Showing papers on "Quadrupole published in 2014"

Symmetry energy from the nuclear collective motion: constraints from dipole, quadrupole, monopole and spin-dipole resonances

Abstract: The experimental and theoretical studies of Giant Resonances, or more generally of the nuclear collective vibrations, are a well-established domain in which sophisticated techniques have been introduced and firm conclusions reached after an effort of several decades. From it, information on the nuclear equation of state can be extracted, albeit not far from usual nuclear densities. In this contribution, which complements other contributions appearing in this topical issue, we survey some of the constraints that have been extracted recently concerning the parameters of the nuclear symmetry energy. Isovector modes, in which neutrons and protons are in opposite phase, are a natural source of information and we illustrate the values of symmetry energy around saturation deduced from isovector dipole and isovector quadrupole states. The isotopic dependence of the isoscalar monopole energy has also been suggested to provide a connection to the symmetry energy: relevant theoretical arguments and experimental results are thoroughly discussed. Finally, we consider the case of the charge-exchange spin-dipole excitations in which the sum rule associated with the total strength gives in principle access to the neutron skin and thus, indirectly, to the symmetry energy.

Shape coexistence in the neutron-deficient even-even Hg182-188 isotopes studied via Coulomb excitation

Abstract: Coulomb-excitation experiments to study electromagnetic properties of radioactive even-even Hg isotopes were performed with 2.85 MeV/nucleon mercury beams from REX-ISOLDE. Magnitudes and relative signs of the reduced E2 matrix elements that couple the ground state and low-lying excited states in Hg182-188 were extracted. Information on the deformation of the ground and the first excited 0(+) states was deduced using the quadrupole sum rules approach. Results show that the ground state is slightly deformed and of oblate nature, while a larger deformation for the excited 0(+) state was noted in Hg-182; 184. The results are compared to beyond mean field and interacting-boson based models and interpreted within a two-state mixing model. Partial agreement with the model calculations was obtained. The presence of two different structures in the light even-mass mercury isotopes that coexist at low excitation energy is firmly established.

Quadrupole moments of rapidly rotating compact objects in dilatonic Einstein-Gauss-Bonnet theory

Abstract: We consider rapidly rotating black holes and neutron stars in dilatonic Einstein-Gauss-Bonnet (EGBd) theory and determine their quadrupole moments, which receive a contribution from the dilaton. The quadrupole moment of EGBd black holes can be considerably larger than the Kerr value. For neutron stars, the universality property of the $\stackrel{^}{I}$-$\stackrel{^}{Q}$ relation between the scaled moment of inertia and the scaled quadrupole moment appears to extend to EGBd theory.

Systematic calculations of energy levels and transition rates of c-like ions with z = 13-36

Abstract: Based on systematic calculations using a combined relativistic configuration interaction and a many-body perturbation theory (MBPT) approach, we provide a complete and consistent data set for 46 levels belonging to the 2s 22p 2, 2s2p 3, 2p 4, 2s 22p3s, 2s 22p3p, and 2s 22p3d configurations in C-like ions with 13 ≤ Z ≤ 36. The data set includes energy levels as well as electric dipole, magnetic dipole, electric quadrupole, and magnetic quadrupole transition properties. Extensive comparisons with available observed and calculated results are made and indicate that the present MBPT calculations are highly accurate. The present data set can be used reliably for many purposes, such as the line identification of observed spectra, and modeling and diagnostics of astrophysical and fusion plasmas.

Near-Field Mapping of Optical Modes on All-Dielectric Silicon Nanodisks

Abstract: We measure, for the first time to our knowledge, the near-field amplitudes and phases of localized optical modes of high-index all-dielectric nanoparticles using apertureless near-field optical microscopy. For individual silicon nanodisks, we observe a four-lobed mode pattern and the formation of deep-subwavelength hot-spots. Our numerical calculations of the optical near-fields of the nanodisks in combination with a multipole expansion of the scattered field based on vector spherical harmonics reveal that the observed modes are dominated by electric quadrupole contributions. The observed mode is of particular interest for the design of low-loss all-dielectric metasurfaces and nanoantennas for a broad range of applications, such as directional and complex-polarization controlled emission, light extraction from multipolar atomic transitions, and coherent multiple-emitter-nanocavity interactions.

Diabatization based on the dipole and quadrupole: the DQ method.

