Showing papers on "Quadrupole published in 1976"

Upper and lower bounds of two‐ and three‐body dipole, quadrupole, and octupole van der Waals coefficients for hydrogen, noble gas, and alkali atom interactions

Abstract: Upper and lower bounds of the multipole van der Waals coefficients C6, C8, and C10 for hydrogen, noble gas, and alkali atoms are established. Nonadditive three‐body coefficients involving dipole, quadrupole, and octupole interactions are also determined. For the dipole polarizabilities a three‐term, two‐point Pade approximant is used to obtain the upper bound and a two‐term Pade approximant is used to obtain the lower bound. For the quadrupole and octupole polarizabilities a one‐term approximation of the dynamic polarizability is used, except for the helium quadrupole polarizability, where extended approximations are possible.

Temperature dependence of the electric field gradient in noncubic metals

Abstract: The quadrupole hyperfine interaction of111Cd in Cd, In, Sn, and of67Zn,69Ge in Zn was measured with high accuracy using TDPAC and TDPAD methods; in addition the systems117In in Cd and In, and113Sn in Cd were investigated. The temperature dependence of the electric field gradienteq(T) can be reproduced by the simple relationeq(T)/eq(0)=1—B⋅T 3/2 over a range of temperatures from a few K up to the melting point. A comparison with other experiments was carried out to test the universality of this empirical relation. In particular, high precision NQR experiments on Ga, In and Sb strongly support this relation. It is discussed whether lattice vibrations can explain the observed temperature variation or whether the experimental data indicate the need for a new description. Some new ideas suggesting a basically different model are given.

The properties of liquid nitrogen: V. Computer simulation with quadrupole interaction

Abstract: A Molecular Dynamics simulation of liquid nitrogen has been carried out using an atom-atom potential together with a point quadrupole-quadrupole interaction. The changes in the properties of the model fluid compared to a previous simulation [1] using the atom-atom potential alone are small but significant. The structure factor is notably closer to experiment. The properties associated with reorientation motion are also closer to experiment but discrepancies remain especially at high temperatures.

Zero-field hyperfine structure measurements of the metastable states 3 d 2 4 s 4 F 3/2, 9/2 of 45 Sc using laser-fluorescence atomic-beam-magnetic-resonance technique

Abstract: In an atomic beam experiment we measured the hyperfine structure (hfs) of the metastable states 3d 2 4s 4 F 3/2,9/2 of Scandium, which were populated by electron impact. A single mode cw dye laser was used to create a population difference between neighbouring hfs states by optical pumping. Rf transitions between these states, equalizing the population numbers, could then be detected by repeating the optical pumping experiment and looking for the laser induced fluorescent light. The following constants of the magnetic dipole and electric quadrupole interactions have been obtained by this method:A 3/2=−158.513(3)MHzB 3/2=−5.19(2)MHzA 9/2=285.967(9)MHzB 9/2=−15.46(70)MHz From these constants and the corresponding values forJ=5/2, 7/2, as measured by [1], the following parameters can be calculated: 〈r −3〉 01 =0.911(4)a 0 −3 〈r −3〉 12 =2.395 (62)a 0 −3 and:α=〈r −3〉 01 /〈r −3〉 12 =0.38(1).

U(5) ⊆O(5) ⊆O(3) and the exact solution for the problem of quadrupole vibrations of the nucleus

Abstract: Over twenty years ago A. Bohr discussed the quantum mechanical problem of the quadrupole vibrations in the liquid drop model of the nucleus. States of definite angular momentum L could not be obtained exactly except when L=0,3. In the present paper we indicate how we can determine states for arbitrary angular momentum L and definite number of quanta ν in terms of polynomials of the creation operators characterized by irreducible representation (IR) of the chain of groups U(5) ⊆O(3). We furthermore characterize the states by a definite IR λ of O(5) by replacing the creation operators by traceless ones. These states are fully determined by an extra label μ that gives the number of triplets of traceless creation operators coupled to angular momentum zero. We show then how all the wavefunctions of the problem discussed by Bohr can be obtained in a recursive fashion and briefly discuss some of their applications.

Temperature Dependence of Electric Field Gradients in Noncubic Metals

Abstract: Temperature dependence of the nuclear quadrupole frequency, ${\ensuremath{ u}}_{Q}$, of noncubic metals has been studied theoretically. It is shown that the electronic contribution to the field gradient is largely responsible for the observed ${T}^{\frac{3}{2}}$ behavior. The conclusions are general and apply to all noncubic metals.

