Study of hot thermally fissile nuclei using relativistic mean field theory

NASA Astrophysics Data System (ADS)

Quddus, Abdul; Naik, K. C.; Patra, S. K.

2018-07-01

We have studied the properties of hot 234,236U and 240Pu nuclei in the framework of relativistic mean field formalism. The recently developed FSUGarnet and IOPB-I parameter sets are implemented for the first time to deform nuclei at finite temperature. The results are compared with the well known NL3 set. The said isotopes are structurally important because of the thermally fissile nature of 233,235U and 239Pu as these nuclei (234,236U and 240Pu) are formed after the absorption of a thermal neutron, which undergoes fission. Here, we have evaluated the nuclear properties, such as shell correction energy, neutron-skin thickness, quadrupole and hexadecapole deformation parameters and asymmetry energy coefficient for these nuclei as a function of temperature.

Towards an accurate representation of electrostatics in classical force fields: Efficient implementation of multipolar interactions in biomolecular simulations

NASA Astrophysics Data System (ADS)

Sagui, Celeste; Pedersen, Lee G.; Darden, Thomas A.

2004-01-01

The accurate simulation of biologically active macromolecules faces serious limitations that originate in the treatment of electrostatics in the empirical force fields. The current use of "partial charges" is a significant source of errors, since these vary widely with different conformations. By contrast, the molecular electrostatic potential (MEP) obtained through the use of a distributed multipole moment description, has been shown to converge to the quantum MEP outside the van der Waals surface, when higher order multipoles are used. However, in spite of the considerable improvement to the representation of the electronic cloud, higher order multipoles are not part of current classical biomolecular force fields due to the excessive computational cost. In this paper we present an efficient formalism for the treatment of higher order multipoles in Cartesian tensor formalism. The Ewald "direct sum" is evaluated through a McMurchie-Davidson formalism [L. McMurchie and E. Davidson, J. Comput. Phys. 26, 218 (1978)]. The "reciprocal sum" has been implemented in three different ways: using an Ewald scheme, a particle mesh Ewald (PME) method, and a multigrid-based approach. We find that even though the use of the McMurchie-Davidson formalism considerably reduces the cost of the calculation with respect to the standard matrix implementation of multipole interactions, the calculation in direct space remains expensive. When most of the calculation is moved to reciprocal space via the PME method, the cost of a calculation where all multipolar interactions (up to hexadecapole-hexadecapole) are included is only about 8.5 times more expensive than a regular AMBER 7 [D. A. Pearlman et al., Comput. Phys. Commun. 91, 1 (1995)] implementation with only charge-charge interactions. The multigrid implementation is slower but shows very promising results for parallelization. It provides a natural way to interface with continuous, Gaussian-based electrostatics in the future. It is

Structure of the Kπ=4+ bands in Os186,188

NASA Astrophysics Data System (ADS)

Phillips, A. A.; Garrett, P. E.; Lo Iudice, N.; Sushkov, A. V.; Bettermann, L.; Braun, N.; Burke, D. G.; Demand, G. A.; Faestermann, T.; Finlay, P.; Green, K. L.; Hertenberger, R.; Leach, K. G.; Krücken, R.; Schumaker, M. A.; Svensson, C. E.; Wirth, H.-F.; Wong, J.

2010-09-01

The (He3,d) single-proton stripping reaction has been performed on targets of Re185,187 to investigate the structures of the 43+ states in Os186,188. The experiment employed 30 MeV He3 beams, and the reaction products were analyzed with a Q3D spectrograph. Absolute cross sections were determined at nine angles between 5° and 50° for states up to approximately 3 MeV in excitation energy. Large (5)/(2)+[402]π+(3)/(2)+[402]π two-quasiparticle components are deduced for the 43+ levels of both isotopes. Their magnitudes are in agreement with calculations performed using the quasiparticle phonon model, which predicts a coexistence of a large hexadecapole with a smaller, but sizable, γ-γ component in the 43+.

Role of hexadecapole deformation of projectile 28Si in heavy-ion fusion reactions near the Coulomb barrier

NASA Astrophysics Data System (ADS)

Kaur, Gurpreet; Hagino, K.; Rowley, N.

2018-06-01

The vast knowledge regarding the strong influence of quadrupole deformation β2 of colliding nuclei in heavy-ion sub-barrier fusion reactions inspires a desire to quest the sensitivity of fusion dynamics to higher order deformations, such as β4 and β6 deformations. However, such studies have rarely been carried out, especially for deformation of projectile nuclei. In this article, we investigated the role of β4 of the projectile nucleus in the fusion of the 28Si+92Zr system. We demonstrated that the fusion barrier distribution is sensitive to the sign and value of the β4 parameter of the projectile, 28Si, and confirmed that the 28Si nucleus has a large positive β4. This study opens an indirect way to estimate deformation parameters of radioactive nuclei using fusion reactions, which is otherwise difficult because of experimental constraints.

Experimental and theoretical determination of the dipole-quadrupole and dipole-octopole polarizabilities of the group IV tetrachlorides TiCl4, ZrCl4, and HfCl4

NASA Astrophysics Data System (ADS)

Hohm, Uwe; Maroulis, G.

2006-03-01

The dipole-quadrupole and dipole-octopole polarizabilities A and E of TiCl4, ZrCl4, and HfCl4 have been determined from collision-induced light-scattering experiments. Our respective experimental results for ∣A ∣ are (165±10), (110±30), and (140±20) e2a03Eh-1, whereas ∣E∣ is determined to be (675±125), (750±200), and (670±400) e2a04Eh-1. Theory predicts values convincingly close to experiment, as A =(181.4±9.1), (167.6±8.4), and (139.8±7.0) e2a03Eh-1, and E =(-671±67), (-688±69), and (-574±57) e2a04Eh-1. In addition our quantum chemical ab initio calculations give reliable values for the dipole polarizability α, as well as for the octopole and hexadecapole moments Ω and Φ for all three substances.

Fission properties of superheavy nuclei for r -process calculations

NASA Astrophysics Data System (ADS)

Giuliani, Samuel A.; Martínez-Pinedo, Gabriel; Robledo, Luis M.

