Electric-hexadecapole (24-pole) Coulomb integrals
NASA Astrophysics Data System (ADS)
Chidichimo, Marita C.; Stastna, Marek
1996-03-01
We obtain the quantal zero-energy-loss limit of the radial integrals arising in the nonrelativistic atomic excitation of electric-hexadecapole transitions. We compare these results to the classical limit and the WKB approximation. We show the different behavior of the Coulomb integrals in the WKB approximation in the cases of repulsive and attractive potentials as functions of the Sommerfeld number η.
Nonaxial hexadecapole deformation effects on the fission barrier
NASA Astrophysics Data System (ADS)
Kardan, A.; Nejati, S.
2016-06-01
Fission barrier of the heavy nucleus 250Cf is analyzed in a multi-dimensional deformation space. This space includes two quadrupole (ɛ2,γ) and three hexadecapole deformation (ɛ40,ɛ42,ɛ44) parameters. The analysis is performed within an unpaired macroscopic-microscopic approach. Special attention is given to the effects of the axial and non-axial hexadecapole deformation shapes. It is found that the inclusion of the nonaxial hexadecapole shapes does not change the fission barrier heights, so it should be sufficient to minimize the energy in only one degree of freedom in the hexadecapole space ɛ4. The role of hexadecapole deformation parameters is also discussed on the Lublin-Strasbourg drop (LSD) macroscopic and the Strutinsky shell energies.
Octupole and hexadecapole bands in 152Sm
Garrett, P E; Kulp, W D; Wood, J L; Bandyopadhyay, D; Christen, S; Choudry, S; Dewald, A; Fitzler, A; Fransen, C; Jessen, K; Jolie, J; Kloezer, A; Kudejova, P; Kumar, A; Lesher, S R; Linnemann, A; Lisetskiy, A; Martin, D; Masur, M; McEllistrem, M T; Moller, O; Mynk, M; Orce, J N; Pejovic, P; Pissulla, T; Regis, J; Schiller, A; Tonev, D; Yates, S W
2005-05-13
The nucleus {sup 152}Sm is characterized by a variety of low-energy collective modes, conventionally described as rotations, {beta} vibrations, and {gamma} vibrations. Recently, it has been suggested that {sup 152}Sm is at a critical point between spherical and deformed collective phases. Consequently, {sup 152}Sm is being studied by a variety of techniques, including radioactive decay, multi-step Coulomb excitation, in-beam ({alpha},2n{gamma}) {gamma}-ray spectroscopy, and (n,n'{gamma}) spectroscopy. The present work focuses on the latter two reactions; these have been used to investigate the low-lying bands associated with the octupole degree of freedom, including one built on the first excited 0{sup +} band. In addition, the K{sup {pi}} = 4{sup +} hexadecapole vibrational band has been identified.
Production and detection of atomic hexadecapole at Earth's magnetic field.
Acosta, V M; Auzinsh, M; Gawlik, W; Grisins, P; Higbie, J M; Jackson Kimball, D F; Krzemien, L; Ledbetter, M P; Pustelny, S; Rochester, S M; Yashchuk, V V; Budker, D
2008-07-21
Optical magnetometers measure magnetic fields with extremely high precision and without cryogenics. However, at geomagnetic fields, important for applications from landmine removal to archaeology, they suffer from nonlinear Zeeman splitting, leading to systematic dependence on sensor orientation. We present experimental results on a method of eliminating this systematic error, using the hexadecapole atomic polarization moment. In particular, we demonstrate selective production of the atomic hexadecapole moment at Earth's magnetic field and verify its immunity to nonlinear Zeeman splitting. This technique promises to eliminate directional errors in all-optical atomic magnetometers, potentially improving their measurement accuracy by several orders of magnitude.
Nuclear Hexadecapole Deformation Effects on the Production of Super-Heavy Elements
NASA Astrophysics Data System (ADS)
Wang, Nan; Dou, Liang; Zhao, En-Guang; Werner, Scheid
2010-06-01
We investigate the effects of the nuclear hexadecapole deformations on the interaction potentials between nuclei, the driving potentials and the fusion probabilities for some cold fusion reactions leading to super-heavy elements. It is found that nuclear hexadecapole deformations change significantly the structure of the driving potentials and the fusion probabilities for some reaction channels.
