Showing papers on "Quadrupole published in 2001"

Spectroscopic nuclear quadrupole moments

Abstract: A ‘year-2001’ set of nuclear quadrupole moments, Q, is presented. Compared to the previous, ‘year-1992’ set, a major revision of the value or a considerable improvement of the accuracy is reported for 6 3Li, 7N, 19 9F (197 keV, I = 5/2), 11Na, 13Al, 21Sc, 22Ti, 26Fe (14 keV, I = 3/2 Mossbauer state), 31Ga, 32Ge, 77 34Se (250 keV, I = 5/2 state), 35Br, 36Kr, 37Rb, 39Y, 40Zr, 100 45Rh, 50Sn (24 keV, I = Mossbauer state), 53I, 54Xe, 55Cs and 83Bi.

Magnetic transport of trapped cold atoms over a large distance

Abstract: We report the transport of magnetically trapped cold atoms over a large distance. Atoms are captured in a magneto-optical trap (MOT) and loaded into a magnetic quadrupole trap. The quadrupole potential is then moved over a distance of 33 cm into an ultra-high-vacuum (UHV) chamber using a chain of quadrupole coils. By running suitable currents through the quadrupole coil pairs the trapping geometry of the potential is maintained during the transport process, thus minimizing heating of the trapped atom cloud. Magnetically trapped ${}^{87}\mathrm{Rb}$ atoms at an initial temperature of $T=125 \ensuremath{\mu}\mathrm{K}$ were heated by less than $20 \ensuremath{\mu}\mathrm{K}$ during the transport process, and up to ${10}^{9}$ atoms were transferred into the UHV chamber. Due to the spatial separation of the final magnetic trap and the MOT we have been able to capture atoms in the MOT, while storing magnetically trapped atoms in the UHV chamber.

A Charge Analysis Derived from an Atomic Multipole Expansion

Abstract: A new charge analysis is presented that gives an accurate description of the electrostatic potential from the charge distribution in molecules. This is achieved in three steps: first, the total density is written as a sum of atomic densities; next, from these atomic densities a set of atomic multipoles is defined; finally, these atomic multipoles are reconstructed exactly by distributing charges over all atoms. The method is generally applicable to any method able to provide atomic multipole moments, but in this article we take advantage of the way the electrostatic potential is calculated within the Density Functional Theory framework. We investigated a set of 31 molecules as well as all amino acid residues to test the quality of the method, and found accurate results for the molecular multipole moments directly from the DFT calculations. The deviations from experimental values for the dipole/quadrupole moments are also small. Finally, our Multipole Derived Charges reproduce both the atomic and molecular multipole moments exactly. c 2000 John Wiley & Sons, Inc. J Comput Chem 22: 79-88, 2001

Nondestructive high-resolution and absolute mass determination of single charged particles in a three-dimensional quadrupole trap

Abstract: A method for the nondestructive high-resolution and absolute mass determination of charged particles is described. It is based on the detection of light scattered from a single particle in an electrodynamical three-dimensional quadrupole trap. From the amplitude modulation of this signal, the eigenfrequencies of the secular motion are determined with high precision. For 500 nm in diameter SiO2 particles, having a mass of 130 fg (≈1011 u), a resolution of 10−4 is achieved in a 10 s measurement. On a longer time scale, the 10−6 range can be accessed. Key features of the method such as reproducibility, long term stability, accuracy, and linearity are characterized in detail. The extension of the mass range of quadrupole traps from atomic masses to micrometer sized particles as well as potential applications are discussed.

An exact form of Lilley's equation with a velocity quadrupole/temperature dipole source term

Abstract: There have been several attempts to introduce approximations into the exact form of Lilley's equation in order to express the source term as the sum of a quadrupole whose strength is quadratic in the fluctuating velocities and a dipole whose strength is proportional to the temperature fluctuations. The purpose of this note is to show that it is possible to choose the dependent (i.e., the pressure) variable so that this type of result can be derived directly from the Euler equations without introducing any additional approximations.