2018-03-01

We computed a new set of static fission properties suited for r -process calculations. The potential energy surfaces and collective inertias of 3640 nuclei in the superheavy region are obtained from self-consistent mean-field calculations using the Barcelona-Catania-Paris-Madrid energy density functional. The fission path is computed as a function of the quadrupole moment by minimizing the potential energy and exploring octupole and hexadecapole deformations. The spontaneous fission lifetimes are evaluated employing different schemes for the collective inertias and vibrational energy corrections. This allows us to explore the sensitivity of the lifetimes to those quantities together with the collective ground-state energy along the superheavy landscape. We computed neutron-induced stellar reaction rates relevant for r -process nucleosynthesis using the Hauser-Feshbach statistical approach and study the impact of collective inertias. The competition between different reaction channels including neutron-induced rates, spontaneous fission, and α decay is discussed for typical r -process conditions.

Microwave spectroscopy of high-L, n=9 Rydberg levels of nickel: Polarizabilities and moments of the Ni+ ion

NASA Astrophysics Data System (ADS)

Woods, Shannon; Smith, Chris; Keele, Julie; Lundeen, S. R.

2013-02-01

The complete pattern of Rydberg binding energies of the 18 n=9 levels of nickel with L=6, 7, and 8 was measured using microwave plus resonant-excitation Stark-ionization spectroscopy. The measured pattern is consistent with the form predicted with the effective potential model, showing significant structure proportional to scalar products of tensor operators of order 0-4. The variation of the structure with L separates the various contributing terms and provides determinations of several properties of the Ni+ core ion. These include the quadrupole moment, Q = -0.469 78(9) a.u., the hexadecapole moment, Π = 0.36(5) a.u., the scalar and tensor dipole polarizabilities, αD,0= 7.949(2) a.u., αD,2=0.905(12) a.u., the scalar quadrupole polarizability, αQ,0=55(8) a.u., the g value, gJ=1.257(14), and the vector hyperpolarizability, βD,1=0.454(24) a.u.

A unified formulation of dichroic signals using the Borrmann effect and twisted photon beams.

PubMed

Collins, Stephen P; Lovesey, Stephen W

2018-05-21

Dichroic X-ray signals derived from the Borrmann effect and a twisted photon beam with topological charge l = 1 are formulated with an effective wavevector. The unification applies for non-magnetic and magnetic materials. Electronic degrees of freedom associated with an ion are encapsulated in multipoles previously used to interpret conventional dichroism and Bragg diffraction enhanced by an atomic resonance. A dichroic signal exploiting the Borrmann effect with a linearly polarized beam presents charge-like multipoles that include a hexadecapole. A difference between dichroic signals obtained with a twisted beam carrying spin polarization (circular polarization) and opposite winding numbers presents charge-like atomic multipoles, whereas a twisted beam carrying linear polarization alone presents magnetic (time-odd) multipoles. Charge-like multipoles include a quadrupole, and magnetic multipoles include a dipole and an octupole. We discuss the practicalities and relative merits of spectroscopy exploiting the two remarkably closely-related processes. Signals using beams with topological charges l ≥ 2 present additional atomic multipoles.

Coexistence of magnetic and charge order in a two-component order parameter description of the layered superconductors

NASA Astrophysics Data System (ADS)

Doria, Mauro M.; Vargas-Paredes, Alfredo A.; Cariglia, Marco

2014-12-01

We consider an effective theory of superconductivity for layered superconductors using a two-component order parameter, and show that it allows the formation of a condensate with magnetic and charge degrees of freedom. This condensate is an inhomogeneous state, topologically stable, that exists without the presence of an applied magnetic field. In particular, it is associated to a charge density in the superconducting layers. We show that well defined angular momentum states have for their lowest moment an hexadecapole charge distribution, i.e. quartic in the momenta. Our approach is based on solving first order equations (FOE) that generalize the Abrikosov-Bogomolny equations of the Ginzburg-Landau theory with one order parameter. The FOE solve the variational equations of the theory in the limit of a small order parameter, which is achieved for the special temperature that corresponds to the crossing of the superconducting dome and the pseudogap transition line. This topologically stable state is a condensate of skyrmions that breaks time reversal symmetry and produces a weak local magnetic field below the threshold of experimental observation.

Structure of the 4^+3 States in ^186,188Os

NASA Astrophysics Data System (ADS)

Phillips, A. A.; Garrett, P. E.; Demand, G. A.; Finlay, P.; Green, K. L.; Leach, K. G.; Schumaker, M. A.; Svensson, C. E.; Wong, J.; Hertenberger, R.; Faestermann, T.; Krücken, R.; Wirth, H.-F.; Bettermann, L.; Braun, N.; Burke, D. G.

2007-10-01

The structures of 4^+3 states in the Os nuclei have been the subject of debate for the past several decades. Based on measured B(E2) values, they were interpreted in ^186-192Os as K^π=4^+ two-phonon γ vibrations, whereas inelastic scattering results, and single-proton transfer (d,^3He) and (t,α) imply a hexadecapole phonon description. Uncertainties in the (t,α) reaction mechanism, however, were cited as preventing a firm conclusion based on those data. To help clarify the nature of these K^π=4^+ bands, we have performed a (^3He,d) stripping reaction on targets of ^185,187Re using 30 MeV ^3He beams provided by the MP-tandem facility of the LMU/TUM in Garching. With an energy resolution of 13 keV, the deuterons were analyzed at 9 angles ranging from 5^o to 50^o with the Q3D spectrograph, and absolute cross sections were obtained for levels up to 3 MeV in excitation energy. Preliminary results will be presented.

Omega from the anisotropy of the redshift correlation function

NASA Technical Reports Server (NTRS)

Hamilton, A. J. S.

1993-01-01

Peculiar velocities distort the correlation function of galaxies observed in redshift space. In the large scale, linear regime, the distortion takes a characteristic quadrupole plus hexadecapole form, with the amplitude of the distortion depending on the cosmological density parameter omega. Preliminary measurements are reported here of the harmonics of the correlation function in the CfA, SSRS, and IRAS 2 Jansky redshift surveys. The observed behavior of the harmonics agrees qualitatively with the predictions of linear theory on large scales in every survey. However, real anisotropy in the galaxy distribution induces large fluctuations in samples which do not yet probe a sufficiently fair volume of the Universe. In the CfA 14.5 sample in particular, the Great Wall induces a large negative quadrupole, which taken at face value implies an unrealistically large omega 20. The IRAS 2 Jy survey, which covers a substantially larger volume than the optical surveys and is less affected by fingers-of-god, yields a more reliable and believable value, omega = 0.5 sup +.5 sub -.25.

