Showing papers on "Quadrupole published in 1969"

Atomic susceptibilities and shielding factors.

Abstract: A calculation of electric and magnetic susceptibilities and shielding factors for closed-shell atomic systems based on relativistic Hartree-Fock-Slater (RHFS) electron theory is presented. Numerical results are given for the electric dipole and quadrupole, and for the magnetic dipole and octupole cases for closed-shell atoms and ions from $Z=2$ to $Z=92$. Comparison is made with previous nonrelativistic uncoupled Hartree-Fock calculations and with experiment.

Energy Transfer in Near‐Resonant Molecular Collisions due to Long‐Range Forces with Application to Transfer of Vibrational Energy from ν3 Mode of CO2 to N2

Abstract: The cross section for the near‐resonant transfer of vibrational energy from CO2(001) to N2(0), CO2(001) + N2(0)→CO2(000) + N2(1) + ΔE, is calculated for the isotopes 14N2 (ΔE = 18 cm−1) and 15N2 (ΔE = 97 cm−1). The impact parameter (semi‐classical) approximation is used, and it is assumed that the vibrational‐energy transfer is caused by the interaction of the instantaneous CO2 dipole moment with the N2 quadrupole moment. When proper account is taken of the rotational motions of the molecules it is found that in collisions of CO2 with 14N2 only the low rotational levels of the CO2 and N2 molecules contribute to Reaction (1). In collisions of CO2 with 15N2, only those rotational levels contribute which undergo transitions cancelling most of the relatively large (97 cm−1) vibrational‐resonance defect. For 14N2 below about 1000°K, where the cross section displays a negative temperature dependence, the results are in excellent qualitative and quantitative agreement with available experimental data, with no ad...

Quadrupole correlations governing the pattern of jet noise

Abstract: The effects of convection and refraction dominate the heart-shaped pattern of jet noise. These can be corrected out to yield the small ‘basic directivity’ of the eddy noise generators. The observed quasi-ellipsoidal pattern was predicted by Ribner (1963, 1964) in a variant of the Lighthill theory postulating isotropic turbulence superposed on a mean shear flow. This had the feature of dealing with the joint effects of the quadrupoles without displaying them individually. The present paper reformulates the theory so as to calculate the relative contributions of the different quadrupole self and cross-correlations to the sound emitted in a given direction. Some minor errors are corrected.Of the thirty-six possible quadrupole correlations only nine yield distinct non-vanishing contributions to the axisymmetric noise pattern of a round jet. The correlations contribute either cos4θ, cos2θ sin2θ or sin4θ directional patterns, where θ is the angle with the jet axis. A separation into parts called ‘self noise’ (from turbulence alone) and ‘shear noise’ (jointly from turbulence and mean flow) may be made.The nine self-noise patterns combine as $A\; cos^4\theta(1)+A\; cos^2sin^2\theta(\frac{7}{8}+\frac{7}{8}+\frac{1}{8}+\frac{1}{8})+A sin^2 \theta (\frac {12}{32} & + & \frac{12}{32}+\frac{7}{32}+\frac{1}{32})\\ & = & A(cos^2\theta+sin^\theta)^2 = A;$ this is uniform in all directions as it must be, arising from isotropic turbulence. The two non-vanishing shear-noise correlation patterns combine as The overall ‘basic’ pattern (self noise plus shear noise) thus has the form A + B(cos2θ + cos4θ)/2; this is a slight change from the previous result. The dimensional constants A and B are of comparable magnitude; the pattern in any plane through the jet axis thus resembles an ellipse of modest eccentricity.Frequency spectra are also discussed, following the earlier work. Since the self noise depends quadratically on turbulent velocity components and the shear noise only linearly, there is a relative shift of the self noise to higher frequencies. This in conjunction with refraction figures in the explanation of the deeper pitch of jet noise radiated at small angles to the axis.Finally, the predictions are shown to be compatible with recent experimental results.

Nuclear Magnetic Resonance Powder Patterns in the Presence of Completely Asymmetric Quadrupole and Chemical Shift Effects: Application to Metavanadates

Abstract: A procedure was developed for the determination of the locations of shoulders and singularities of polycrystalline nuclear magnetic resonance (NMR) powder patterns in the presence of both nuclear quadrupole and anisotropic magnetic shift interactions. This determination was performed for both the satellites and the central transition of the NMR spectra of nuclei with half‐integral spin I. Typical theoretical behavior of the powder pattern for the central transition in the presence of both quadrupolar and magnetic shift interactions is shown in a series of examples. In addition, a computer program was devised which calculated the powder pattern for arbitrary quadrupolar and magnetic shift parameters, convoluted it with a function that simulates the effects of dipolar broadening, and took the derivative of the result. The quadrupolar and magnetic shift parameters in three metavanadate compounds (NH4VO3, KVO3, and NaVO3) are determined using these methods.