Dipole, dipole–quadrupole, and dipole–octopole polarizability of adamantane, C10H16, from refractive index measurements, depolarized collision-induced light scattering, conventional ab initio and density functional theory calculations

Abstract: Refractive index (RI) measurements, depolarized collision-induced light (CILS) scattering and ab initio quantum chemical calculations are used to determine the dipole (α), dipole–quadrupole (A), and dipole–octopole polarizability (E) of adamantane, C10H16. For this molecule of symmetry group Td the three polarizabilities can be represented by a single scalar quantity. From experiment we obtain for the static dipole polarizability at T≈400–500 K 107.5±1.1 e2a02Eh−1, and for the higher polarizabilities |A|=102.0±7.8 e2a03Eh−1, and |E|=720±80 e2a04Eh−1. We have performed conventional ab initio and density functional theory calculations with specifically designed basis sets. A very large [4s3p3d1f/3s2p1d] basis set consisting of 574 basis functions is thought to provide near-Hartree–Fock values for α,A and E: α=101.72 e2a02Eh−1, A=−6.5 e2a03Eh−1, and E=−71.0 e2a04Eh−1. Our final theoretical estimates for these properties are α=107.5±1.0 e2a02Eh−1, A=−8.0±1.5 e2a03Eh−1, and E=−76.5±5.5 e2a04Eh−1. Very strong e...

Understanding the Optical Band Shape: Coumarin-153 Steady-State Spectroscopy

Abstract: We have developed a band-shape analysis of optical transitions in polarizable chromophores characterized by large magnitudes of the transition dipole (intense transitions). The model is tested on steady-state spectra of the coumarin-153 optical dye, employing an explicit solvent description accounting for dipole moment, quadrupole moment, and polarizability of the solvent molecules. The calculations are performed for solvents ranging from nondipolar to strongly dipolar. The solvent dependence of both the experimental Stokes shift and the spectral width is satisfactorily reproduced over the whole polarity range. The optical width is shown to demonstrate a qualitatively different solvent dependence for absorption and emission. The solvent-induced absorption width increases with solvent polarity, whereas the solvent-induced emission width passes through a maximum. This is a result of non-Gaussian statistics of the energy gap fluctuations in polarizable/electronically delocalized chromophores. The total (i.e....

Nuclear quadrupole moment of 57Fe from microscopic nuclear and atomic calculations.

Abstract: The nuclear quadrupole moment (NQM) of the Ipi = 3/2(-) excited nuclear state of 57Fe at 14.41 keV, important in Mossbauer spectroscopy, is determined from the large-scale nuclear shell-model calculations for 54Fe, 57Fe, and also from the electronic ab initio and density functional theory calculations including solid state and electron correlation effects for the molecules Fe(CO)(5) and Fe(C5H5)(2). Both independent methods yield very similar results. The recommended value is 0.15(2) e b. The NQM of the isomeric 10+ in 54Fe has also been calculated. The new NQM values for 54Fe and 57Fe are consistent with the perturbed angular distribution data.

Wideband dual sphere detector of gravitational waves.

Abstract: We present the concept of a sensitive and broadband resonant mass gravitational wave detector. A massive sphere is suspended inside a second hollow one. Short, high-finesse Fabry-Perot optical cavities read out the differential displacements of the two spheres as their quadrupole modes are excited. At cryogenic temperatures, one approaches the standard quantum limit for broadband operation with reasonable choices for the cavity finesses and the intracavity light power. A molybdenum detector, of overall size of 2 m, would reach spectral strain sensitivities of 2x10(-23) Hz(-1/2) between 1000 and 3000 Hz.

Gravitational multipole moments of the Sun determined from helioseismic estimates of the internal structure and rotation

Abstract: We determine the gravitational multipole momentsJ2n ;n =1 ; 5, of the sun using a model of the interior structure and of solar rotation obtained from helioseismic inversions. The dierential rotation of the convective zone and the underlying transition zone make only a small (0:5%) contribution to the quadrupole moment J2 which is found to have a value2:21 10 7 .