Stability of superheavy nuclei

NASA Astrophysics Data System (ADS)

Pomorski, K.; Nerlo-Pomorska, B.; Bartel, J.; Schmitt, C.

2018-03-01

The potential-energy surfaces of an extended set of heavy and superheavy even-even nuclei with 92 ≤Z ≤126 and isospins 40 ≤N -Z ≤74 are evaluated within the recently developed Fourier shape parametrization. Ground-state and decay properties are studied for 324 different even-even isotopes in a four-dimensional deformation space, defined by nonaxiality, quadrupole, octupole, and hexadecapole degrees of freedom. Nuclear deformation energies are evaluated in the framework of the macroscopic-microscopic approach, with the Lublin-Strasbourg drop model and a Yukawa-folded mean-field potential. The evolution of the ground-state equilibrium shape (and possible isomeric, metastable states) is studied as a function of Z and N . α -decay Q values and half-lives, as well as fission-barrier heights, are deduced. In order to understand the transition from asymmetric to symmetric fission along the Fm isotopic chain, the properties of all identified fission paths are investigated. Good agreement is found with experimental data wherever available. New interesting features about the population of different fission modes for nuclei beyond Fm are predicted.

Measuring the reionization 21 cm fluctuations using clustering wedges

NASA Astrophysics Data System (ADS)

Raut, Dinesh; Choudhury, Tirthankar Roy; Ghara, Raghunath

2018-03-01

One of the main challenges in probing the reionization epoch using the redshifted 21 cm line is that the magnitude of the signal is several orders smaller than the astrophysical foregrounds. One of the methods to deal with the problem is to avoid a wedge-shaped region in the Fourier k⊥ - k∥ space which contains the signal from the spectrally smooth foregrounds. However, measuring the spherically averaged power spectrum using only modes outside this wedge (i.e. in the reionization window) leads to a bias. We provide a prescription, based on expanding the power spectrum in terms of the shifted Legendre polynomials, which can be used to compute the angular moments of the power spectrum in the reionization window. The prescription requires computation of the monopole, quadrupole, and hexadecapole moments of the power spectrum using the theoretical model under consideration and also the knowledge of the effective extent of the foreground wedge in the k⊥ - k∥ plane. One can then calculate the theoretical power spectrum in the window which can be directly compared with observations. The analysis should have implications for avoiding any bias in the parameter constraints using 21 cm power spectrum data.

Influence of sticking vs non-sticking limits of moment of inertia and higher order deformations in the decay of 214,216Rn* compound systems

NASA Astrophysics Data System (ADS)

Mittal, Rajni; Jain, Deepika; Sharma, Manoj K.

2017-12-01

The dynamical cluster decay model (DCM) is employed to explore the relative effect of sticking (IS) and non-sticking (INS) limits of moment of inertia (MOI) in the decay of hot and rotating 214,216Rn* compound nuclei, formed in 16,18O + 198Pt reactions. Beside this, the nuclear deformation effects i.e. quadrupole β2 (static and dynamic) and higher order static deformations up to hexadecapole (β4) are duly incorporated and studied within DCM. The influence of both 'INS/IS' addressing rotational energy component and 'deformations' is gauged through the barrier characteristics, preformation factor and barrier lowering effects. The experimentally given ER and ff data is addressed by optimizing the neck-length ΔR, that strongly depends on the limiting angular momentum, which in turn depends on the sticking or non-sticking limits of interaction. In addition to this, the influence of increase in energy and neutron number is probed in reference to ER survival probability of Rn compound nucleus. Finally, the ff cross-sections of 214,216Rn* nuclei are predicted within sticking limit of moment of inertia as the same seems to be more suitable for such decay paths.

HPAM: Hirshfeld Partitioned Atomic Multipoles

PubMed Central

Elking, Dennis M.; Perera, Lalith; Pedersen, Lee G.

2011-01-01

An implementation of the Hirshfeld (HD) and Hirshfeld-Iterated (HD-I) atomic charge density partitioning schemes is described. Atomic charges and atomic multipoles are calculated from the HD and HD-I atomic charge densities for arbitrary atomic multipole rank lmax on molecules of arbitrary shape and size. The HD and HD-I atomic charges/multipoles are tested by comparing molecular multipole moments and the electrostatic potential (ESP) surrounding a molecule with their reference ab initio values. In general, the HD-I atomic charges/multipoles are found to better reproduce ab initio electrostatic properties over HD atomic charges/multipoles. A systematic increase in precision for reproducing ab initio electrostatic properties is demonstrated by increasing the atomic multipole rank from lmax = 0 (atomic charges) to lmax = 4 (atomic hexadecapoles). Both HD and HD-I atomic multipoles up to rank lmax are shown to exactly reproduce ab initio molecular multipole moments of rank L for L ≤ lmax. In addition, molecular dipole moments calculated by HD, HD-I, and ChelpG atomic charges only (lmax = 0) are compared with reference ab initio values. Significant errors in reproducing ab initio molecular dipole moments are found if only HD or HD-I atomic charges used. PMID:22140274

Static electric and magnetic multipole susceptibilities for Dirac one-electron atoms in the ground state

NASA Astrophysics Data System (ADS)

Szmytkowski, Radosław; Łukasik, Grzegorz

2016-09-01

We present tabulated data for several families of static electric and magnetic multipole susceptibilities for hydrogenic atoms with nuclear charge numbers from the range 1 ⩽ Z ⩽ 137. Atomic nuclei are assumed to be point-like and spinless. The susceptibilities considered include the multipole electric polarizabilities α E L → E L and magnetizabilities (magnetic susceptibilities) χ M L → M L with 1 ⩽ L ⩽ 4 (i.e., the dipole, quadrupole, octupole and hexadecapole ones), the electric-to-magnetic cross-susceptibilities α E L → M(L - 1) with 2 ⩽ L ⩽ 5 and α E L → M(L + 1) with 1 ⩽ L ⩽ 4, the magnetic-to-electric cross-susceptibilities χ M L → E(L - 1) with 2 ⩽ L ⩽ 5 and χ M L → E(L + 1) with 1 ⩽ L ⩽ 4 (it holds that χ M L → E(L ∓ 1) =α E(L ∓ 1) → M L), and the electric-to-toroidal-magnetic cross-susceptibilities α E L → T L with 1 ⩽ L ⩽ 4. Numerical values are computed from general exact analytical formulas, derived by us elsewhere within the framework of the Dirac relativistic quantum mechanics, and involving generalized hypergeometric functions 3F2 of the unit argument.