Extracting the hexadecapole deformation from backward quasi-elastic scattering
NASA Astrophysics Data System (ADS)
Jia, H. M.; Lin, C. J.; Yang, F.; Xu, X. X.; Zhang, H. Q.; Liu, Z. H.; Wu, Z. D.; Yang, L.; Ma, N. R.; Bao, P. F.; Sun, L. J.
2014-09-01
Background: The hexadecapole deformation β4 is usually difficult to determine experimentally, especially its sign. The rapidly accumulated knowledge of β2 inspires the desire of β4 for radioactive nuclei, but the current low-quality beam is a severe experimental challenge. Therefore, a simple but sensitive method to extract β4 in such a condition is urgently called for. Purpose: To study the feasibility of extracting β4 from the lower-energy backward quasi-elastic (QEL) scattering. Methods: The QEL scattering at sub-barrier energy region is sensitive to the coupled-channels (CC) effect and consequently may be used to extract β4. The QEL scattering excitation functions for O16+Sm152,Er170, and Yb174 were measured at a backward angle with small energy intervals at energies near the Coulomb barrier. Experimental fusion barrier distributions were also derived. The lower-energy data were analyzed to extract β4 with the help of the CC calculations. Results: The obtained β4 agrees with the available results reasonably well. Conclusions: We have demonstrated that the QEL scattering at sub-barrier energies provides a feasible and sensitive method to extract the value of β4, which is essentially meaningful for the radioactive nucleus because of its low beam intensity.
NASA Astrophysics Data System (ADS)
Alavi, S. A.; Dehghani, V.
2017-06-01
Alpha-induced reactions on 154Sm, 233,235,236,238U, and 237Np deformed nuclei are studied theoretically. The effects of hexadecapole deformation, deformed surface diffuseness parameter, and orientation on barrier height and position, fusion cross-section at any angle, and fusion cross-section have been investigated. Both hexadecapole deformation and deformed surface diffuseness can affect barrier characteristics and enhance fusion cross-section. Good agreement between experimental data and theoretical calculations with quadrupole and hexadecapole deformation and deformed surface diffuseness were observed for the 4He+154Sm, 235U, 237Np reactions.
NASA Astrophysics Data System (ADS)
Will, Clifford M.
2017-07-01
We analyze the secular evolution of hierarchical triple systems in the post-Newtonian approximation to general relativity. We expand the Newtonian three-body equations of motion in powers of the ratio a /A , where a and A are the semimajor axis of the inner binary's orbit and of the orbit of the third body relative to the center of mass of the inner binary, respectively. The leading order "quadrupole" terms, of order (a /A )3 relative to the 1 /a2 acceleration within the inner binary, are responsible for the well-known Kozai-Lidov oscillations of orbital inclination and eccentricity. The octupole terms, of order (a /A )4 have been shown to allow the inner orbit to "flip" from prograde relative to the outer orbit to retrograde and back, and to permit excursions to very large eccentricities. We carry the expansion of the equations of motion to hexadecapole order, corresponding to contributions of order (a /A )5. We also include the leading orbital effects of post-Newtonian theory, namely the pericenter precessions of the inner and outer orbits. Using the Lagrange planetary equations for the orbit elements of both binaries, we average over orbital time scales, obtain the equations for the secular evolution of the elements through hexadecapole order, and employ them to analyze cases of astrophysical interest. We find that, for the most part, the orbital flips found at octupole order are robust against both relativistic and hexadecapole perturbations. We show that, for equal-mass inner binaries, where the octupole terms vanish, the hexadecapole contributions can alone generate orbital flips and excursions to very large eccentricities.
Mixed-symmetry octupole and hexadecapole excitations in the N =52 isotones
NASA Astrophysics Data System (ADS)
Hennig, A.; Spieker, M.; Werner, V.; Ahn, T.; Anagnostatou, V.; Cooper, N.; Derya, V.; Elvers, M.; Endres, J.; Goddard, P.; Heinz, A.; Hughes, R. O.; Ilie, G.; Mineva, M. N.; Petkov, P.; Pickstone, S. G.; Pietralla, N.; Radeck, D.; Ross, T. J.; Savran, D.; Zilges, A.