Abstract: In this work, we present a method, called the DQ scheme (where D and Q stand for dipole and quadrupole, respectively), for transforming a set of adiabatic electronic states to diabatic states by using the dipole and quadrupole moments to determine the transformation coefficients. It is more broadly applicable than methods based only on the dipole moment; for example, it is not restricted to electron transfer reactions, and it works with any electronic structure method and for molecules with and without symmetry, and it is convenient in not requiring orbital transformations. We illustrate this method by prototype applications to two cases, LiH and phenol, for which we compare the results to those obtained by the fourfold-way diabatization scheme.

Bound states for a Coulomb-type potential induced by the interaction between a moving electric quadrupole moment and a magnetic field

Abstract: We discuss the arising of bound states solutions of the Schrodinger equation due to the presence of a Coulomb-type potential induced by the interaction between a moving electric quadrupole moment and a magnetic field Furthermore, we study the influence of the Coulomb-type potential on the harmonic oscillator by showing a quantum effect characterized by the dependence of the angular frequency on the quantum numbers of the system, whose meaning is that not all values of the angular frequency are allowed

Origin of the phonon Hall effect in rare-earth garnets.

Abstract: The phonon Hall effect has been observed in the paramagnetic insulator Tb3Gd5O12. A magnetic field applied perpendicularly to a heat current induces a temperature gradient that is perpendicular to both the field and the current. We show that this effect is due to resonant skew scattering of phonons from the crystal field states of superstoichiometric Tb(3+) ions. This scattering originates from the coupling between the quadrupole moment of Tb(3+) ions and the lattice strain. The estimated magnitude of the effect is consistent with experimental observations at T∼5 K and can be significantly enhanced by increasing temperature.

Multi-spectral plasmon induced transparency via in-plane dipole and dual-quadrupole coupling.

Abstract: We experimentally demonstrated an approach based on dipole and dual-quadrupole coupling to construct a planar metamaterial supporting multi-spectral plasmon induced transparency. The structure consists of two short silver wires (dipole) and two long silver wires (dual-quadrupole). The in-plane coupling between the dipole and the dual-quadrupole leads to two transmission windows even in the absorbance linewidth of the dipole. This phenomenon is well described and understood by numerical analyses and a classical oscillator model.

Statistical Anisotropies in Gravitational Waves in Solid Inflation

Abstract: Solid inflation can support a long period of anisotropic inflation. We calculate the statistical anisotropies in the scalar and tensor power spectra and their cross-correlation in anisotropic solid inflation. The tensor-scalar cross-correlation can either be positive or negative, which impacts the statistical anisotropies of the TT and TB spectra in CMB map more significantly compared with the tensor self-correlation. The tensor power spectrum contains potentially comparable contributions from quadrupole and octopole angular patterns, which is different from the power spectra of scalar, the cross-correlation or the scalar bispectrum, where the quadrupole type statistical anisotropy dominates over octopole.

Quadrupole-enhanced Raman scattering.

Abstract: Dark, nonradiating plasmonic modes are important in the Raman enhancement efficiency of nanostructures. However, it is challenging to engineer such hotspots with predictable enhancement efficiency through synthesis routes. Here, we demonstrate that spiky nanoshells have designable quadrupole resonances that efficiently enhance Raman scattering with unprecedented reproducibility on the single particle level. The efficiency and reproducibility of Quadrupole Enhanced Raman Scattering (QERS) is due to their heterogeneous structure, which broadens the quadrupole resonance both spatially and spectrally. This spectral breadth allows for simultaneous enhancement of both the excitation and Stokes frequencies. The quadrupole resonance can be tuned by simple modifications of the nanoshell geometry. The combination of tunability, high efficiency, and reproducibility makes these nanoshells an excellent candidate for applications such as biosensing, nanoantennaes, and photovoltaics.

Superscattering of Light from Core–Shell Nonlocal Plasmonic Nanoparticles

Abstract: We study the scattering properties of coated nanoparticles with high-permittivity core and nonlocal plasmonic shell with full-wave nonlocal Mie theory. Both electric and artificial magnetic resonances of different orders are supported simultaneously for such coated particles. By properly engineering the aspect ratio, we can achieve not only the overlapping of electric dipole (ED) and magnetic dipole (MD) modes but also that of electric quadrupole (EQ) and magnetic quadrupole (MQ). We numerically demonstrate that there are two overlapping ways to obtain the superscattering state for core–shell nanoparticles. Furthermore, we show that the nonlocality becomes less important in the scattering of coated nanoparticles with ultrathin shell thickness but large total size due to the fact that nonlocality is essentially a surface effect.