New Distributed Multipole Methods for Accurate Electrostatics for Large-Scale Biomolecular Simultations

NASA Astrophysics Data System (ADS)

Sagui, Celeste

2006-03-01

An accurate and numerically efficient treatment of electrostatics is essential for biomolecular simulations, as this stabilizes much of the delicate 3-d structure associated with biomolecules. Currently, force fields such as AMBER and CHARMM assign ``partial charges'' to every atom in a simulation in order to model the interatomic electrostatic forces, so that the calculation of the electrostatics rapidly becomes the computational bottleneck in large-scale simulations. There are two main issues associated with the current treatment of classical electrostatics: (i) how does one eliminate the artifacts associated with the point-charges (e.g., the underdetermined nature of the current RESP fitting procedure for large, flexible molecules) used in the force fields in a physically meaningful way? (ii) how does one efficiently simulate the very costly long-range electrostatic interactions? Recently, we have dealt with both of these challenges as follows. In order to improve the description of the molecular electrostatic potentials (MEPs), a new distributed multipole analysis based on localized functions -- Wannier, Boys, and Edminston-Ruedenberg -- was introduced, which allows for a first principles calculation of the partial charges and multipoles. Through a suitable generalization of the particle mesh Ewald (PME) and multigrid method, one can treat electrostatic multipoles all the way to hexadecapoles all without prohibitive extra costs. The importance of these methods for large-scale simulations will be discussed, and examplified by simulations from polarizable DNA models.

An inventory of bispectrum estimators for redshift space distortions

NASA Astrophysics Data System (ADS)

Regan, Donough

2017-12-01

In order to best improve constraints on cosmological parameters and on models of modified gravity using current and future galaxy surveys it is necessary maximally exploit the available data. As redshift-space distortions mean statistical translation invariance is broken for galaxy observations, this will require measurement of the monopole, quadrupole and hexadecapole of not just the galaxy power spectrum, but also the galaxy bispectrum. A recent (2015) paper by Scoccimarro demonstrated how the standard bispectrum estimator may be expressed in terms of Fast Fourier Transforms (FFTs) to afford an extremely efficient algorithm, allowing the bispectrum multipoles on all scales and triangle shapes to be measured in comparable time to those of the power spectrum. In this paper we present a suite of alternative proxies to measure the three-point correlation multipoles. In particular, we describe a modal (or plane wave) decomposition to capture the information in each multipole in a series of basis coefficients, and also describe three compressed estimators formed using the skew-spectrum, the line correlation function and the integrated bispectrum, respectively. As well as each of the estimators offering a different measurement channel, and thereby a robustness check, it is expected that some (especially the modal estimator) will offer a vast data compression, and so a much reduced covariance matrix. This compression may be vital to reduce the computational load involved in extracting the available three-point information.

Polarizable atomic multipole X-ray refinement: application to peptide crystals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schnieders, Michael J.; Fenn, Timothy D.; Howard Hughes Medical Institute

2009-09-01

A method to accelerate the computation of structure factors from an electron density described by anisotropic and aspherical atomic form factors via fast Fourier transformation is described for the first time. Recent advances in computational chemistry have produced force fields based on a polarizable atomic multipole description of biomolecular electrostatics. In this work, the Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) force field is applied to restrained refinement of molecular models against X-ray diffraction data from peptide crystals. A new formalism is also developed to compute anisotropic and aspherical structure factors using fast Fourier transformation (FFT) of Cartesian Gaussianmore » multipoles. Relative to direct summation, the FFT approach can give a speedup of more than an order of magnitude for aspherical refinement of ultrahigh-resolution data sets. Use of a sublattice formalism makes the method highly parallelizable. Application of the Cartesian Gaussian multipole scattering model to a series of four peptide crystals using multipole coefficients from the AMOEBA force field demonstrates that AMOEBA systematically underestimates electron density at bond centers. For the trigonal and tetrahedral bonding geometries common in organic chemistry, an atomic multipole expansion through hexadecapole order is required to explain bond electron density. Alternatively, the addition of interatomic scattering (IAS) sites to the AMOEBA-based density captured bonding effects with fewer parameters. For a series of four peptide crystals, the AMOEBA–IAS model lowered R{sub free} by 20–40% relative to the original spherically symmetric scattering model.« less

The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: structure growth rate measurement from the anisotropic quasar power spectrum in the redshift range 0.8 < z < 2.2

NASA Astrophysics Data System (ADS)

Gil-Marín, Héctor; Guy, Julien; Zarrouk, Pauline; Burtin, Etienne; Chuang, Chia-Hsun; Percival, Will J.; Ross, Ashley J.; Ruggeri, Rossana; Tojerio, Rita; Zhao, Gong-Bo; Wang, Yuting; Bautista, Julian; Hou, Jiamin; Sánchez, Ariel G.; Pâris, Isabelle; Baumgarten, Falk; Brownstein, Joel R.; Dawson, Kyle S.; Eftekharzadeh, Sarah; González-Pérez, Violeta; Habib, Salman; Heitmann, Katrin; Myers, Adam D.; Rossi, Graziano; Schneider, Donald P.; Seo, Hee-Jong; Tinker, Jeremy L.; Zhao, Cheng

2018-06-01

We analyse the clustering of the Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey Data Release 14 quasar sample (DR14Q). We measure the redshift space distortions using the power-spectrum monopole, quadrupole, and hexadecapole inferred from 148 659 quasars between redshifts 0.8 and 2.2, covering a total sky footprint of 2112.9 deg2. We constrain the logarithmic growth of structure times the amplitude of dark matter density fluctuations, fσ8, and the Alcock-Paczynski dilation scales that allow constraints to be placed on the angular diameter distance DA(z) and the Hubble H(z) parameter. At the effective redshift of zeff = 1.52, fσ8(zeff) = 0.420 ± 0.076, H(z_eff)=[162± 12] (r_s^fid/r_s) {km s}^{-1} Mpc^{-1}, and D_A(z_eff)=[1.85± 0.11]× 10^3 (r_s/r_s^fid) Mpc, where rs is the comoving sound horizon at the baryon drag epoch and the superscript `fid' stands for its fiducial value. The errors take into account the full error budget, including systematics and statistical contributions. These results are in full agreement with the current Λ-Cold Dark Matter cosmological model inferred from Planck measurements. Finally, we compare our measurements with other eBOSS companion papers and find excellent agreement, demonstrating the consistency and complementarity of the different methods used for analysing the data.