2014-11-01
Background: Excitations with mixed proton-neutron symmetry have been previously observed in the N =52 isotones. Besides the well-established quadrupole mixed-symmetry states (MSS), octupole and hexadecapole MSS have been recently proposed for the nuclei 92Zr and 94Mo. Purpose: The heaviest stable N =52 isotone 96Ru was investigated to study the evolution of octupole and hexadecapole MSS with increasing proton number. Methods: Two inelastic proton-scattering experiments on 96Ru were performed to extract branching ratios, multipole mixing ratios, and level lifetimes. From the combined data, absolute transition strengths were calculated. Results: Strong M 1 transitions between the lowest-lying 3- and 4+ states were observed, providing evidence for a one-phonon mixed-symmetry character of the 32(-) and 42+ states. Conclusions: s d g -IBM-2 calculations were performed for 96Ru. The results are in excellent agreement with the experimental data, pointing out a one-phonon hexadecapole mixed-symmetry character of the 42+ state. The <31-||M 1 ||32(-)> matrix element is found to scale with the <2s+||M 1 ||2ms+> matrix element.
Magnetic hexadecapole order and magnetopiezoelectric metal state in Ba1 -xKxMn2As2
NASA Astrophysics Data System (ADS)
Watanabe, Hikaru; Yanase, Youichi
2017-08-01
We study an odd-parity magnetic multipole order in Ba1 -xKxMn2As2 and related materials. Although BaMn2As2 is a seemingly conventional Mott insulator with G -type antiferromagnetic order, we identify the ground state as a magnetic hexadecapole ordered state accompanied by simultaneous time-reversal and space-inversion symmetry breaking. A symmetry argument and microscopic calculations reveal the ferroic ordering of leading magnetic hexadecapole moment and admixed magnetic quadrupole moment. Furthermore, we clarify electromagnetic responses characterizing the magnetic hexadecapole state of semiconducting BaMn2As2 and doped metallic systems. A magnetoelectric effect and antiferromagnetic Edelstein effect are shown. Interestingly, a counterintuitive current-induced nematic order occurs in the metallic state. The electric current along the z axis induces the x y -plane nematicity in sharp contrast to the spontaneous nematic order in superconducting Fe-based 122 compounds. Thus, the magnetic hexadecapole state of doped BaMn2As2 is regarded as a magnetopiezoelectric metal. Other candidate materials for magnetic hexadecapole order are proposed.
Influence of hexadecapole deformation on production cross sections of superheavy nuclei
NASA Astrophysics Data System (ADS)
Bao, X. J.; Guo, S. Q.; Zhang, H. F.; Li, J. Q.
2016-12-01
The current heaviest superheavy nuclei (SHN) are experimentally synthesized by using 48Ca to bombard actinide nuclei via fusion reactions. Actinide nuclei often have considerable hexadecapole deformation in addition to quadrupole deformation, which was not considered in previous theoretical studies. With the dinuclear system concept, and by taking the hexadecapole deformation in to consideration in addition to the quadrupole deformation, the hot fusion probability leading to the synthesis of SHN is investigated systematically. Synthesis of superheavy elements 296118 and 295118 by using the 48Ca+251Cf reaction channel is evaluated and discussed, and the maximal evaporation residue cross sections (ERCSs) of the 3n and 4n channels are predicted to be 1.90 and 0.11 pb, respectively. The predicted maximum ERCSs in 3n and 4n evaporation channels of the 249Bk(50Ti,xn){}299-x119 reaction are 0.12 and 0.04 pb, respectively. The most favorable reaction to synthesize the element Z = 120 turns out to be 251Cf(50Ti,xn){}301-x120, but the predicted maximum cross section for this reaction is only 67 fb. Therefore, superheavy element 119 may be the most hopeful new element for Z\\gt 118 to be synthesized under some improved experimental conditions in the near future.