Electric-dipole, electric-quadrupole, magnetic-dipole, and magnetic-quadrupole transitions in the neon isoelectronic sequence

Abstract: Excitation energies for $2l\ensuremath{-}{3l}^{\ensuremath{'}}$ hole-particle states of Ne-like ions are determined to second order in relativistic many-body perturbation theory (MBPT). Reduced matrix elements, line strengths, and transition rates are calculated for electric-dipole $(E1),$ magnetic-quadrupole $(E2),$ magnetic-dipole $(M1),$ and magnetic-quadrupole $(M2)$ transitions in Ne-like ions with nuclear charges ranging from $Z=11$ to 100. The calculations start from a ${1s}^{2}{2s}^{2}{2p}^{6}$ closed-shell Dirac-Fock potential and include second-order Coulomb and Breit-Coulomb interactions. First-order many-body perturbation theory (MBPT) is used to obtain intermediate-coupling coefficients, and second-order MBPT is used to determine the matrix elements. Contributions from negative-energy states are included in the second-order $E1,$ $M1,$ $E2,$ and $M2$ matrix elements. The resulting transition energies are compared with experimental values and with results from other recent calculations. Trends of $E1,$ $E2,$ $M1,$ and $M2$ transition rates as functions of nuclear charge Z are shown graphically for all transitions to the ground state.

51V MAS NMR Investigation of 51V Quadrupole Coupling and Chemical Shift Anisotropy in Divalent Metal Pyrovanadates

Abstract: Magnitudes and relative orientations of 51V quadrupole coupling and chemical shift tensors have been determined from 51V magic-angle spinning (MAS) NMR spectra at 14.1 T for seven divalent metal pyrovanadates: α- and β-Mg2V2O7, Ca2V2O7, α-Zn2V2O7, Cd2V2O7, BaCaV2O7, and α-BaZnV2O7. This has been accomplished by least-squares fitting of the integrated spinning sideband intensities observed for the central and satellite transitions employing spectral widths up to 4 MHz. Numerical error analysis of the optimized data reveals that the five NMR parameters characterizing the magnitudes of the quadrupole coupling and chemical shift tensors are obtained with high precision while somewhat larger error limits are observed for the three Euler angles, describing the relative orientation of the two tensors. The optimized data exhibit a significantly higher precision when compared to earlier reported parameters for some of the pyrovanadates, determined from 51V static-powder or MAS NMR of the central transition only. ...

The multipole polarizabilities and hyperpolarizabilities of the water molecule in liquid state: an ab initio study

Abstract: A charge perturbation variant of the finite-field method has been used to calculate dipole and quadrupole moments, dipole polarizability, hyper- and principal components of high-order polarizabilities of the water molecule in gas and in liquid phase conditions. Calculations were performed for the ground-state water molecule at the MP2 and MP4 levels of theory. The gas phase values determined allow our methodology for extracting polarizabilities to be tested and a properly balanced, moderate-sized basis set to be selected; the results obtained are in very good agreement with experiment and the most accurate previous theoretical estimates. A local field approach is introduced to mimic the electrostatic environment experienced by a water molecule in the liquid. Within this approach, sets of fixed charges are used to generate the desired electric fields and field gradients. Three different liquid phase models and the corresponding sets of electrical properties are examined. The values obtained from these mode...

Dipole and quadrupole polarizabilities and shielding factors of beryllium from exponentially correlated Gaussian functions

Abstract: Dynamic dipole and quadrupole polarizabilities as well as shielding factors of the beryllium atom in the ground state were computed at real frequencies by using the variation-perturbation method. The zeroth- and the first-order wave functions were expanded in many-electron basis of exponentially correlated Gaussian functions. The 1600-term expansion of the unperturbed wave function yielded the ground-state energy accurate to 1c m 21 . The first-order wave functions were expanded in very large bases ~4800 and 4400 terms!. The nonlinear parameters of the first-order correction functions were optimized with respect to both the static and dynamic polarizabilities, and with respect to the excited-state energies. The procedure employed ensures a high accuracy of determination of dynamic properties in a wide range of frequencies and correct positions of the transition poles. Test calculations, performed on He and Li, confirmed the ability of this method to obtain the atomic properties with very high accuracy. The final values of the static properties of Be were 37.755e 2 a 0 E H1 and 300.96e 2 a0 EH1 for the dipole and quadrupole polarizabilities, respectively, and 1.4769 for the quadrupole shielding factor. The convergence of the atomic properties with the size of the expansion of both the zerothand first-order functions was checked. Thanks to very high accuracy of the unperturbed wave function and the efficient method of construction of the first-order wave functions, the dynamic polarizability results presented in this work are of benchmark quality. As a by-product of this project, a set of the most accurate upper bounds to the energies of 1 P and 1 D states of Be was obtained.

