Showing papers on "Quadrupole published in 1990"

Angular dependence of X-ray absorption spectra

Abstract: A detailed account of the dependence of X-ray absorption spectra (XAS) on polarisation and light beam directions is given. Anisotropic XAS measured on single crystals, layered compounds, polymers and oriented powders are tabulated. The X-ray absorption cross section by non-magnetic samples is derived, including electric dipole and quadrupole contributions. Orders of magnitude are found for magnetic dipole and electric dipole-octupole terms. Using a spherical tensor expansion of the absorption cross section, simple analytical formulae are given for the angular dependence of the electric dipole and quadrupole contributions to XAS for all crystal point groups. These formulae are valid down to the edge and include many-body effects. The are applied to two experimental examples, the iron K-edge in haematite and the copper K-edge in CuCl42-. For the latter case, spherical tensor components are interpreted in terms of molecular orbitals. The influence of unpolarised and circularly polarised X-rays is discussed, as well as various experimental problems met in angle-resolved XAS. In an appendix, the quadrupole contribution to angular XAS is derived within the multiple-scattering formalism, along with closed expressions for the dipole and quadrupole spherical tensor components.

Ab initio calculation of the OH (X 2Π, A 2Σ+)+Ar potential energy surfaces and quantum scattering studies of rotational energy transfer in the OH (A 2Σ+) state

Abstract: The potential energy surfaces of OH+Ar, which correlate asymptotically with OH(X 2Π)+Ar(1S) and OH(A 2Σ+)+Ar(1S), have been calculated using the coupled electron pair approximation (CEPA) and a very large basis set. The OH–Ar van der Waals complex is found to be bound by about 100 cm−1 in the electronic ground state. In agreement with several recent experimental studies the first excited state is found to be much more stable. The A state potential energy surface has two minima at collinear geometries which correspond to isomeric OH–Ar and Ar–OH structures. The dissociation energies De are calculated to be 1100 and 1000 cm−1, respectively; both forms are separated by a barrier of about 1000 cm−1. The equilibrium distances for OH–Ar and Ar–OH are calculated to be 2.9 and 2.2 A, respectively, relative to the center of mass of OH. In order to investigate the nature of the strong binding in the A state, we have calculated accurate dipole and quadrupole moments as well as dipole and quadrupole polarizabilities ...

Dichroism in the x-ray absorption spectra of magnetically ordered systems.

Abstract: A general formulation of linear and circular dichroism in the absorption of x rays in magnetically ordered systems is presented. The processes which induce sensitivity to magnetic properties are discussed. We demonstrate that the usually neglected electric quadrupole transitions can be as important as the dipole terms for the interpretation of magnetic dichroism experiments on transition metals and rare earths.

Pulsed‐nozzle Fourier‐transform microwave spectroscopy of laser‐vaporized metal oxides: Rotational spectra and electric dipole moments of YO, LaO, ZrO, and HfO

Abstract: The rotational spectra of YO, LaO, ZrO, and HfO have been measured using a Fourier‐transform microwave spectrometer in combination with a laser‐ablation source. Here, a Q‐switched Nd:YAG laser (532 nm) was used to vaporize the metal oxides from a target source rod located in the throat of a pulsed‐molecular‐beam valve. A description of the instrument is given. The electric dipole moments of the four species have been measured and compared to ab initio results, where available. The experimental values are μYO =4.524(7), μLaO =3.207(11), μZrO =2.551(11), and μHfO =3.431(5) D. Of special note are the extremely large nuclear quadrupole coupling constants, eQq, determined for the 177HfO and 179HfO isotopic species, with values of −5952.649(35) MHz and −6726.981(39) MHz, respectively. This is the first determination of nuclear quadrupole coupling constants for a molecule containing the Hf atom.

A method for determining the effective conductivity of dispersions of particles

Abstract: A general method is developed to predict the effective conductivity of an infinite, statistically homogeneous suspension of particles in an arbitrary (ordered or disordered) configuration. The method follows closely that of 'stokesian dynamics', and captures both far-field and near-field particle interactions accurately with no convergence difficulties. This is accomplished by forming a capacitance matrix, the electrostatic analogue of the low-Reynolds-number resistance matrix, which relates the monopole (charge), dipole and quadrupole of the particles to the potential field of the system. A far-field approximation to the capacitance matrix is formed via a moment expansion of the integral equation for the potential. The capacitance matrix of the infinite system is limited to a finite number of equations by using periodic boundary conditions, and the Ewald method is used to form rapidly converging lattice sums of particle interactions. To include near-field effects, exact two-body interactions are added to the far-field approximation of the capacitance matrix. The particle dipoles are then calculated directly to determine the effective conductivity of the system. The Madelung constant of cohesive energy of ionic crystals is calculated for simple and body-centred cubic lattices as a check on the method formulation. The results are found to be in excellent agreement with the accepted values. Also, the effective conductivities of spherical particles in cubic arrays are calculated for particle to matrix conductivity ratios of infinity, 10 and 0.01.

