Quadrupole Polarizabilities Research Articles

High pressure line shapes for Cs D1 and D2 lines and empirically informed interaction potentials

Line shapes for the Cs D1 (6 2S1/2–6 2P1/2) and D2 (6 2S1/2–6 2P3/2) transitions for He, Ne, and Ar collisions at pressures of 100–2280Torr and temperatures of 294–448K have been experimentally observed and compared to predictions from the Anderson–Talman theory. Asymmetry in the core of the line shape is generally correlated with shift rates, except for the Ne D1 line, which is red shifted, but blue shaded. There is a dramatic difference between the D1 and D2 lines for the shift and asymmetry parameters, particularly for He and Ne. A blue satellite is observed in the far wing of the D2 line at 827.2, 833.4, and 834.9nm for He, Ne, and Ar, respectively. The amplitude of the blue satellite scales linearly with pressure, exceeding 0.014% of the peak cross-section at 2280Torr. Modest red shoulders are observed for both the D1 and D2 lines associated with extrema in the difference potentials. Existing ab initio potential surfaces require empirical modification to adequately describe the observed spectra. However, the long-range dipole and quadrupole polarizabilities are sufficient to establish the observed broadening and shifting rates. Two distinct sets of difference potentials are developed that adequately represent the line shape observations. Predictions for the temperature dependence of the collision induced shift are significantly different for the two sets of empirically modified potentials.

Detection of barium6sng→6snh,6sni, and6snkmicrowave transitions using selective excitation to autoionizing states

We use selective laser excitation to an autoionizing state to observe the microwave transitions of Ba from the $6sng$ Rydberg states to the $6snh$, $6sni$, and $6snk$ states for $15\ensuremath{\le}n\ensuremath{\le}18$. We extract the dipole and quadrupole polarizabilities of Ba${}^{+}$ from the measured $\ensuremath{\Delta}\ensuremath{\ell}$ intervals of the Ba $6sn\ensuremath{\ell}$ states of $\ensuremath{\ell}\ensuremath{\ge}5$ using a nonadiabatic core polarization model. The values we determine for the dipole and quadrupole polarizabilities are ${\ensuremath{\alpha}}_{d}=124.81(25){a}_{0}^{3}$ and ${\ensuremath{\alpha}}_{q}=2478(50){a}_{0}^{5}$, respectively.

Underpinning Hybridization Intuition for Complex Nanoantennas by Magnetoelectric Quadrupolar Polarizability Retrieval

A central idea in plasmonics and metamaterials is to interpret scattering resonances as resulting from hybridization of electric dipoles. Recent developments in metamaterials as well as in plasmonic Fano systems have further included magnetic dipoles and electric quadrupoles in this reasoning. We derive a method to retrieve dipole and quadrupole polarizability tensors of nano scatterers from full-wave simulations, which allows us to underpin this intuitive reasoning by quantifying the existent modes and their strengths in complex nano antennas. By application to a dolmen plasmon structure, we show how the retrieval sheds new light on plasmon induced transparency. Further, we show how to implement radiative corrections to a dipole–quadrupole model applicable when scatterers are placed near a surface, sphere, or stratified medium, similar to the known correction of dipole polarizabilities by the local density of optical states. We demonstrate how this model allows us to interpret near field excitation data ...

Dipole and quadrupole polarizabilities of Ni II and parameters of an effective potential for Ni I Rydberg states

The relativistic configuration interaction method has been used to evaluate the bound and continuum portions of summation expressions for the dipole and quadrupole polarizabilities, yielding the Ni II results αD,0 = 7.686 au for 3d9 2D3/2 and αQ,0 = 61.940 au for 3d9 2D5/2. The experimental value for the latter is estimated to be 55(8) au. From the reduced matrix elements, we have evaluated the first non-adiabatic scalar dipole polarizability βD,0 for 2D5/2 to be 9.243 au (experimental estimate is 8.9 (1.2)) and the off-diagonal tensor dipole polarizability αD,2 to be = −0.220 au (experimental estimate is −0.04 au). Significant cancellations occur in this last quantity (see text).

Galaxy rotation curves from a fourth order gravity

While the standard and most popular explanation for the flatness of galaxy rotation curves is dark matter, one cannot at this stage rule out an explanation based on a modified law of gravitation, which agrees with Newtonian gravitation on the scale of the Solar system, but differs from it on larger length scales. Examples include Modfied Newtonian Dynamics (MOND) and Scalar-Tensor-Vector Gravity (STVG). Here, we have reported on a fourth order modification of the Poisson equation, which yields the same Yukawa type modification of Newtonian gravity as STVG, and which can explain flat galaxy rotation curves for a large sample of galaxies, once specific values for two parameters have been chosen. We have speculated on two possible origins for this modified Poisson equation: First, a possible fourth order modification of general relativity, and second, quadrupole gravitational polarization induced on a galaxy because of the pull of neighbouring galaxies.