One‐Electron Properties of Near‐Hartree–Fock Wavefunctions. II. HCHO, CO

Abstract: The results of Hartree–Fock level self‐consistent‐field molecular orbital calculations using contracted Gaussian basis sets are reported for the ground states of the formaldehyde and carbon monoxide molecules. The best computed wavefunctions are shown to have total energies, at most, 0.05 a.u. from their Hartree–Fock limits. A large number of one‐electron properties were computed from the wavefunctions. Results for the carbon monoxide molecule are in excellent agreement with the Slater basis Hartree–Fock results of Huo [J. Chem. Phys. 43, 624 (1965)]. For formaldehyde the calculated molecular properties are in good agreement with experiment. Our best estimates for several of the properties in HCHO are: dipole moment, μz = 2.82 D; quadrupole moment, θaa = 0.0056 × 10−26 esu·cm2, θbb = 0.250 × 10−26esu·cm2, θcc = − 0.256 × 10−26esu·cm2; diamagnetic shielding at the proton, σaad(H) = 92.63 ppm, σbbd(H) = 94.68 ppm, σabd(H) = 52.80 ppm, σccd(H) = 147.13 ppm, and σAvd(H) = 111.48 ppm; diamagnetic shielding at 13C, σaad(C) = 288.50 ppm, σbbd(C) = 355.34 ppm, σccd(C) = 371.60 ppm, and σAvd(C) = 338.48 ppm, diamagnetic susceptibilities, χaad = − 27.99, χbbd = − 54.19, χccd = − 61.53, and χAvd = − 47.91 emu/mole; deuteron quadrupole coupling constants, (eqQ/h)AA = 172.4 kc/sec, (eqQ/h)BB = − 87.22 kc/sec, and (eqQ/h)CC = − 85.21 kc/sec; 17O quadrupole coupling constants, (eqQ/h)aa = − 2.28 Mc/sec, (eqQ/h)bb = 12.8 Mc/sec, and (eqQ/h)cc = −10.5 Mc/sec.

Absorption spectrum of the NO molecule. IX. The structure of the f complexes, the ionization potential of NO, and the quadrupole moment of NO+

Abstract: The 0–0 bands at 1474 A and 1422 A of the first two members of the nf–X2Π Rydberg series of NO have been observed under high resolution in the absorption spectrum of cold nitric oxide gas. They sho...

Storage‐Ring Ion Trap Derived from the Linear Quadrupole Radio‐Frequency Mass Filter

Abstract: The storage of protons and 3He ions in a circular storage‐ring ion trap with background gas collision‐limited loss time constants up to 8 min long under ultrahigh‐vacuum conditions is described. Storage‐ring traps were derived from the linear quadrupole rf mass filter by shaping the electrodes into circular and racetrack configurations. Operation of the traps with a trapping rf frequency Ω large compared to the secular ion oscillation frequency ω inhibited ion loss due to nonlinearities in the trapping fields. Long‐term ion storage in such traps may prove useful for radio‐frequency ion spectroscopic purposes.

Oxygen‐17 Quadrupole Coupling Parameters for Water in Its Various Phases

Abstract: Analysis of 17O NMR data in D217O ice yields a quadrupole coupling constant, e2qQ / h = 6.66 ± 0.10MHz, and an asymmetry parameter, η = 0.935 ± 0.01. Comparison with the data for liquid and gas indicates a temperature dependence of the 17O quadrupole coupling constant in the liquid and explains the unusual linewidth behavior for liquid D217O. Charge distributions in the water molecule in both the solid and gaseous states have been obtained by a valence‐shell atomic‐orbital population analysis based on the experimental data for the 17O quadrupole coupling parameters and the molecular dipole moment. The results were used to calculate the quadrupole coupling constant for the deuterium nucleus. Good agreement with experimental data was obtained for both the solid and gaseous states. Comparison of the calculations for the two phases suggests that the intermolecular effects in ice are mostly electrostatic.

Estimation of rotational line widths of carbon dioxide bands

Abstract: Anderson's theory on the non-adiabatic collision broadening of the infrared spectral lines has been applied to CO2-CO2 and CO2-N2 collisions. The intermolecular attractive force assumed in this study is that due to either CO2 quadrupole-CO2 quadrupole interaction or CO2 quadrupole-N2 quadrupole interaction. The self-and N2-broadened line widths are calculated on four important bands in the 15μ and 4·3 μ band regions, assuming several different values for the CO2 and N2 quadrupole moments and taking into account the Maxwell-Boltzmann distribution law of the colliding velocity. The results are then used for the determination of plausible values of CO2 and N2 quadrupole moments by comparing with available experimental results.