Rotation dependence of electric quadrupole hyperfine interaction in the ground state of molecular iodine by high-resolution laser spectroscopy

Abstract: Doppler-free high-resolution spectroscopy is applied to molecular iodine at 532 nm by Nd:YAG lasers. The main hyperfine components as well as the crossover lines are measured for R(56)32-0 and P(54)32-0 transitions by heterodyne beating of two I2-stabilized lasers. The measured hyperfine splittings including both main and crossover lines are fitted to a four-term Hamiltonian, which includes the electric quadrupole, spin–rotation, tensor spin–spin, and scalar spin–spin interactions, with an average deviation of ∼1 kHz. Absolute values of the electric quadrupole hyperfine constants for both the upper and the lower states are obtained. The rotation dependence of the ground-state (v″=0) electric quadrupole constant eQq″ is found to be eQq″(J)=-2452.556(2)-0.000164(5)J(J+1)-0.000000005(2)J2(J+1)2 MHz.

Measurement of molecular motion in solids by nuclear magnetic resonance spectroscopy of half-integer quadrupole nuclei

Abstract: An accurate and efficient formalism is presented for simulating the effects of molecular motion on satellite and central transition nuclear magnetic resonance (NMR) spectra of half-integer quadrupole nuclei. The approach is based on the principles of the density operator and the stochastic Liouville–von Neumann equation and may be applied for both rotating and nonrotating samples. The symmetry properties of nuclear spin ensembles have been used to rewrite the stochastic Liouville–von Neumann equation in the form of a linear homogeneous system of coupled first-order differential equations among the alignments and coherences. This system is highly stiff and can only be solved by methods that are sufficiently accurate and stable. The properties of Cartan–Weyl operators have been used to obtain the most efficient solution for secular interactions. The methodology has been incorporated into computer programs to simulate the effects of motion for any half-integer quadrupole nucleus. These programs include the f...

MCSCF response calculations of the excited states properties of the O2 molecule and a part of its spectrum

Abstract: A number of transitions including the triplet–singlet band f′1Σu+←X3Σg−, have been studied by ab initio multi-configurational self-consistent field (MCSCF) response methods. Potential energy curves for eight excited states obtained by linear response calculation are in a good agreement with recent experimental data and exhibit some new findings. Quadrupole moments for the 12 lowest states have been calculated which can be used for intermolecular interaction analysis and solvent shift estimations. The nuclear quadrupole coupling constant, magnetizability tensor, nuclear spin–rotation coupling constant and rotational g-factor are also presented. For the three lowest singlet states these parameters are analyzed in detail.

Ground-state properties and spins of the odd Z=N+1 nuclei 61 Ga- 97 In

Abstract: Binding energies, quadrupole deformation parameters, spins and parities of the neutron-deficient odd $Z=N+1$ nuclei in the $A\sim 80$ region are calculated in the relativistic mean field approximation. The ground-state and low-lying configurations of the recently observed $^{77}$Y, $^{79}$Zr and $^{83}$Mo nuclei are analyzed. The calculated results are compared with other theoretical predictions.

Comparison of ab initio and density functional calculations of electric field gradients: The 57Fe nuclear quadrupole moment from Mössbauer data

Abstract: The difficulty in accurate determination of the nuclear quadrupole moment of the first I=3/2 excited nuclear state of 57Fe from electronic structure calculations of the iron electric field gradient combined with Mossbauer measurements of the nuclear quadrupole splitting in the isomer shift is addressed by comparing ab initio with density functional calculations for iron pentacarbonyl, Fe(CO)5, ferrocene, Fe(C5H5)2, and the 5Δg electronic ground states of FeCl2 and FeBr2. While the ligand field gradient tensor components change relatively little with the method applied, the iron electric field gradient is sensitive to the specific density functional used. Single reference many-body perturbation theory for electron correlation also performs poorly for the iron electric field gradient and shows extreme oscillatory behavior with a change in the order of the perturbation series. Even with larger basis sets and coupled cluster techniques a precise value for the iron electric field gradient could not be determin...