Relativistic many-body calculations of van der Waals coefficients for Yb-Li and Yb-Rb dimers

We derive the relativistic formulas for the van der Waals coefficients of Yb--alkali-metal dimers that correlate to ground and excited separated-atom limits. We calculate ${C}_{6}$ and ${C}_{8}$ coefficients of particular experimental interest. We also derive a semiempirical formula that expresses the ${C}_{8}$ coefficient of heteronuclear $A+B$ dimers in terms of the ${C}_{6}$ and ${C}_{8}$ coefficients of homonuclear dimers and the static dipole and quadrupole polarizabilities of the atomic states $A$ and $B$. We report results of calculation of the ${C}_{6}$ coefficients for the Yb-Rb ${}^{3}{P}_{1}^{o}+5s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ and ${}^{1}{S}_{0}+5p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2}^{o}$ dimers, and the ${C}_{8}$ coefficients for the Yb-Li ${}^{1}{S}_{0}+2s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ and Yb-Rb ${}^{1}{S}_{0}+5s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ dimers. Uncertainties are estimated for all predicted properties.

Blackbody radiation shift of the Ga+ clock transition

The blackbody radiation shift of the Ga+ clock transition is computed to be −0.0140 ± 0.0062 Hz at 300 K. The small shift is consistent with the blackbody radiation shifts of the clock transitions of other group III ions which are of a similar size. The polarizabilities of the Ga+ , , and states were computed using the configuration interaction method with an underlying semi-empirical core potential. Quadrupole and non-adiabatic dipole polarizabilities were also computed. A byproduct of the analysis involved calculations of the low-lying spectrum and oscillator strengths, including polarizabilities, of the Ga2 + ion.

Electric quadrupole moment and quadrupole polarizability of the copper dimer from high level ab initio and some density functional theory calculations

We have employed flexible, purpose-oriented, molecule-specific basis sets to calculate the electric multipole moments and quadrupole polarizability of the copper dimer with ab initio and some density functional theory methods. At the CCSD(T)/[9s8p7d1f] level of theory the quadrupole moment and mean quadrupole polarizability vary around the experimental bond length (Re=2.2197Å) as [Θ(R)-Θ(Re)]/ea02=1.07(R-Re)-0.55(R-Re)2+0.15(R-Re)3-0.08(R-Re)4[C¯(R)-C¯(Re)]/e2a04Eh-1=224.9(R-Re)+51.5(R-Re)2+6.8(R-Re)3+6.1(R-Re)4with −0.4 ⩽ (R−Re)/Å ⩽ 0.4.A discrepancy is observed between ab initio and density functional theory methods in the calculation of the quadrupole moment while the two classes of methods are seen to be in fair agreement as regards the calculation of the hexadecapole moment and the quadrupole polarizability.

CONSTRAINING THE SYMMETRY PARAMETERS OF THE NUCLEAR INTERACTION

One of the major uncertainties in the dense matter equation of state has been the nuclear symmetry energy. The density dependence of the symmetry energy is important in nuclear astrophysics, as it controls the neutronization of matter in core-collapse supernovae, the radii of neutron stars and the thicknesses of their crusts, the rate of cooling of neutron stars, and the properties of nuclei involved in r-process nucleosynthesis. We show that fits of nuclear masses to experimental masses, combined with other experimental information from neutron skins, heavy ion collisions, giant dipole resonances and dipole polarizabilities, lead to stringent constraints on parameters that describe the symmetry energy near the nuclear saturation density. These constraints are remarkably consistent with inferences from theoretical calculations of pure neutron matter, and, furthermore, with astrophysical observations of neutron stars. The concordance of experimental, theoretical and observational analyses suggests that the symmetry parameters S_v and L are in the range 29.0 - 32.7 MeV and 40.5 - 61.9 MeV, respectively, and that the neutron star radius, for a 1.4 M_sun star, is in the narrow window 10.7 km < R < 13.1 km (90% confidence). We can also set tight limits to the size of neutron star crusts and the fractional moment of inertia they contain, as well as the overall moment of inertia and quadrupole polarizability of 1.4 M_sun stars. Our results also have implications for the disk mass and ejected mass of compact mergers involving neutron stars.