Electric quadrupole moment of graphene and its effect on intermolecular interactions.

Abstract: Carbon atoms in aromatic compounds exhibit a permanent electric quadrupole moment due to the aromatic π electron distribution. In the case of small aromatic hydrocarbons, this quadrupole contributes significantly to their intermolecular interactions, but when the honeycomb lattice is expanded to infinity, the quadrupolar field sums to zero and its significance vanishes. Therefore, electrostatic interactions with graphene are often omitted in force field molecular modeling. However, for a finite sheet, the electrostatic field decays only slowly with increasing size and is always non-negligible near edges. In addition, in a corrugated graphene sheet, the electrostatic field near the surface does not vanish completely and remains sizeable. In the present study, we investigated the magnitude of the graphene quadrupolar field as a function of model size and graphene corrugation, and estimated the error resulting from its neglect in molecular dynamics simulations. Exfoliation energies in benzene and hexafluorobenzene were calculated using the potential of mean force method with and without explicit quadrupoles. The effect on exfoliation energies was found to be quite small. However, the quadrupole moment may be important for graphene sheet association (aggregation) as it affects barrier heights, and consequently kinetics of association. Our results indicate that quadrupolar interactions may need to be considered in molecular modeling when graphene is corrugated or bent.

Inflationary power asymmetry from primordial domain walls

Abstract: We study the asymmetric primordial fluctuations in a model of inflation in which translational invariance is broken by a domain wall. We calculate the corrections to the power spectrum of curvature perturbations; they are anisotropic and contain dipole, quadrupole, and higher multipoles with non-trivial scale-dependent amplitudes. Inspired by observations of these multipole asymmetries in terms of two-point correlations and variance in real space, we demonstrate that this model can explain the observed anomalous power asymmetry of the cosmic microwave background (CMB) sky, including its characteristic feature that the dipole dominates over higher multipoles. We test the viability of the model and place approximate constraints on its parameters by using observational values of dipole, quadrupole, and octopole amplitudes of the asymmetry measured by a local-variance estimator. We find that a configuration of the model in which the CMB sphere does not intersect the domain wall during inflation provides a good fit to the data. We further derive analytic expressions for the corrections to the CMB temperature covariance matrix, or angular power spectra, which can be used in future statistical analysis of the model in spherical harmonic space.

Fano Resonances Induced by Strong Interactions Between Dipole and Multipole Plasmons in T-Shaped Nanorod Dimer

Abstract: A simple T-shaped plasmonic nanostructure composed of two perpendicular coupled nanorods is proposed to produce strong Fano resonances By the near-field coupling between the “bright” dipole and “dark” quadrupole plasmons of the nanorods, a deep Fano dip is formed in the extinction spectrum, which can be well fitted by the Fano interference model The effects of the geometry parameters including nanorod length, coupling gap size, and coupling location to the Fano resonances are analyzed in detail, and a very high refractive index sensitivity is achieved by the Fano resonance Also by adjusting the incident polarization direction, double Fano resonances can be formed by the interferences of the dipole, quadrupole, and hexapole plasmons The proposed nanorod dimer structure is agile, and a trimer which supports double Fano resonances can be easily formed by introducing a third perpendicular coupled nanorod The proposed T-shaped nanorod dimer structure may have applications in the fields of biological sensing and plasmon-induced transparency

Multipole analysis of unidirectional light scattering from plasmonic dimers

Abstract: We analyze unidirectional scattering produced by sub-wavelength plasmonic dimers formed by two silver strips separated by a thin dielectric spacer and embedded in a uniform dielectric medium. Achieving the Kerker condition, which requires matching the strengths of the electric and magnetic-type contributions of the same multipolar order, is possible with such structures for both forward and backward unidirectional scattering by matching the geometric shape-leveraged resonant magnetic dipolar response with the off-resonant electric dipolar contribution. However, unidirectionality is strongly affected by coupling between the two elements in the dimer structure, leading to the manifestation of the electric quadrupole response in the far field. We develop an approach allowing for an easy inverse scattering retrieval of various multipole contributions to the far-field pattern produced by this type of geometry. The retrieval shows unambiguously that the electric quadrupole response contributes up to 30% of the scattered far-field intensity, in addition to strong manifestation of both electric and magnetic dipolar modes. A modified condition for unidirectionality can be developed based on the principle that suppression of radiation in either the forward or backward direction can be achieved whenever the combined strength of multipolar modes of a certain parity, radiating along the propagation direction, matches that of an opposite parity, and noting that parities of electric and magnetic modes interchange with increasing multipole order. With this condition satisfied, unidirectionality of 26 dB/17 dB for forward/backward scattering, respectively, can be achieved with dimer geometries. We also perform a detailed quantitative analysis of scattering cross sections of dimer structures compared to those of Si and gold spheres, accounting for the actual material losses. We show that dimer structures allow for improving backscattering unidirectionality by 10 dB compared to what is achievable with Si spheres, owing to their reliance on off-resonant electric dipolar response; they also allow for a significant (below ) reduction of the size of a unidirectionally scattering nanoelement.