Abinitio vertical spectra and linear bent correlation diagrams for the valence states of CO2 and its singly charged ions

Abstract: Correlated and uncorrelated ab initio vertical spectra are reported for the valence states of CO2, CO2+, and CO2−. Calculations with polarized and unpolarized basis sets are compared at each level. Ground state quadrupole moments are computed. Linear molecule to bent molecule SCF correlation diagrams are also reported.

Extended VMI model for asymmetric deformed nuclei

Abstract: The nature of the ground and theγ band is studied in the asymmetric rotator model for larger asymmetric deformationsγ and higher angular momenta. Properties of theγ band are found which may make it possible to search experimentally for staticγ deformations. Sum rules for quadrupole moments and energies are derived. For the description of higher angular momenta the softness of the nucleus is included by an extension of the VMI model to asymmetric deformations. Energies, quadrupole moments andE 2 transitions are given for the Os region and compared with the available data.

Additive model for 119Sn Mössbauer quadrupole splitting in five-co-ordinate organotin(IV) compounds

Abstract: Mossbauer parameters are reported for ten cationic organotin(IV) complexes of type [R3SnL2][BPh4](R = alkyl or phenyl, L = electrongegative ligand). Details are given of a regression method which is used to distinguish structural isomers of trigonal-bipyramidal [R3SnL2] species by their 119Sn quadrupole splittings. By use of new and literature data, partial quadrupole splitting (p.q.s.) parameters are calculated for a variety of ligands in trigonal-bipyramidal structures. Comparison of theory with experiment indicates that the additive model gives a consistent account of the relationship between quadrupole splitting and stereochemistry in trigonal-bipyramidal organotin(IV) compounds. The 119Sn parameters are used to calculate p.q.s. parameters for 121SbV, thus extending recent work on application of the additive model to five-co-ordinate organoantimony(V) compounds.

Determination of molecular multipole moments and potential function parameters of non-polar molecules from far infra-red spectra

Abstract: The quadrupole, Θ, and hexadecapole, Φ, moments of N2 and O2, and the octupole, Ω, and hexadecapole moments of CF4 and SiH4 are obtained from far infra-red collision-induced absorption in the gas phase at low densities where bimolecular collisions predominate. An accurate theory for evaluating Θ and Φ for non-polar diatomic molecules is presented here ; the theory for evaluating Ω and Φ for tetrahedral molecules has been presented previously. A reliable value of a multipole moment obtained by a direct method which does not depend on the intermolecular potential can be used to obtain an accurate value of the molecular diameter, σ. Thus using the quadrupole moment of N2 obtained by induced birefringence and the far infra-red value of Θ2/σ5, we obtain σ and with this the value of Φ.

A many-body calculation of the hyperfine interaction in the lowest 2 S and 2 P states of li-like systems

Abstract: A non-relativistic perturbation method of Brueckner-Goldstone type is used to calculate the hyperfine interactions in the lowest2 S and2 P states of the Li-like systems, Li, Be+, B2+, C3+, N4+, O5+ and F6+. The effect of the polarization of the closed shell is treated to all orders of perturbation, while the correlation effect is calculated in the lowest order, i.e. in the third order of the perturbation expansion. Experimental data are at present available only for Li, Be+ and F6+, and the agreement with the calculated values is in these cases very good, usually within the experimental uncertainties. This implies that the predictions made in the remaining cases should be quite reliable, which may simplify the experimental determination of these quantities. Theoretical values are also given for the quadrupole interaction, which can be used to determine the nuclear quadrupole moments, when accurate experimental information becomes available.

Nuclear Deformations, Level Assignments and Static Nuclear Moments of Isotopes in the Region 72Hf-77Ir

Abstract: A comparison is made between experimental and theoretical level assignments and static electromagnetic moments of nuclei in the region 72Hf-77Ir. The theoretical calculations are based on the modified oscillator model. Equilibrium deformation values, and 4, are determined for doubly-even and odd-mass nuclei from the minima in the potential energy surfaces. The influence of the different parameters entering the expressions for the magnetic dipole moment is analysed. The electric quadrupole and hexadecapole moments are calculated on the assumption that the nucleus is a homogeneously charged body with a sharp surface and a shape corresponding to that of an equipotential surface. In some selected cases, the electric multipole moments are evaluated by use of the single-particle wave functions.