Effect of the Pauli exclusion principle and the polarization of nuclei on the potential of their interaction for the example of the 16O+16O system

On the basis of the energy-density method, the effect of simultaneously taking into account the Pauli exclusion principle and the monopole and quadrupole polarizations of interacting nuclei on their interaction potential is considered for the example of the 16O + 16O system by using the wave function for the two-center shell model. The calculations performed in the adiabatic approximation reveal that the inclusion of the Pauli exclusion principle and the polarization of interacting nuclei, especially their quadrupole polarization, has a substantial effect on the potential of the nucleus-nucleus interaction.

DEUTERON ELECTRIC QUADRUPOLE AND OCTUPOLE POLARIZABILITIES

The direct transition-matrix approach to determination of the electric polarizabilities of quantum bound systems developed in my preceding work is applied to study the electric multipole polarizabilities of a two-particle bound complex with a central interaction between the particles. Expressions for the electric quadrupole and octupole polarizabilities of the deuteron are derived and their values in the case of the S-wave separable interaction potential are calculated.

ALOS PALSAR Analysis of the Archaeological Site of Pelusium

ABSTRACTAn analysis of the archaeological site of Pelusium on the northeastern edge of the Nile Delta, Egypt, was carried out using phased array type L‐band synthetic aperture radar (PALSAR) data. The aim was to assess the potential of PALSAR to identify buried archaeological structures. The 18 PALSAR images acquired in various polarimetric modes were obtained for the analysis through a European Space Agency Category‐1 project. Processing included co‐registration and summation of images for each polarimetric mode in order to reduce speckle. The summed images were then compared with each other and with optical imagery to identify any features that may be of archaeological interest. Features identified on the summed images were also viewed in the individual images to assess their ephemeral nature. One image was available in quadrupole polarization (quad‐pol) mode with which polarimetric analysis was undertaken, including extraction of target decompositions and analysis of the scattering characteristics of the study area. Linear and geometric features that may be archaeological structures were visible in the processed SAR imagery. Possible palaeolandscape features were also identified. Some of these are visible in the optical imagery, but not clearly delineated. The results of the polarimetric analysis show that single‐bounce scattering dominates over the study area, and that over the sandy regions the signal is much weaker in all polarizations, with mixed scattering. Although the spatial resolution did not enable clear identification and characterization of the physical scattering properties of small‐scale features, the PALSAR data demonstrate a capability to highlight features that become almost invisible in optical imagery at the synoptic scale (even if they are visible up close) leading to the conclusion that PALSAR may be a useful tool in the first stages of archaeological surveys to analyse the spatial pattern of features, and identify where to focus smaller scale surveys in areas with land cover similar to that of the study area. Copyright © 2013 John Wiley &amp; Sons, Ltd.

Multipole moments using extended coupled cluster method

Using analytic extended coupled cluster (ECC) response approach quadrupole moments, dipole–quadrupole polarizabilities and dipole polarizabilities are studied. In the current implementation of the functional we have included all the double linked terms within (CCSD) approximation. These terms will be important for the accurate description of properties at the stretched geometries. We report the properties for carbon monoxide and hydrogen fluoride molecules, as a function of bond distance and compare our results for carbon monoxide with the full CI results. We have also reported the properties of methane, tetrafluoromethane, acetylene, difluoroacetylene, water and ammonia.

A transferable H2O interaction potential based on a single center multipole expansion: SCME

A transferable potential energy function for describing the interaction between water molecules is presented. The electrostatic interaction is described rigorously using a multipole expansion. Only one expansion center is used per molecule to avoid the introduction of monopoles. This single center approach turns out to converge and give close agreement with ab initio calculations when carried out up to and including the hexadecapole. Both dipole and quadrupole polarizability are included. All parameters in the electrostatic interaction as well as the dispersion interaction are taken from ab initio calculations or experimental measurements of a single water molecule. The repulsive part of the interaction is parametrized to fit ab initio calculations of small water clusters and experimental measurements of ice Ih. The parametrized potential function was then used to simulate liquid water and the results agree well with experiment, even better than simulations using some of the point charge potentials fitted to liquid water. The evaluation of the new interaction potential for condensed phases is fast because point charges are not present and the interaction can, to a good approximation, be truncated at a finite range.