Isobaric analog states in rare-earth nuclei studied with the ( 3He, t) charge-exchange reaction at θL = 0°

NASA Astrophysics Data System (ADS)

Jänecke, J.; Aarts, E. H. L.; Drentje, A. G.; Harakeh, M. N.; Gaarde, C.

1983-02-01

The ( 3He, t) charge-exchange reaction leading to the ground-state isobaric analog states (IAS) of 152, 154, 156, 158, 160Gd, 160,162Dy, 162,164,166,168,170Er, 170, 172, 174, 176Yb and 176, 178, 180Hf has been studied at θL = 0° and E( 3He) = 60.5 MeV. The reaction 28Si( 3He, t) 28P was used for energy calibration. The centroid energies of most IAS were determined to ±6 keV. Coulomb displacement energies have been extracted from the measured Q-values. They display the influence of non-spherical nuclear shapes which increase the rms radii and lower the Coulomb displacement energies. The dependence on both quadrupole and hexadecapole deformations is apparent with deformation parameters in good agreement with results from other measurements. The total widths Γ of the IAS are in the range 30 to 110 keV. They increase more strongly with neutron excess than is known for the IAS of the Sn and Te isotopes. The width of the IAS of 176Yb is anomalously low. The zero-degree ( 3He, t) cross sections are in the range 5 to 20 μb/sr. They generally increase with neutron excess except for the sequence of Yb isotopes. No systematic dependence on ( N - Z) appears to exist. Excitation energies and zero-degree cross sections for the reactions 28Si( 3He, t) 28P, 16O( 3He,t) 16F and 12C( 3He,t) 12N are reported.

Role of higher-multipole deformations in exotic {sup 14}C cluster radioactivity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sawhney, Gudveen; Sharma, Manoj K.; Gupta, Raj K.

2011-06-15

We have studied nine cases of spontaneous emission of {sup 14}C clusters in the ground-state decays of the same number of parent nuclei from the trans-lead region, specifically from {sup 221}Fr to {sup 226}Th, using the preformed cluster model (PCM) of Gupta and collaborators, with choices of spherical, quadrupole deformation ({beta}{sub 2}) alone, and higher-multipole deformations ({beta}{sub 2}, {beta}{sub 3}, {beta}{sub 4}) with cold ''compact'' orientations {theta}{sup c} of decay products. The calculated {sup 14}C cluster decay half-life times are found to be in nice agreement with experimental data only for the case of higher-multipole deformations ({beta}{sub 2}-{beta}{sub 4}) andmore » {theta}{sup c} orientations of cold elongated configurations. In other words, compared to our earlier study of clusters heavier than {sup 14}C, where the inclusion of {beta}{sub 2} alone, with ''optimum'' orientations, was found to be enough to give the best comparison with data, here for {sup 14}C cluster decay the inclusion of higher-multipole deformations (up to hexadecapole), together with {theta}{sup c} orientations, is found to be essential on the basis of the PCM. Interestingly, whereas both the penetration probability and assault frequency work simply as scaling factors, the preformation probability is strongly influenced by the order of multipole deformations and orientations of nuclei. The possible role of Q value and angular-momentum effects are also considered in reference to {sup 14}C cluster radioactivity.« less

Measurement of the dipole in the cross-correlation function of galaxies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gaztanaga, Enrique; Bonvin, Camille; Hui, Lam, E-mail: gazta@ice.cat, E-mail: camille.bonvin@unige.ch, E-mail: lhui@astro.columbia.edu

It is usually assumed that in the linear regime the two-point correlation function of galaxies contains only a monopole, quadrupole and hexadecapole. Looking at cross-correlations between different populations of galaxies, this turns out not to be the case. In particular, the cross-correlations between a bright and a faint population of galaxies contain also a dipole. In this paper we present the first attempt to measure this dipole. We discuss the four types of effects that contribute to the dipole: relativistic distortions, evolution effect, wide-angle effect and large-angle effect. We show that the first three contributions are intrinsic anti-symmetric contributions thatmore » do not depend on the choice of angle used to measure the dipole. On the other hand the large-angle effect appears only if the angle chosen to extract the dipole breaks the symmetry of the problem. We show that the relativistic distortions, the evolution effect and the wide-angle effect are too small to be detected in the LOWz and CMASS sample of the BOSS survey. On the other hand with a specific combination of angles we are able to measure the large-angle effect with high significance. We emphasise that this large-angle dipole does not contain new physical information, since it is just a geometrical combination of the monopole and the quadrupole. However this measurement, which is in excellent agreement with theoretical predictions, validates our method for extracting the dipole from the two-point correlation function and it opens the way to the detection of relativistic effects in future surveys like e.g. DESI.« less

Collisional disruptions of rotating targets

NASA Astrophysics Data System (ADS)

Ševeček, Pavel; Broz, Miroslav

2017-10-01

Collisions are key processes in the evolution of the Main Asteroid Belt and impact events - i.e. target fragmentation and gravitational reaccumulation - are commonly studied by numerical simulations, namely by SPH and N-body methods. In our work, we extend the previous studies by assuming rotating targets and we study the dependence of resulting size-distributions on the pre-impact rotation of the target. To obtain stable initial conditions, it is also necessary to include the self-gravity already in the fragmentation phase which was previously neglected.To tackle this problem, we developed an SPH code, accelerated by SSE/AVX instruction sets and parallelized. The code solves the standard set of hydrodynamic equations, using the Tillotson equation of state, von Mises criterion for plastic yielding and scalar Grady-Kipp model for fragmentation. We further modified the velocity gradient by a correction tensor (Schäfer et al. 2007) to ensure a first-order conservation of the total angular momentum. As the intact target is a spherical body, its gravity can be approximated by a potential of a homogeneous sphere, making it easy to set up initial conditions. This is however infeasible for later stages of the disruption; to this point, we included the Barnes-Hut algorithm to compute the gravitational accelerations, using a multipole expansion of distant particles up to hexadecapole order.We tested the code carefully, comparing the results to our previous computations obtained with the SPH5 code (Benz and Asphaug 1994). Finally, we ran a set of simulations and we discuss the difference between the synthetic families created by rotating and static targets.