14N nuclear quadrupole resonance and relaxation measurements of sodium nitrite

Abstract: Measurements of the quadrupole coupling constant, asymmetry parameter, inverse linewidth parameter T*2, spin–spin relaxation time T2, and spin–lattice relaxation times T1s and T1l are reported for sodium nitrite in the temperature region from 77–467 °K. The relations between the spin–lattice relaxation times and the transition probabilities W+, WΔ, and W− are derived for a spin one system, and the transition probabilities are calculated from the T1 data. The results are compared with other NaNO2 studies and support the work of Avagadro et al. in the temperature region near the ferroelectric phase transition. They also indicate the existence of short‐range order above this transition.

Proton- 14 N double resonance study of the structural phase transitions in the perovskite type layer compound (CH 3 NH 3 ) 2 CdCl 4 .

Abstract: Using a proton-nitrogen double resonance technique we have determined the quadrupole coupling of14N in the room temperature orthorhombic (Cmca), the low temperature tetragonal (P42/ncm), and the monoclinic low temperature (P21/c) phases of (CH3NH3)2CdCl4. In all these phases all nitrogens are chemically equivalent demonstrating that the disorder in the orientations and H-bonding arrangements of the CH3-NH3 groups in theC m c a andP42/ncm phases is indeed dynamic and not static. In the monoclinic phase the14N quadrupole coupling constant equalse2qQ/h=880 kHz and the asymmetry parameter isη=0.20, wherease2qQ/h=790 kHz,η=0.1 in the tetragonal low temperature phase ande2qQ/h=726 kHz,η=0.21 in the room temperature orthorhombic phase. The observed increase in the14N quadrupole coupling constant on going from the orthorhombic phase to the tetragonal low temperature phase which is coupled with a simultaneous decrease in the asymmetry parameter can be understood in terms of a partial freezing in of the dynamic disorder in the C-N bond directions whereas the14N quadrupole coupling tensor in the monoclinic phase is characteristic of a frozen in C-N bond in a deformed lattice, where the N-H — Cl bonds are of different length.

Optical Quadrupole Sum-Frequency Generation in Sodium Vapor

Abstract: We show that second-order coherent sum-frequency generation via quadrupole transitions in metal vapors can be easily detected. The process is as strong as the allowed third-order processes. Our experimental results agree very well with theoretical predictions. (AIP)

Investigation of the systems LaNi5Hx and LaNi5Dx by proton and deuteron nuclear magnetic resonance

Abstract: We report on the results of a study of the LaNi5 hydride and deuteride systems by means of c.w. (wide-line) nuclear magnetic resonance (NMR). The NMR spectra of samples of LaNi5Hx (2.1 ⩽ x ⩽ 6.8) and of LaNi5Dx (3.4 ⩽ x ⩽ 6.7) were obtained at resonance frequencies in the range 3–100 MHz for protons and at 16 MHz for deuterons, at temperatures in the range 4.2–380 K. The temperature dependence of the shape, line-width, and second moment of the proton resonance and of the nuclear quadrupole interaction parameters characterising the deuteron resonance spectrum reflect the effects of the rapid diffusive motion of the hydrogen species at temperatures above approximately 140 K. At low temperatures (4.2–140 K) the proton resonance shape is distinctly non-Gaussian, with a second moment of 12.78 ± 0.26 Oe2, independent of composition, and the deuteron spectrum may be characterised by two or three quadrupole interactions, also independent of composition. Both observations indicate the existence of a single hydride phase possessing a narrow range of stoichiometry. At temperatures above approximately 270 K the deuteron spectrum reflects only a single, weak, though well-resolved, quadrupole interaction. These results are discussed in terms of several models for hydrogen (deuterium) interstitial site occupation. Measurements are also reported bearing on the existence of an adsorbed hydrogen surface layer at temperatures in the range 4.2–100 K.

Potentials and displacements for two theoretical seismic sources

Abstract: Theoretical, P, SV, and SH displacement potentials and displacements for a double couple or point shear dislocation source and for a ‘mixed quadrupole’ source at any arbitrary orientation in an isotropic homogeneous elastic space are expressed as multiple integral and derivative operations on the source history in the time domain and their algebraic equivalent in the frequency domain. These sources have the same angle orientation functions, which are given explicitly. The double couple and ‘mixed quadrupole’ are both quadrupole sources but, unlike the double couple, the P and S waves from a ‘mixed quadrupole’ have different source histories. Analytic displacements are obtained using as examples the Ohnaka shear dislocation history for a double couple and the Randall and Archambeau tectonic release histories for ‘mixed quadrupole’ sources. The displacement fields are investigated numerically, in order to establish a criterion for estimating the minimum range for applying far-field theory results to the total displacement field. The chosen criterion is the ratio of the far-field peak amplitude, which is a function of source rise or duration time, to the static displacement, which is a near-field phenomenon. The proposed criterion is found to be conservative as to the minimum range for the farfield, predicted (1/R) dependence of the total field peak amplitude, but quite satisfactory for time domain estimates of moment and corner frequency based on far-field theory.