Polarizabilities and hyperpolarizabilities of carbon dioxide

Abstract: The dipole (α), quadrupole (C), and dipole–octopole (E) polarizabilities, the dipole–dipole–quadrupole (B) and second dipole (γ) hyperpolarizabilities, and the quadrupole (θ) and hexadecapole (Φ) moments are calculated for the ground state of CO2 at its equilibrium geometry. The values are obtained from fourth‐order many‐body perturbation theory energies of CO2 in the presence of various configurations of point charges. Electron correlation affects the longitudinal components more than the transverse ones; hence, electron correlation effects are greater for the anisotropies than for the isotropic averages of these properties. Our best vibrationless estimates for the isotropic values are ᾱ≂17.63 e2a20E−1h, C≂77.8 e2a40E−1h, B≂−2.1×102 e3a40E−2h, γ≂1.20×103 e4a40E−3h, and θzz≂−3.24 ea20. The quadrupole moment, mean dipole polarizability and hyperpolarizability are in satisfactory agreement with experiment. On the other hand, the polarizability anisotropy Δα≂14.3 e2a20E−1h agrees with experimental estimat...

Light Propagation in Cubic and other Anisotropic Crystals

Abstract: A consistent multipole theory is presented to describe light propagation in non-absorbing non-magnetic crystals. Although valid for the 32 crystal classes, the theory is applied here to all except the five members of the triclinic and monoclinic systems. To account for the birefringence that has been observed in certain cubic crystals and also for the predicted Jones birefringence, the theory has to allow for electric octopoles and magnetic quadrupoles induced by the light wave. At the earlier stage of electric quadrupoles and magnetic dipoles, it is able to describe optical activity in crystals. An expression for this is derived which, when electric quadrupole contributions are omitted, yields the familiar Nye result. As a criterion for the correct inclusion in the theory of all relevant induced multipole moments, tensor expressions for observables are shown to be independent of the choice of origin. Finally, the concepts of O-ray and E-ray are found to break down beyond the electric dipole approximation and alternatives are proposed.

Rotational spectrum, structure, and chlorine nuclear quadrupole tensor of the vinyl fluoride–HCl dimer

Abstract: The ground‐state rotational spectrum of the dimer formed between vinyl fluoride and hydrogen chloride has been detected by using a pulsed‐nozzle Fourier‐transform microwave spectrometer. The rotational constants A0, B0, and C0; the centrifugal distortion constants ΔJ, ΔJK, δJ and δJK; and the components χaa, χbb−χcc, and χab of the Cl nuclear quadrupole coupling tensor have been determined for each of the three isotopomers CH2CHF⋅⋅⋅H 35Cl, CH2CHF⋅⋅⋅H 37Cl, and CH2CHF⋅⋅⋅D 35Cl. An accidental near degeneracy of the 211 and 303 levels allows an accurate evaluation of the off‐diagonal component χab. Interpretation of the rotational constants establishes a near‐planar geometry for CH2CHF⋅⋅⋅HCl, with HCl forming a hydrogen bond to F and RF⋅⋅⋅Cl=3.382(3) A. The angle CF⋅⋅⋅H is 116.1(1)° and there is some evidence that the HCl subunit lies slightly out of the plane (φ=8.0±1.5°). Diagonalization of the Cl nuclear quadrupole coupling tensor to give the principal components χxx, χyy, and χzz leads to an angle of 30....

Orientation fluctuations and the angular distribution of the giant-dipole-resonance gamma rays in hot rotating nuclei.

Abstract: A recent macroscopic approach to the giant dipole resonances in hot rotating nuclei is extended to include the angular distributions of the {gamma} rays emitted in the resonance decay. It provides a uniform description of thermal fluctuations in all quadrupole shape degrees of freedom within the framework of the Landau theory. In particular, the inclusion of fluctuations in the nuclear orientation with respect to the rotation axis is crucial in reproducing the observed attenuation of the angular anisotropy. The theory is applied to recent precision measurements in {sup 90}Zr and {sup 92}Mo and is the first to reproduce well both the observed giant-dipole-resonance cross sections and the angular anisotropies.

Lifetime measurements in the superdeformed band of 192Hg.

Abstract: Lifetimes were measured for transitions in the superdeformed band of {sup 192}Hg with the Doppler-shift attenuation method. The results yield an essentially constant quadrupole moment of 20{plus minus}2 {ital e} b and indicate that the sidefeeding lifetimes are of the same order as the state lifetimes. The data are consistent with calculations using the cranked Woods-Saxon Strutinsky method with pairing.