An optimal FFT-based anisotropic power spectrum estimator

NASA Astrophysics Data System (ADS)

Hand, Nick; Li, Yin; Slepian, Zachary; Seljak, Uroš

2017-07-01

Measurements of line-of-sight dependent clustering via the galaxy power spectrum's multipole moments constitute a powerful tool for testing theoretical models in large-scale structure. Recent work shows that this measurement, including a moving line-of-sight, can be accelerated using Fast Fourier Transforms (FFTs) by decomposing the Legendre polynomials into products of Cartesian vectors. Here, we present a faster, optimal means of using FFTs for this measurement. We avoid redundancy present in the Cartesian decomposition by using a spherical harmonic decomposition of the Legendre polynomials. With this method, a given multipole of order l requires only 2l+1 FFTs rather than the (l+1)(l+2)/2 FFTs of the Cartesian approach. For the hexadecapole (l = 4), this translates to 40% fewer FFTs, with increased savings for higher l. The reduction in wall-clock time enables the calculation of finely-binned wedges in P(k,μ), obtained by computing multipoles up to a large lmax and combining them. This transformation has a number of advantages. We demonstrate that by using non-uniform bins in μ, we can isolate plane-of-sky (angular) systematics to a narrow bin at 0μ simeq while eliminating the contamination from all other bins. We also show that the covariance matrix of clustering wedges binned uniformly in μ becomes ill-conditioned when combining multipoles up to large values of lmax, but that the problem can be avoided with non-uniform binning. As an example, we present results using lmax=16, for which our procedure requires a factor of 3.4 fewer FFTs than the Cartesian method, while removing the first μ bin leads only to a 7% increase in statistical error on f σ8, as compared to a 54% increase with lmax=4.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hand, Nick; Seljak, Uroš; Li, Yin

Measurements of line-of-sight dependent clustering via the galaxy power spectrum's multipole moments constitute a powerful tool for testing theoretical models in large-scale structure. Recent work shows that this measurement, including a moving line-of-sight, can be accelerated using Fast Fourier Transforms (FFTs) by decomposing the Legendre polynomials into products of Cartesian vectors. Here, we present a faster, optimal means of using FFTs for this measurement. We avoid redundancy present in the Cartesian decomposition by using a spherical harmonic decomposition of the Legendre polynomials. With this method, a given multipole of order ℓ requires only 2ℓ+1 FFTs rather than the (ℓ+1)(ℓ+2)/2 FFTsmore » of the Cartesian approach. For the hexadecapole (ℓ = 4), this translates to 40% fewer FFTs, with increased savings for higher ℓ. The reduction in wall-clock time enables the calculation of finely-binned wedges in P ( k ,μ), obtained by computing multipoles up to a large ℓ{sub max} and combining them. This transformation has a number of advantages. We demonstrate that by using non-uniform bins in μ, we can isolate plane-of-sky (angular) systematics to a narrow bin at 0μ ≅ while eliminating the contamination from all other bins. We also show that the covariance matrix of clustering wedges binned uniformly in μ becomes ill-conditioned when combining multipoles up to large values of ℓ{sub max}, but that the problem can be avoided with non-uniform binning. As an example, we present results using ℓ{sub max}=16, for which our procedure requires a factor of 3.4 fewer FFTs than the Cartesian method, while removing the first μ bin leads only to a 7% increase in statistical error on f σ{sub 8}, as compared to a 54% increase with ℓ{sub max}=4.« less

Extending the modeling of the anisotropic galaxy power spectrum to k = 0.4 h Mpc{sup −1}

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hand, Nick; Seljak, Uroš; Beutler, Florian

We present a model for the redshift-space power spectrum of galaxies and demonstrate its accuracy in describing the monopole, quadrupole, and hexadecapole of the galaxy density field down to scales of k = 0.4 h Mpc{sup −1}. The model describes the clustering of galaxies in the context of a halo model and the clustering of the underlying halos in redshift space using a combination of Eulerian perturbation theory and N -body simulations. The modeling of redshift-space distortions is done using the so-called distribution function approach. The final model has 13 free parameters, and each parameter is physically motivated rather thanmore » a nuisance parameter, which allows the use of well-motivated priors. We account for the Finger-of-God effect from centrals and both isolated and non-isolated satellites rather than using a single velocity dispersion to describe the combined effect. We test and validate the accuracy of the model on several sets of high-fidelity N -body simulations, as well as realistic mock catalogs designed to simulate the BOSS DR12 CMASS data set. The suite of simulations covers a range of cosmologies and galaxy bias models, providing a rigorous test of the level of theoretical systematics present in the model. The level of bias in the recovered values of f σ{sub 8} is found to be small. When including scales to k = 0.4 h Mpc{sup −1}, we find 15-30% gains in the statistical precision of f σ{sub 8} relative to k = 0.2 h Mpc{sup −1} and a roughly 10–15% improvement for the perpendicular Alcock-Paczynski parameter α{sub ⊥}. Using the BOSS DR12 CMASS mocks as a benchmark for comparison, we estimate an uncertainty on f σ{sub 8} that is ∼10–20% larger than other similar Fourier-space RSD models in the literature that use k ≤ 0.2 h Mpc{sup −1}, suggesting that these models likely have a too-limited parametrization.« less

Extending the modeling of the anisotropic galaxy power spectrum to k = 0.4 hMpc-1

NASA Astrophysics Data System (ADS)