Magnetic Susceptibility Anisotropy, Molecular Quadrupole Moment, and the Sign of the Electric Dipole Moment in OCS

Abstract: The molecular Zeeman effects of 16O12C32S and 16O12C34S have been observed under high resolution in magnetic fields up to 30 000 G. Conventional microwave spectroscopy is combined with a 6‐ft long magnet to yield accurate first‐ and second‐order magnetic field parameters. The magnetic susceptibility anisotropy of the OCS molecule is χ⊥–χ∥ = (9.27 ± 0.10) × 10−6erg/G2·mole. The molecular g values for the two isotopes obtained from the J = 0 → J = transitions are g⊥(16O12C32S) = − 0.028711 ± 0.00004 and g⊥(16O12C34S) = − 0.028127 ± 0.00004. These data yield the sign of the molecular electric dipole moment which has −OCS+ polarity. Combining χ⊥–χ∥ and g⊥(16O12C32S) gives the molecular quadrupole moment of Q∥(16O12C32S) = − (0.88 ± 0.15) × 10−26esu·cm2.

Sound Generation by Turbulent Two-Phase Flow,

Abstract: Sound generation by turbulent two-phase flow is considered by the methods of Lighthill's theory of aerodynamic noise. An inhomogeneous wave equation is derived, in which the effects of one phase on the other are represented by monopole, dipole and quadrupole distributions. The resulting power outputs are obtained for the case of a distribution of small air bubbles in water. The monopole radiation resulting from volumetric response of the bubbles to the turbulent pressure field overwhelms that from the quadrupoles equivalent to the turbulent flow, the increase in acoustic power output being about 70 dB for a volume concentration of 10%. The monopole radiation occurs through the forced response of the bubbles at the turbulence frequency; resonant response is shown to be impossible when the excitation is due to turbulence alone. Surface radiation arises from the edge of a cloud of bubbles. This radiation is important when the region containing bubbles is in the form of a sheet with thickness smaller than the length scale of the turbulent motion. Dipole radiation is also considered, and found to be negligible whenever monopole sources are present. In the case of a dusty gas, only dipole and quadrupole sources are present, and here it is shown that the dipole radiation is equivalent to an increase in the usual quadrupole radiation. The increase depends upon the mass concentration of dust, and is significant for mass concentrations in excess of unity.

Theory of the Influence of Environment on the Angular Distribution of Nuclear Radiation

Abstract: The effect of electronic relaxation processes on the angular correlation and on the angular distribution of radiation from oriented nuclei is investigated. The influence of the environment on the radioactive nuclei is taken into account by reducing the density operator for the total system (nucleus and surroundings mutually interacting) to a density operator for the nucleus alone. Elimination of the unobserved bath variables is performed with the help of Zwanzig's projection-operator technique. The Liouville formalism is used throughout. The (initially unspecified) properties of the environment enter the theory via second-order correlation functions, which are defined in terms of equilibrium ensemble averages of certain bath operators, like, e.g., the hyperfine-field operator. The matrix elements of the nuclear-evolution operator (which is a superoperator in Liouville space) with respect to a complete orthonormal set of multipole operators are just the usual perturbation factors ${{G}_{k{k}^{\ensuremath{'}}}}^{q{q}^{\ensuremath{'}}}$ of perturbed-angular-correlations theory. The consequent use of the multipole representation yields immediately the final formulas needed in the expression for both the angular distribution of radiation from oriented nuclei and the angular correlation function. The general theory includes relaxation processes due to magnetic and quadrupole interactions. The important case of purely magnetic interactions is discussed in more detail. Specialization to relaxation caused by randomly fluctuating fields yields a formula which contains both the Abragam-Pound result for time-fluctuating quadrupole interaction and Micha's extension to randomly time-varying magnetic fields in multidomain ferromagnets. Exact high-temperature solutions are presented for single crystals in a static magnetic field and with magnetic-type relaxation processes (axially symmetric case). For nuclei with spin $I=1$, the extension to arbitrary temperatures has been considered. The application of the present theory to the problem of multipole relaxation (which arises, e.g., in spin-lattice relaxation measurements with NMR/ON technique) is discussed.

