Li quadrupole coupling constant is deduced from a simple point charge model with the following assumptions: (1) only contributions from the six oxygen atoms of the inner coordination sphere are included, and (2) the charge assigned to each oxygen atom is negative. This result is compared to the low-temperature 7 Li NMR work of Kuhns and Waugh (J. Chem. Phys. 1992, 97, 2166-2167), in which the sign of the 7 Li quadrupole coupling constant was found to be positive

Distribution of low lying quadrupole phonon strength in nuclei.

Abstract: The distribution of quadrupole phonon strength to low-lying states in nuclei is examined. It is found that the 2[sub 1][sup +] and 4[sub 1][sup +] states of all nuclei from [ital Z]=30 to 100 display almost perfect quadrupole phonon character even though they encompass widely ranging structures. The interacting boson approximation reproduces both the very small deviations from phonon purity and the distribution of those deviations as a function of mean field structure in a natural fashion. Simple physical mechanisms explain these results.

Microwave spectroscopic investigation of the mixed rare gas van der Waals trimers Ne2–Kr and Ne2–Xe

Abstract: Pure rotational spectra of six isotopomers of the rare gas trimer Ne2–Kr and five isotopomers of the trimer Ne2–Xe have been measured in their ground vibrational states using a Balle–Flygare‐type cavity pulsed microwave Fourier transform spectrometer. Rotational constants have been evaluated, from which the geometries of the complexes have been derived. In the case of Ne2–Kr it has been possible to obtain centrifugal distortion constants and to carry out a force field analysis. The magnitudes of the induced dipole moments of these trimers have been estimated from the ‘‘π/2 condition.’’ The nuclear quadrupole hyperfine patterns due to 83Kr and 131Xe have been resolved, and the corresponding quadrupole coupling constants have been obtained. Observation of the spectra of these fundamental trimers has made it possible to compare their properties to those of their constituent rare gas dimers. The effects of three‐body nonpairwise additive forces have been discussed in light of the structures obtained, the estimated induced dipole moments, and the nuclear quadrupole coupling constants.

Ab initio studies of the dipole polarizabilities of conjugated molecules: Part 2. Monocyclic azines

Abstract: We report high quality ab initio calculations of the dipole polarizability and first hyperpolarizability of the following single monoeyclic azines: pyridine, pyridazine, pyrimidine, pyrazine, s-triazine and s-tetrazine. A study of the sensitivity of such calculated properties to the variation of basis set shows that increasing the number of multiple d and p diffuse functions in the 6-31 + G(nd, mp) basis set at Hartree-Fock level gives values of the polarizability tensor components that are comparable with the experimental ones, and consistent values of hyperpolarizability tensor components. We have also found that correlation effects are negligible, provided that such calculations are performed at the SCF level with very extended basis sets. We show that standard sp basis sets need to be extended in the sp space, to have extra diffuse functions added and also to include suitable d and p gaussian primitives in order to be useful for the calculation of response functions. We find that the average dipole polarizability (αave) is related to the number of nitrogen atoms N in the ring by αave/10−40(CV−1 m2) = 10.90–0.90N We also find that the calculated average and anisotropy polarizability components are both linearly related to the sum of the HOMO and LUMO orbital energies. We also give the first ever high-quality calculation of the hyperpolarizability tensors for these molecules. Electric dipole and quadrupole moments agree well with experiment, as do the asymmetry parameter and the nitrogen quadrupole coupling constants.

Multipole sources in a fluid‐filled borehole surrounded by a transversely isotropic elastic solid

Abstract: In this paper, the acoustic field excited by multipole sources in a fluid‐filled borehole surrounded by a transversely isotropic elastic solid is systematically analyzed and numerically simulated. Not only have the mode waves been analyzed thoroughly, but the propagation mechanism of the critical refracted P and S waves corresponding to the multipole branch cut integration for the transversely isotropic formation has also been investigated for the first time. In the presence of a fast or a slow transversely isotropic elastic solid formation, the component waves excited by a monopole, a dipole, and a quadrupole source have been studied in the time and frequency domains. It is found that the critical refracted arrival of the S wave is a dominant factor, while the mode wave is not in the low‐frequency multipole direct shear wave logging. When the formation is changed from isotropic to transversely isotropic, the amplitudes of the component waves vary significantly, but the variation of the cutoff frequencies...