Hand, Nick; Seljak, Uroš; Beutler, Florian; Vlah, Zvonimir

2017-10-01

We present a model for the redshift-space power spectrum of galaxies and demonstrate its accuracy in describing the monopole, quadrupole, and hexadecapole of the galaxy density field down to scales of k = 0.4 hMpc-1. The model describes the clustering of galaxies in the context of a halo model and the clustering of the underlying halos in redshift space using a combination of Eulerian perturbation theory and N-body simulations. The modeling of redshift-space distortions is done using the so-called distribution function approach. The final model has 13 free parameters, and each parameter is physically motivated rather than a nuisance parameter, which allows the use of well-motivated priors. We account for the Finger-of-God effect from centrals and both isolated and non-isolated satellites rather than using a single velocity dispersion to describe the combined effect. We test and validate the accuracy of the model on several sets of high-fidelity N-body simulations, as well as realistic mock catalogs designed to simulate the BOSS DR12 CMASS data set. The suite of simulations covers a range of cosmologies and galaxy bias models, providing a rigorous test of the level of theoretical systematics present in the model. The level of bias in the recovered values of f σ8 is found to be small. When including scales to k = 0.4 hMpc-1, we find 15-30% gains in the statistical precision of f σ8 relative to k = 0.2 hMpc-1 and a roughly 10-15% improvement for the perpendicular Alcock-Paczynski parameter α⊥. Using the BOSS DR12 CMASS mocks as a benchmark for comparison, we estimate an uncertainty on f σ8 that is ~10-20% larger than other similar Fourier-space RSD models in the literature that use k <= 0.2 hMpc-1, suggesting that these models likely have a too-limited parametrization.

α-cluster versus non-α-cluster decay of the excited compound nucleus Ce124* using the dynamical cluster-decay model

NASA Astrophysics Data System (ADS)

Kaur, Arshdeep; Chopra, Sahila; Gupta, Raj K.

2014-03-01

The dynamical cluster-decay model (DCM), an extended version of the preformed cluster model (PCM) for ground-state (T =0) decays, is applied to study the decay of the proton-rich compound nucleus Ce124* formed in the S32 + Mo92 reaction at an above-barrier beam energy of 150 MeV. Application of the statistical code pace4 to experimental data shows large deviations in all cases of proton clusters' (2p, 3p, and 4p) evaporation residue (ER) and the non-α nucleus Be6 intermediate mass fragment (IMF). Furthermore, the α-nucleus Be8 decay is not observed in this experiment (not even the upper limit is given). Using the DCM, with effects of deformations up to hexadecapole and "compact" orientations included, for the best-fitted cross sections of 2p and 3p ERs and of Li5 and Be6 IMFs, the relative cross section of Be8 is found to be more than that of Be6, possibly due to the α-nucleus structure of Be8. The same is shown to be true for C12 versus C10, i.e., α-nuclei clusters are populated strongly relative to non-α clusters, similar to what was predicted by one of us (R.K.G.) et al. [S. Kumar, D. Bir, and R. K. Gupta, Phys. Rev. C 51, 1762 (1995), 10.1103/PhysRevC.51.1762] for ground-state decays of such nuclei and the decay of Ba116* formed in the Ni58 + Ni58 reaction at various compound nucleus excitation energies [R. K. Gupta et al., J. Phys. G: Nucl. Part. Phys. 32, 345 (2006), 10.1088/0954-3899/32/3/009]. The only parameter of the DCM is the neck-length ΔR, related to the "barrier-lowering" parameter. The compound nucleus formation probability and "barrier-lowering/-modification" effects are analyzed, and the role of varying the deformations of Be6 and/or Be8 nuclei on relative cross sections is studied, since the measured deformations are not available. The ones used here are from relativistic mean-field calculations [β2(6Be )=-0.087 and β2(8Be)=-0.094]. Calculations are also presented for a beam energy of 140 MeV, supporting the above result.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Okumura, Teppei; Seljak, Uroš; McDonald, Patrick

Measurement of redshift-space distortions (RSD) offers an attractive method to directly probe the cosmic growth history of density perturbations. A distribution function approach where RSD can be written as a sum over density weighted velocity moment correlators has recently been developed. In this paper we use results of N-body simulations to investigate the individual contributions and convergence of this expansion for dark matter. If the series is expanded as a function of powers of μ, cosine of the angle between the Fourier mode and line of sight, then there are a finite number of terms contributing at each order. Wemore » present these terms and investigate their contribution to the total as a function of wavevector k. For μ{sup 2} the correlation between density and momentum dominates on large scales. Higher order corrections, which act as a Finger-of-God (FoG) term, contribute 1% at k ∼ 0.015hMpc{sup −1}, 10% at k ∼ 0.05hMpc{sup −1} at z = 0, while for k > 0.15hMpc{sup −1} they dominate and make the total negative. These higher order terms are dominated by density-energy density correlations which contributes negatively to the power, while the contribution from vorticity part of momentum density auto-correlation adds to the total power, but is an order of magnitude lower. For μ{sup 4} term the dominant term on large scales is the scalar part of momentum density auto-correlation, while higher order terms dominate for k > 0.15hMpc{sup −1}. For μ{sup 6} and μ{sup 8} we find it has very little power for k < 0.15hMpc{sup −1}, shooting up by 2–3 orders of magnitude between k < 0.15hMpc{sup −1} and k < 0.4hMpc{sup −1}. We also compare the expansion to the full 2-d P{sup ss}(k,μ), as well as to the monopole, quadrupole, and hexadecapole integrals of P{sup ss}(k,μ). For these statistics an infinite number of terms contribute and we find that the expansion achieves percent level accuracy for kμ < 0.15hMpc{sup −1} at 6-th order, but

Accurate electric multipole moment, static polarizability and hyperpolarizability derivatives for N2

NASA Astrophysics Data System (ADS)