Electric Octupole Order in Bilayer Ruthenate Sr3Ru2O7

Abstract: Although the odd-parity multipole order barely occurs in crystals with high symmetry, it can be formed in locally noncentrosymmetric crystals. We illustrate the odd-parity electric octupole order generated in a bilayer structure. When the local electric quadrupole is alternatively stacked between layers, it is regarded as an electric octupole order from the viewpoint of symmetry. We show that the pysx + pxsy spin nematic order is induced by the spin–orbit coupling in the electric octupole state, and it results from the spontaneous inversion symmetry breaking leading to the D2d point group symmetry. We investigate the possible realization of the electric octupole order in the bilayer ruthenate Sr3Ru2O7, assuming a local electric quadrupole arising from the Pomeranchuk instability and/or the orbital order. Effects of the lattice distortion and magnetic field are also clarified, and the nature of the “electronic nematic state” of Sr3Ru2O7 is discussed. It is proposed that the asymmetric band structure is a s...

Observation of quadrupole helix chirality and its domain structure in DyFe3(BO3)4.

Abstract: In addition to the structural chirality of materials, there has recently been a rise in interest in the chirality arising from their magnetic and electronic structure. Using a spatially resolved resonant X-ray diffraction technique, a helical arrangement of the Dy 4f quadrupole moments in the ferroborate system DyFe3(BO3)4 is uncovered.

A self-consistent study of multipole response in neutron-rich nuclei using a modified realistic potential

Abstract: The multipole response of neutron-rich O and Sn isotopes is computed in Tamm–Dancoff and random-phase approximations using the canonical Hartree–Fock–Bogoliubov quasi-particle basis The calculations are performed using an intrinsic Hamiltonian composed of a Vlowk potential, deduced from the CD-Bonn nucleon–nucleon interaction, corrected with phenomenological density dependent and spin–orbit terms The effect of these two pieces on energies and multipole responses is discussed The problem of removing the spurious admixtures induced by the center-of-mass motion and by the violation of the number of particles is investigated The differences between the two theoretical approaches are discussed quantitatively Attention is then focused on the dipole strength distribution, including the low-lying transitions associated with the pygmy resonance Monopole and quadrupole responses are also briefly investigated A detailed comparison with the available experimental spectra contributes to clarify the extent of validity of the two self-consistent approaches

Solar Cycle Variation of the Sun’s Low-Order Magnetic Multipoles: Heliospheric Consequences

Abstract: The Sun’s dipole and quadrupole components play a central role in the solar cycle evolution of the interplanetary magnetic field (IMF). The long-term variation of the radial IMF component approximately tracks that of the total dipole moment, with additional contributions coming near sunspot maximum from the quadrupole moment and from CMEs. The axial and equatorial components of the dipole vary out of phase with each other over the solar cycle. The equatorial dipole, whose photospheric sources are subject to rotational shearing, decays on a timescale of ∼1 yr and must be continually regenerated by new sunspot activity; its fluctuating strength depends not only on the activity level, but also on the longitudinal phase relationships among the active regions. During cycles 21–23, the equatorial dipole and IMF reached their peak strength ∼2 yrs after sunspot maximum; conversely, large dips or “Gnevyshev gaps” occurred when active regions emerged longitudinally out of phase with each other. The 10Be-inferred phase shift in the IMF variation during the Maunder Minimum may be explained by a decrease in the amplitude of the equatorial dipole relative to the axial dipole, due either to a systematic weakening of the emerging bipoles or to an increase in their tilt angles. In mid-2012, during the polarity reversal of cycle 24, the nonaxisymmetric quadrupole component became so dominant that the heliospheric current sheet (HCS) split into two cylindrical components. Hemispheric asymmetries in sunspot activity give rise to an axisymmetric quadrupole component, which has combined with the axial dipole to produce a systematic southward displacement of the HCS since cycle 20.