Quadrupole Effects in Electron Paramagnetic Resonance Spectra of Polycrystalline Copper and Cobalt Complexes

Abstract: A second-order theory, including quadrupole effects and transitions with Δm I > 0, for the calculation of EPR spectra of polycrystalline samples of S = ½ transition-metal ion complexes possessing axial symmetry has been developed. With this theory the EPR spectrum of Cu(acac)2 in Pd(acac)2 and that of Na4CoPTS in DMSO could be explained in detail. The effects of electric quadrupole interaction together with a large anisotropy in the nuclear hyperfine coupling are shown. The advantages of obtaining spectra at two frequencies for the determination of reliable spin-Hamiltonian parameters are demonstrated.

NMR Determination of Deuterium Quadrupole Coupling Constants in Nematic Solutions

Abstract: The analysis of the NMR spectra of suitable nematic liquid‐crystal solutions appears to offer a convenient and desirable method for the determination of small nuclear quadrupole coupling constants for molecules in the liquid state. Nuclear quadrupole coupling constants have been determined for deuterium in the C–H bond of a number of small molecules. Assuming that the field gradient has axial symmetry, values of e2qQ/h along the bond axis are as follows: CH3CD3167± 18 kHzC3D6184± 20C2D2198± 7CH3C2D199.4± 2.0DCN199.0± 3.0. The results are discussed in terms of various theoretical calculations of the field gradient at the deuteron, and a compilation of some of the accurate experimentally determined deuterium coupling constants is presented.

Deuteron Quadrupole Coupling in Some Solid Chlorinated Hydrocarbons

Abstract: We report deuteron quadrupole coupling constants in solids CDCl3, CD2Cl2, CD2ClCD2Cl, CD3CCl3, and CD3CCl2CD3. At 77°K these are 167.6 ± 0.8, 169.6 ± 1.1, 171.7 ± 0.8, 174.3 ± 1.6, and 174.7 ± 1.9 kHz, respectively, assuming an axial quadrupole interaction. We also report here a coupling constant of 149.3 ± 0.5 kHz for D in DCl at 77°K, in agreement with the data of Genin, O'Reilly, Peterson, and Tsang. Deuteron pure quadrupole spectra were observed by a pulse double‐resonance technique suggested by Hahn and co‐workers, in which the halogen serves as indicator nucleus. Interpretation of the results in terms of the electronic structure is briefly discussed.

Evaluation of multipoles for photo- and electroproduction of pions

Abstract: With this paper we start a systematic study of the multipole amplitudes for electro- and photoproduction of pions in the low energy region. It is based on the integral equations following from fixedt dispersion relations and the Watson theorem. We start with a discussion of general mathematical problems one encounters when solving the singular integral equations. Especially the non-uniqueness of their solutions poses difficult problems which cannot be solved within the framework of the dispersion theory. As boundary conditions “from outside” we use at threshold the predictions of the static theory. But thereby only the magnetic dipole excitation of the first isobar is determined. For the electric quadrupole amplitude one needs additional conditions.

Deuteron Quadrupole Coupling Constants in Deuterocarbons

Abstract: The dependence of the deuteron quadrupole coupling constant (DQCC) on the nature of hybridization of carbon in deuterocarbons is examined in detail. A simple molecular orbital description of the C–D fragment, with various effective nuclear charges on carbon, is used. The calculated values are shown to be comparable to experimental results and other theoretical models which treat the entire molecules rather than simply the C–D fragment. It is shown that DQCC(sp) > DQCC(sp2) > DQCC(sp3) which may be attributed to the fact that the nuclear contribution to the electric field gradient decreases faster than the electronic part in the series sp, sp2, sp3. A collection of experimental data, establishing the same trend obtained theoretically, is presented including new deuterium NMR results on phenylacetylene‐d and ferrocene‐d10.

Microwave spectrum, structure, low frequency vibrations, dipole moment and quadrupole coupling constants of dinitrogen trioxide

Abstract: The structure of N2O3 has been determined from the microwave spectrum of seven isotopic species. The detailed structure associated with the following planar configuration is: [graphic omitted] d(N2N3)= 1.864 A; d(N2O1)= 1.142 A; d(N3O4)= 1.202 A; d(N3O5)= 1.217 A; ∠O1N2N3= 105.1°∠O4N3N2= 112.7°∠O5N3N2= 117.5°. The torsional vibrational frequency has been measured as 124 ± 25 cm–1. The quadrupole coupling constants for the nitrosyl nitrogen are χaa=–2.34 MHz, χbb= 1.12 MHz, and χcc= 1.22 MHz. The dipole moment has been determined as |µa|= 2.05 D; |µb|= 0.54 D; and |µt|= 2.12 D inclined at an angle of 9.1° to the N—N bond. On the basis of these data, the bonding is discussed.