Maroulis, George

2003-02-01

We report accurate values of the electric moments, static polarizabilities, hyperpolarizabilities and their respective derivatives for N2. Our values have been extracted from finite-field Møller-Pleset perturbation theory and coupled cluster calculations performed with carefully designed basis sets. A large [15s12p9d7f] basis set consisting of 290 CGTF is expected to provide reference self-consistent-field values of near-Hartree-Fock quality for all properties. The Hartree-Fock limit for the mean hyperpolarizability is estimated at γ¯=715±4e4a04Eh-3 at the experimental bond length Re=2.074 32a0. Accurate estimates of the electron correlation effects were obtained with a [10s7p6d4f] basis set. Our best values are Θ=-1.1258ea02 for the quadrupole and Φ=-6.75ea04 for the hexadecapole moment, ᾱ=11.7709 and Δα=4.6074e2a02Eh-1 for the mean and the anisotropy of the dipole polarizability, C¯=41.63e2a04Eh-1 for the mean quadrupole polarizability and γ¯=927e4a04Eh-3 for the dipole hyperpolarizability. The latter value is quite close to Shelton's experimental estimate of 917±5e4a04Eh-3 [D. P. Shelton, Phys. Rev. A 42, 2578 (1990)]. The R dependence of all properties has been calculated with a [7s5p4d2f] basis set. At the CCSD(T) level of theory the dipole polarizability varies around Re as ᾱ(R)/e2a02Eh-1=11.8483+6.1758(R-Re)+0.9191(R-Re)2-0.8212(R-Re)3-0.0006(R-Re)4, Δα(R)/e2a02Eh-1=4.6032+7.0301(R-Re)+1.9340(R-Re)2-0.5708(R-Re)3+0.1949(R-Re)4. For the Cartesian components and the mean of γαβγδ, (dγzzzz/dR)e=1398, (dγxxxx/dR)e=867, (dγxxzz/dR)e=317, and (dγ¯/dR)e=994e4a03Eh-3. For the quadrupole polarizability Cαβ,γδ, we report (dCzz,zz/dR)e=19.20, (dCxz,xz/dR)e=16.55, (dCxx,xx/dR)e=10.20, and (dC¯/dR)e=23.31e2a03Eh-1. At the MP2 level of theory the components of the dipole-octopole polarizability (Eα,βγδ) and the mean dipole-dipole-octopole hyperpolarizability B¯ we have obtained (dEz,zzz/dR)e=36.71, (dEx,xxx/dR)e=-12.94e2a03Eh-1, and

Collision-Induced Absorption Spectra of Binary Mixtures of Molecular Hydrogen with Molecular Deuterium and Argon and of Pure Hydrogen, D

NASA Astrophysics Data System (ADS)

Hsieh, Chang-Tsang William

In the present research project a systematic study of the collision-induced infrared absorption (CIA) spectra of the binary mixtures of H_2 - D_2 in the region of the double fundamental vibrations of H_2 and D_2, and H_2 - Ar in the fundamental band of H_2, and of pure HD in its fundamental and first overtone regions was undertaken. The experiments were carried out with a 2.0 m high-pressure low-temperature transmission-type absorption cell at 77, 201 and 296 K at total gas densities up to 550 amagat. Infrared prism and grating spectrometers equipped with a microprocessor -controlled stepping motor were used to record the spectra. All the experimental results obtained represent first-time observations in collision-induced absorption. Collision-induced infrared absorption spectra of the double transitions of H_2(v=1>=ts 0) and D_2(v=1>=ts 0) have been observed at 77 and 201 K in the spectral region 7000-8000 cm^{-1} for total gas densities up to 550 amagat with a partial gas density ratio of 1:1 of H_2 and D_2. The observed spectra are interpreted in terms of the transitions, Q_1(J) of H_2+Q_1(J) of D _2, Q_1(J) of H_2+S _1(J) of D_2, S_1(J) of H_2 + Q_1(J) of D_2, and S_1(J) of H_2 + S_1(J) of D_2 for J = 0 and 1 for H _2 and J = 0, 1, and 2 for D_2. Analysis of the experimental absorption profiles was carried out using appropriate lineshape functions. The absorption coefficients, lineshape parameters, etc., are obtained from the analysis. Collision-induced enhancement absorption spectra of the fundamental band of H_2 in H_2 - Ar mixtures were recorded at room temperature for a base density of 72 amagat of H_2 for several partial densities of Ar up to 440 amagat. Hexadecapole-induced U transitions, U_1(1), U_1(2), Q_1(0)+U _0(1), and Q_1(1) + U_0(1) have been identified in the spectral region 5400 -6200 cm^{-1}. A "cage" model has been proposed to account for the double transitions of H_2 - H_2 in the H _2 - Ar enhancement spectra. From the analysis of the

A systematic study of basis set, electron correlation, and geometry effects on the electric multipole moments, polarizability, and hyperpolarizability of HCl

NASA Astrophysics Data System (ADS)

Maroulis, George

1998-04-01

The electric multipole moments, dipole and quadrupole polarizability and hyperpolarizability of hydrogen chloride have been determined from an extensive and systematic study based on finite-field fourth-order many-body perturbation theory and coupled-cluster calculations. Our best values for the dipole, quadrupole, octopole and hexadecapole moment at the experimental internuclear separation of Re=2.408645a0 are μ=0.4238ea0, Θ=2.67ea02, Ω=3.94ea03, and Φ=13.37ea04, respectively. For the mean and the anisotropy of the dipole polarizability ααβ we recommend ᾱ=17.41±0.02 and Δα=1.60±0.03e2a02Eh-1. For the mean value of the first dipole hyperpolarizability βαβγ we advance β¯=-6.8±0.3e3a03Eh-2. Extensive calculations with a [8s6p6d3f/5s4p2d1f] basis set at the CCSD(T) level of theory yield the R-dependence of the Cartesian components and the mean of the second dipole hyperpolarizability γαβγδ(R)/e4a04Eh-3 around Re as γzzzz(R)=1907+1326(R-Re)+570(R-Re)2+10(R-Re)3-40(R-Re)4, γxxxx(R)=3900+747(R-Re)-65(R-Re)2-38(R-Re)3-7(R-Re)4, γxxzz(R)=962+222(R-Re)+88(R-Re)2+49(R-Re)3+5(R-Re)4, γ¯(R)=3230+841(R-Re)+151(R-Re)2+21(R-Re)3-9(R-Re)4, with z as the molecular axis. The present investigation suggests an estimate of (26.7±0.3)×102e4a04Eh-3 for the Hartree-Fock limit of the mean value γ¯ at Re. CCSD(T) calculations with basis sets of [8s6p6d3f/5s4p2d1f] and [9s7p5d4f/6s5p4d1f] size and MP4 calculations with the even larger [15s12p7d3f/12s7p2d1f] give (7.0±0.3)×102e4a04Eh-3 for the electron correlation effects for this property, thus leading to a recommended value of γ¯=(33.7±0.6)×102e4a04Eh-3. For the quadrupole polarizability Cαβ,γδ/e2a04Eh-1 at Re our best values are Czz,zz=41.68, Cxz,xz=26.11, and Cxx,xx=35.38, calculated with the [9s7p5d4f/6s5p4d1f] basis set at the CCSD(T) level of theory. The following CCSD(T) values were obtained with [8s6p6d3f/5s4p2d1f] at Re: dipole-quadrupole polarizability Aα,βγ/e2a03Eh-1, Az,zz=14.0, and