Critical Slowing Down of Quadrupole and Hexadecapole Orderings in Iron Pnictide Superconductor
NASA Astrophysics Data System (ADS)
Kurihara, Ryosuke; Mitsumoto, Keisuke; Akatsu, Mitsuhiro; Nemoto, Yuichi; Goto, Terutaka; Kobayashi, Yoshiaki; Sato, Masatoshi
2017-06-01
Ultrasonic measurements have been carried out to investigate the critical dynamics of structural and superconducting transitions due to degenerate orbital bands in iron pnictide compounds with the formula Ba(Fe1-xCox)2As2. The attenuation coefficient αL[110] of the longitudinal ultrasonic wave for (C11 + C12 + 2C66)/2 for x = 0.036 reveals the critical slowing down of the relaxation time around the structural transition at Ts = 65 K, which is caused by ferro-type ordering of the quadrupole Ox'2 - y'2 coupled to the strain ɛxy. The attenuation coefficient α66 of the transverse ultrasonic wave for C66 for x = 0.071 also exhibits the critical slowing down around the superconducting transition at TSC = 23 K, which is caused by ferro-type ordering of the hexadecapole Hzα(ri,rj) = Ox'y'(ri)Ox'2 - y'2(rj) + Ox'2 - y'2(ri)Ox'y'(rj) of the bound two-electron state coupled to the rotation ωxy. It is proposed that the hexadecapole ordering associated with the superconductivity brings about spontaneous rotation of the macroscopic superconducting state with respect to the host tetragonal lattice.
Fragmentation of low-lying hexadecapole states in even 74-82Se and a RPA calculation
NASA Astrophysics Data System (ADS)
Ogino, K.; Kadota, Y.; Haga, H.; Matsuki, S.; Higo, T.; Shiba, T.; Sakamoto, N.; Okuma, Y.; Yanabu, T.
1983-10-01
The level schemes of the even 74-82Se up to Ex = 5.0 MeV have been investigated with high-resolution inelastic proton scattering at Ep = 64.8 MeV. Several 4+ states with comparable strengths were found at EX = 2.0-5.0 MeV in all isotopes studied. The energy weighted sum-rule fraction of the 4+ states in this region increases with decreasing neutron number from 82Se (1.0%) up to 76Se (3.7%), and then decreases in 74Se (2.6%). A RPA calculation with a pairing plus hexa-decapole-hexadecapole interaction can well reproduce the distribution of the excitation energies and transition strengths for the hexadecapole states.
Gupta, Raj K.; Manhas, Monika; Greiner, Walter
2006-05-15
Based on fragmentation theory extended to include the orientation degrees of freedom and higher multipole deformations up to hexadecapole deformations, the compactness of {sup 48}Ca induced reactions on various actinides is studied for Ds (Z=110) to 118 nuclei. It is shown that the reactions leading to Z{>=}114 nuclei are 'compact' hot fusion reactions at {theta}=90 deg. orientation angles (equatorial compact or ec; collisions that are in the direction of the minor axis of the deformed reaction partner), but the ones for Z<114 nuclei are compact at {theta}<90 deg. (not-equatorial compact or nec). The phenomenon of 'barrier distribution in orientation degrees of freedom' is observed for the first time to be related to the magnitudes of both the quadrupole and hexadecapole deformations of the deformed reaction partner. The ec configurations are obtained for the cases of quadrupole deformation alone and with small (including negative values) hexadecapole deformations. The presence of large (positive) hexadecapole deformations result in the nec configurations. These results are found to be quite general, applicable also to other lighter targets such as W and Ra with the {sup 48}Ca beam and to Pb based reactions. Furthermore, for compact hot fusion reactions, in addition to the {sup 48}Ca reaction valley, a number of other new reaction valleys (target-projectile combinations) are obtained, the most important one (next to {sup 48}Ca) being the {sup 54}Ti nucleus used previously in Pb based cold fusion reaction studies but now proposed with deformed actinide nuclei such as {sup 226}Ra, {sup 232}Th, {sup 238}U, and {sup 242}Pu.