Systematic Improvement of Potential-Derived Atomic Multipoles and Redundancy of the Electrostatic Parameter Space

Abstract: We assess the accuracy of force field (FF) electrostatics at several levels of approximation from the standard model using fixed partial charges to conformational specific multipole fits including up to quadrupole moments. Potential-derived point charges and multipoles are calculated using least-squares methods for a total of ∼1000 different conformations of the 20 natural amino acids. Opposed to standard charge fitting schemes the procedure presented in the current work employs fitting points placed on a single isodensity surface, since the electrostatic potential (ESP) on such a surface determines the ESP at all points outside this surface. We find that the effect of multipoles beyond partial atomic charges is of the same magnitude as the effect due to neglecting conformational dependency (i.e., polarizability), suggesting that the two effects should be included at the same level in FF development. The redundancy at both the partial charge and multipole levels of approximation is quantified. We present an algorithm which stepwise reduces or increases the dimensionality of the charge or multipole parameter space and provides an upper limit of the ESP error that can be obtained at a given truncation level. Thereby, we can identify a reduced set of multipole moments corresponding to ∼40% of the total number of multipoles. This subset of parameters provides a significant improvement in the representation of the ESP compared to the simple point charge model and close to the accuracy obtained using the complete multipole parameter space. The selection of the ∼40% most important multipole sites is highly transferable among different conformations, and we find that quadrupoles are of high importance for atoms involved in π-bonding, since the anisotropic electric field generated in such regions requires a large degree of flexibility.

Electric Octupole Order in Bilayer Ruthenate Sr$_3$Ru$_2$O$_7$

Abstract: Although the odd-parity multipole order barely occurs in crystals with high symmetry, it can be formed in locally noncentrosymmetric crystals. We illustrate the odd-parity electric octupole order generated in a bilayer structure. When the local electric quadrupole is alternatively stacked between layers, it is regarded as an electric octupole order from the viewpoint of symmetry. We show that the $p_y s_x + p_x s_y$ spin nematic order is induced by the spin-orbit coupling in the electric octupole state, and it results from the spontaneous inversion symmetry breaking leading to the $D_{2d}$ point group symmetry. We investigate the possible realization of the electric octupole order in the bilayer ruthenate Sr$_3$Ru$_2$O$_7$, assuming a local electric quadrupole arising from the Pomeranchuk instability and/or the orbital order. Effects of the lattice distortion and magnetic field are also clarified, and the nature of the "electronic nematic state" of Sr$_3$Ru$_2$O$_7$ is discussed. It is proposed that the asymmetric band structure is a signature of the electric octupole order in Sr$_3$Ru$_2$O$_7$. The odd-parity multipole order in other strongly correlated electron systems is discussed.

The electric quadrupole moment of molecular hydrogen ions and their potential for a molecular ion clock

Abstract: The systematic shifts of the transition frequencies in the molecular hydrogen ions are of relevance to ultra-high-resolution radio-frequency, microwave and optical spectroscopy of these systems, performed in ion traps. We develop the ab initio description of the interaction of the electric quadrupole moment of this class of molecules with the static electric field gradients present in ion traps. In good approximation, it is described in terms of an effective perturbation Hamiltonian. An approximate treatment is then performed in the Born–Oppenheimer approximation. We give an expression of the electric quadrupole coupling parameter valid for all hydrogen molecular ion species and evaluate it for a large number of states of H 2 + , HD+, and D 2 + . The systematic shifts can be evaluated as simple expectation values of the perturbation Hamiltonian. Results on radio-frequency, one-photon electric dipole (E1), and two-photon E1 transitions between hyperfine states in HD+ are reported. For two-photon E1 transitions between rotationless states, the shifts vanish. For a large subset of rovibrational one-photon transitions, the absolute values of the quadrupole shifts range from 0.3 to 10 Hz for an electric field gradient of 108 V/m2. We point out an experimental procedure for determining the quadrupole shift which will allow reducing its contribution to the uncertainty of unperturbed rovibrational transition frequencies to the 1 × 10−15 fractional level and, for selected transitions, even below it. The combined contributions of black-body radiation, Zeeman, Stark and quadrupole effects are considered for a large set of transitions, and it is estimated that the total transition frequency uncertainty of selected transitions can be reduced below the 1 × 10−15 level.