Natural circular dichroism in X-ray spectroscopy

Abstract: The measurement of natural circular dichroism has been extended to the X-ray region. XNCD spectra have been measured for uniaxial single crystals of the chiral coordination compounds Na3[Nd(digly)3]·2NaBF4·6H2O (digly = 2,2‘-oxydiacetate) and {[Co(en)3]Cl3}2·NaCl·6H2O (en = ethane-1,2-diamine) and for ionic crystals such as LiIO3. The XANES part of the XNCD shows circular dichroism corresponding to chiral multiple scattering paths of the photoelectron. In addition, both the Nd(III) and Co(III) compounds show quadrupole allowed pre-edge features (2p → 4f for Nd and 1s → 3d for Co) which have exceptionally large Kuhn dissymmetry factors. The theory of XNCD is discussed and the circular dichroism is shown to be due to the interference between allowed electric dipole and electric quadrupole transition moments (E1−E2 mechanism). This new spectroscopy represents a useful extension to techniques for the study of both molecular and crystal structural enantiomorphism.

Nuclear quadrupole moments for Al-27 and Ga-69 derived from four-component molecular coupled cluster calculations

Abstract: In this work we investigate different approaches for calculating electric field gradients in order to provide accurate theoretical values for the nuclear quadrupole moments (NQM) for aluminum and gallium. Electron correlation is included in a fully four-component framework at the CCSD(T) level. The resulting NQM for 27Al (146.0±0.4 mb) is in good agreement with earlier work, while the value for 69Ga (171±2 mb) is higher than suggested on basis of previous molecular calculations.

Fourier transform millimeter-wave spectroscopy of chlorocarbene (HCCl)

Abstract: The 101–000 and 202–101 rotational transitions of HC35Cl and HC37Cl in the X 1A′ ground vibronic state have been observed with a Fourier transform millimeter-wave spectrometer. The HCCl molecule is produced by discharging a gaseous sample of CH2Cl2 diluted in Ar with a pulsed discharge nozzle. The effective rotational constant (B+C)/2, the centrifugal distortion constant ΔJ, the nuclear quadrupole interaction constants, and the nuclear-spin rotation interaction constant are determined for each isotopic species. The nuclear-spin rotation interaction is found to make a significant contribution to the hyperfine structure of this molecule, which originates from the relatively low-lying electronic excited state. The nuclear quadrupole interaction tensor is highly asymmetric, indicating a significant π character of the C–Cl bond. This can be interpreted in terms of the backdonation of π electrons from the chlorine atom to the carbon atom.

Moment of inertia and quadrupole response function of a trapped superfluid

Abstract: We derive an explicit relationship between the moment of inertia and the quadrupole response function of an interacting gas confined in a harmonic trap. The relationship holds for both Bose and Fermi systems and is well-suited to reveal the effects of irrotationality of the superfluid motion. Recent experimental results on the scissors mode are used to extract the value of the moment of inertia of a trapped Bose gas and to point out the deviations from the rigid value due to superfluidity.

Means and method for guiding ions in a mass spectrometer

Abstract: A multipole ion guide capable of incorporating a plurality of ion sources (i.e., MALDI, ESI, EI/CI, etc.) to provide and analyze ions in a mass analyzer (i.e., ICR, TOF, quadrupole, etc.) has been designed. Such multipole ion guides comprise an array of pairs of parallel conducting rods (i.e., 3 pair, 4 pair, 5 pair, etc.), each pair being equally spaced from one another, with the array being bound on its top and bottom as well as its ends by DC electrodes. The ion guide then utilizes RF/DC potentials to accept ions from any of a multitude of ion sources to facilitate their transmission through differentially pumped regions to a high pressure mass analysis region.