Microwave spectrum, structure, barrier to internal rotation, dipole moment, and deuterium quadupole coupling constants of the ethylene–sulfur dioxide complex

Abstract: The microwave spectra of the complex between ethylene and sulfur dioxide and nine of its isotopic species have been observed in a Fourier transform microwave spectrometer. The spectra exhibit a and c dipole selection rules; transitions of the normal species and several of the isotopically substituted species occur as tunneling doublets. The complex has a stacked structure with Cs symmetry; the C2H4 and SO2 moieties both straddle the mirror plane with the C2 axis of SO2 crossed at 90 ° to the carbon–carbon bond axis (i.e., only the S atom lies in the symmetry plane). The distance between the centers of mass (Rcm) of C2H4 and SO2 is 3.504(1) A and the deviation of their planes from perpendicular to Rcm is 21(2) ° and 12(2) °, respectively. The tunneling splittings arise from a rotation of the ethylene subunit in its molecular plane. The barrier to internal rotation is 30(2) cm−1. The dipole moment of the complex is 1.650(3)D. The deuterium nuclear quadrupole coupling constants for C2H3D⋅SO2 are χaa=−0.119(1) MHz, χbb=0.010(1) MHz, and χcc=0.109(1) MHz. The binding energy is estimated to be 490 cm−1 from the pseudo‐diatomic approximation. A distributed multipole electrostatic model is explored to rationalize the structure and binding energies.

Non-abelian effects in a quadrupole system rotating around two axes

Abstract: The 35 Cl nuclear quadrupole resonance spectrum of a single crystal of sodium chlorate rotating about two axes reflects a non-Abelian gauge potential. This gauge potential is an example of Wilczek and Zee's generalization of Berry's phase to the adiabatic transport of degenerate states

A dipole moment of the microwave background as a cosmological effect

Abstract: A spherically symmetrical Tolman-Bondi cosmological model is presented in which the curvature of space and the entropy variety with distance from the center. The dipole and quadrupole moments in the distribution of the microwave background radiation are calculated as a function of cosmic time and position of an observer, assuming that the distance to the horizon is much smaller than any characteristic scale in the model. The quadrupole moment is found to be affected mostly by the gradient in the curvature of space while the dipole moment is dominated by the gradient of entropy. The results indicate that the observed dipole in the microwave background may be cosmological in origin. Observational tests of this argument are suggested.

Cu nuclear quadrupole resonance and magnetic phase transition in CuO

Abstract: Cu‐nuclear quadrupole resonance (NQR) frequency and relaxation rates measurements in CuO, in the vicinity of the antiferromagnetic ordering temperature TN, are presented. As T→T+N divergent behaviors of the relaxation rates T−11,2 and an anomalous decrease in the NQR frequency are observed. These effects are discussed in light of the temperature dependence expected for conventional one‐dimensional Heisenberg paramagnet and some anomalies are interpreted as possible results of valence fluctuations in the CuO bond character.

Nonlinear effects in the detection of stored ions.

Abstract: Ions stored in a radio-frequency quadrupole trap were subjected to pulses of a small oscillating potential The frequency of oscillation within each pulse (dipolar or quadrupolar) was variable up to one-half of the rf drive frequency Ions that were ejected axially from the trap were detected with an electron multiplier Ion signal intensity was observed as a function of the small oscillating potential frequency for pulsed excitation in each of two time domains in the duty cycle Thus it was possible to see either the ejection in the z direction, or the ejection in the x or y direction and the z direction According to the nature of the ejection pulse, the signal shows lines at secular frequencies, at doubled secular frequencies, and other lines that can be sharp and numerous The influence of space charge is clearly shown The observed couplings are discussed by taking into account anharmonicity and relaxation mechanisms

The very strong and unusual magnetic field of the Bp silicon star HD 133880

Abstract: The Ap Si star HD 133880 is found to have a very nonsinusoidal magnetic field curve. It is argued that this star is one of a very small number of Ap stars that have predominantly nondipolar field geometries. One possible family of models that reproduces the observed magnetic curve may be found using a collinear dipole and quadrupole; these models suggest that the quadrupolar field component is at least 1.3 times larger than the dipolar component. 14 refs.

Doppler-free laserspectroscopic investigations of hyperfine structure in the atomic cobalt spectrum

Abstract: Performing Doppler-free laserspectroscopic investigations in the red wavelength region (640–670 nm) we were able to determine 10A-factors and 9B-factors of atomic cobalt levels. Now precise values of 18A-factors and 16B-factors of levels belonging to the configurations (3d+4s)9 are known. Fitting of the one-electron radial parameters to introduce agreement between experimental and theoretical hfs constants allows the prediction of hfs constants of not yet investigated fine structure levels. Values of the electric quadrupole moment of the Co59 nucleus are determined in two electron configurations. The resulting mean value of the spectroscopic quadrupole moment isQ=0.35(3) barn.