Results from the GSFC fluxgate magnetometer on Pioneer 11

Abstract: A high-field triaxial fluxgate magnetometer was mounted on Pioneer 11 to measure the main magnetic field of Jupiter. It is found that this planetary magnetic field is more complex than that indicated by the results of the Pioneer 10 vector helium magnetometer. At distances less than 3 Jupiter radii, the magnetic field is observed to increase more rapidly than an inverse-cubed distance law associated with any simple dipole model. Contributions from higher-order multipoles are significant, with the quadrupole and octupole being 24 and 21 percent of the dipole moment, respectively. Implications of the results for the study of trapped particles, planetary radio emission, and planetary interiors are discussed. Major conclusions are that the deviation of the main planetary magnetic field from a simple dipole leads to distortion of the L shells of the charged particles and to warping of the magnetic equator. Enhanced absorption effects associated with Amalthea and Io are predicted.

Nuclear Radiation Detected Optical Pumping of neutron-deficient Hg isotopes

Abstract: The extension of the Nuclear Radiation Detected Optical Pumping method to mass-separated samples of isotopes far off stability is presented for a series of light Hg isotopes produced at the ISOLDE facility at CERN. The isotope under investigation is transferred by an automatic transfer system into the optical pumping apparatus. Zeeman scanning of an isotopically pure Hg spectral lamp is used to reach energetic coincidence with the hyperfine structure components of the 6s 2 1 S 06s6p 3P1,λ=2,537 A resonance line of the investigated isotope and the Hg lamp. The orientation built up by optical pumping is monitored via the asymmetry or anisotropy of the nuclear radiation. Nuclear spins, magnetic moments, electric quadrupole moments and the isotope shifts are obtained for181Hg-191Hg using theβ asymmetry as detector. The extension of the method using theγ anisotropy is discussed and test measurements on193Hg are presented. This paper describes the experimental procedure, results, and discussion are given in a following publication.

Comments on the classical theory of energy transfer. II. Extension to higher multipoles and anisotropic media

Abstract: The classical electromagnetic theory of the fluorescence emission and energy transfer in layered systems is extended to describe magnetic dipole and electric quadrupole radiation and anisotropic media. A general formulation is developed for energy transfer from various emitter types and orientations to isotropic acceptors. The description is exact within the classical framework and requires none of the usual assumptions as to the nature of the acceptor layer. The theory is further extended to describe one‐ and two‐dimensional acceptors and electric dipole radiation in an anisotropic medium. The latter case is the actual situation in the fatty‐acid layer experiments. The coupling to the surface plasmon modes of the acceptor is discussed as it relates to the various systems described here.

O2(1Σg+) relaxation in collisions. I. The influence of long range forces in the quenching by diatomic molecules

Abstract: Rate constants for the quenching of O2(1Σg+) to O2(1Δg) by nine diatomic molecules have been calculated on the assumption that the relaxation results from long‐range interactions between the transition quadrupole of O2(1Σg+) and the transition dipole and quadrupole of the quenchers The results suggest that in most cases this may be the dominant mode by which the relaxation of O2(1Σg+) is induced With this assumption, the major channels for the quenching processes have been identified for most quenchers

Charge overlap effects and the validity of the multipole results for first-order molecule-molecule interaction energies. Formalism and an application to H2-H2

Abstract: For the interaction of two molecules, the first-order coulomb energy, E e (1), is expressed as a sum of non-expanded partial wave components which exhibit the orientation dependence of the energy explicitly. By comparing these non-expanded results with the analogous multipolar results for the first-order energy, the effects of charge overlap on the multipole representation of the energy can be investigated as a function of intermolecular separation and orientation, and the validity of the multipole results for E e (1) assessed. The interaction of two ground-state hydrogen molecules is considered as a specific example of this approach for studying the validity of the multipole expansion as a representation of molecular first-order Coulomb energies. All calculations are presented as a function of four molecular wave functions of varying degrees of sophistication in order to assess the sensitivity of (1) the representation of charge overlap effects and (2) the calculated quadrupole and hexadecapole moments o...