Electric Multipole Polarizabilities of Quantum Bound Systems in the Transition Matrix Formalism

A new general formalism for determining the electric multipole polarizabilities of quantum (atomic and nuclear) bound systems based on the use of the transition matrix in momentum space has been developed. As distinct from the conventional approach with the application of the spectral expansion of the total Green’s function, our approach does not require preliminary determination of the entire unperturbated spectrum; instead, it makes possible to calculate the polarizability of a few-body bound complex directly based on solving integral equations for the wave function of the ground bound state and the transition matrix at negative energy, both of them being real functions of momenta. A formula for the multipole polarizabilities of a two-body bound complex formed by a central interaction potential has been derived and studied. To test, the developed t-matrix formalism has been applied to the calculation of the dipole, quadrupole and octupole polarizabilities of the hydrogen atom.

Resonance properties of optical all-dielectric metamaterials using two-dimensional multipole expansion

We examine the electromagnetic response of metamaterial unit elements consisting of dielectric rods embedded in a nonmagnetic background medium. We establish a theoretical framework in which the response is described through the electric and magnetic multipole moments that are simultaneously generated via the polarization currents that are excited upon the incidence of plane waves. The corresponding dipole and quadrupole polarizabilities are then calculated as a function of the Mie scattering coefficients, and their resonances are mapped for the case of dielectric cylindrical rods as a function of the geometry and the material parameters used. The results provide critical insight into the anisotropic response of two-dimensional rod-type metamaterials and can be used as a unified methodology in the calculation of exotic effective electromagnetic parameters involved in phenomena such as optical magnetism.

Static and dynamic polarizabilities of the non-relativistic hydrogen molecular ion

Static and dynamic polarizabilities are calculated for the non-relativistic hydrogen molecular ion by solving the three-body Schrödinger equation in perimetric coordinates with the Lagrange-mesh method. The static dipole polarizabilities of the ground-state rotational band are computed for total orbital (or rotational) angular momenta from L = 0 to 39 with an absolute accuracy of about 10−9 au. For L = 0, 1 and 2, slightly less accurate results are also given for the first three vibrational excited levels. For the ground state, dynamic dipole polarizabilities as well as static and dynamic quadrupole polarizabilities are computed. To illustrate the versatility of the method, the static dipole polarizability of the hydrogen molecular ion in a Debye plasma is also determined.

Blackbody radiation shift of the B+clock transition

A calculation of the blackbody radiation shift of the B$^+$ clock transition is performed. The polarizabilities of the B$^+$ $2s^2$ $^1$S$^e$, $2s2p$ $^1$P$^o$, and $2s2p$ $^3$P$^o$ states are computed using the configuration interaction method with an underlying semi-empirical core potential. The recommended dipole polarizabilities are 9.64(3) $a_0^3$, 7.78(3) $a_0^3$ and 16.55(5) $a_0^3$ respectively. The derived frequency shift for the $2s^2$ $^1$S$^e$ $\to$ $2s2p$ $^3$P$^o_0$ transition at 300 K is 0.0160(5) Hz. The dipole polarizabilities agree with an earlier relativistic calculation (Safronova {\em et al.} Phys. Rev. Lett. {\bf 107} 143006 (2011)) to better than 0.2%. Quadrupole and octupole polarizabilities and non-adiabatic multipole polarizabilities are also reported.

Dispersion coefficients for interactions among H, Li, Na, K atoms with Debye–Hückel potentials

The effect of Debye–Hückel screening on the dispersion coefficients C6, C8, C10 for interactions among H, Li, Na and K atoms has been investigated using the symplectic algorithm. The C6, C8, C10 coefficients for interactions among alkali-metal atoms along with the dipole, quadrupole and octupole polarizabilities of K atom for various screening parameters are reported for the first time in the literature. In free-atomic cases, our results are comparable with available theoretical and experimental results.

Positron scattering from O2

We report on recent cross section results for positron scattering from molecular oxygen (O2). Total cross sections (TCSs) were measured with a positron spectrometer in the energy range from 0.1 to 50 eV and with an energy resolution of the positron beam of ∼0.25 eV. In addition, TCSs as well as elastic and inelastic integral cross sections were computed within the independent atom model and screening corrected additivity rule approach, with both dipole and dipole plus quadrupole polarization potentials, between 1 and 1000 eV impact energy. An overall fair level of accord is found between the experimental TCS and that calculated with the model that includes the quadrupole term. Comparison to earlier measurements shows very good agreement with the present measured TCS and fair agreement with the TCS computed with our most physical model above ∼8 eV. Conversely, we find only a marginal level of accord when comparing our experimental TCS with previous computations, while the present TCS calculated with the dipole plus quadrupole potentials appears to agree reasonably well with most of the existing theoretical results above ∼100 eV.