NASA Astrophysics Data System (ADS)
Cassan, Arnaud
2017-07-01
The exoplanet detection rate from gravitational microlensing has grown significantly in recent years thanks to a great enhancement of resources and improved observational strategy. Current observatories include ground-based wide-field and/or robotic world-wide networks of telescopes, as well as space-based observatories such as satellites Spitzer or Kepler/K2. This results in a large quantity of data to be processed and analysed, which is a challenge for modelling codes because of the complexity of the parameter space to be explored and the intensive computations required to evaluate the models. In this work, I present a method that allows to compute the quadrupole and hexadecapole approximations of the finite-source magnification with more efficiency than previously available codes, with routines about six times and four times faster, respectively. The quadrupole takes just about twice the time of a point-source evaluation, which advocates for generalizing its use to large portions of the light curves. The corresponding routines are available as open-source python codes.
Elliptic and Hexadecapole Flow of Charged Hadrons in Au+Au Collisions at s_NN = 200 GeV
Adare, A.; Awes, Terry C; Cianciolo, Vince; Efremenko, Yuri; Enokizono, Akitomo; Read Jr, Kenneth F; Silvermyr, David O; Sorensen, Soren P; Stankus, Paul W; PHENIX, Collaboration
2010-01-01
Differential measurements of the elliptic (v{sub 2}) and hexadecapole (v{sub 4}) Fourier flow coefficients are reported for charged hadrons as a function of transverse momentum (p{sub T}) and collision centrality or number of participant nucleons (N{sub part}) for Au+Au collisions at {radical}s{sub NN} = 200 GeV. The v{sub 2,4} measurements at pseudorapidity |{eta}| {le} 0.35, obtained with four separate reaction-plane detectors positioned in the range 1.0 < |{eta}| < 3.9, show good agreement, indicating the absence of significant {Delta}{eta}-dependent nonflow correlations. Sizable values for v{sub 4}(p{sub T}) are observed with a ratio v{sub 4}(p{sub T},N{sub part})/v{sub 2}{sup 2}(p{sub T},N{sub part}) {approx} 0.8 for 50 {le} N{sub part} {le} 200, which is compatible with the combined effects of a finite viscosity and initial eccentricity fluctuations. For N{sub part} {ge} 200 this ratio increases up to 1.7 in the most central collisions.
NASA Astrophysics Data System (ADS)
Bruna, Pablo J.; Grein, Friedrich
2007-08-01
The number of independent components, n, of traceless electric 2l-multipole moments is determined for C∞v molecules in Σ ±, Π, Δ, and Φ electronic states (Λ=0,1,2,3). Each 2l pole is defined by a rank-l irreducible tensor with (2l+1) components Pm(l) proportional to the solid spherical harmonic rlYml(θ,φ). Here we focus our attention on 2l poles with l =2,3,4 (quadrupole Θ, octopole Ω, and hexadecapole Φ). An important conclusion of this study is that n can be 1 or 2 depending on both the multipole rank l and state quantum number Λ. For Σ±(Λ=0) states, all 2l poles have one independent parameter (n=1). For spatially degenerate states—Π, Δ, and Φ (Λ=1,2,3)—the general rule reads n =1 for l <2∣Λ∣ (when the 2l-pole rank lies below 2∣Λ∣) but n =2 for higher 2l poles with l ⩾2∣Λ∣. The second nonzero term is the off-diagonal matrix element ⟨ψ+Λ∣P∣m∣=2Λ(l)∣ψ-Λ⟩. Thus, a Π(Λ =1) state has one dipole (μz) but two independent 2l poles for l ⩾2—starting with the quadrupole [Θzz,(Θxx-Θyy)]. A Δ(Λ =2) state has n =1 for 2(1,2,3) poles (μz,Θzz,Ωzzz) but n =2 for higher 2(l⩾4) poles—from the hexadecapole Φ up. For Φ(Λ =3) states, it holds that n =1 for 21 to 25 poles but n =2 for all 2(l⩾6) poles. In short, what is usually stated in the literature—that n =1 for all possible 2l poles of linear molecules—only applies to Σ± states. For degenerate states with n =2, all Cartesian 2l-pole components (l⩾2∣Λ∣) can be expressed as linear combinations of two irreducible multipoles, Pm=0(l ) and P∣m∣=2Λ(l) [parallel (z axis) and anisotropy (xy plane)]. Our predictions are exemplified by the Θ, Ω, and Φ moments calculated for Λ =0-3 states of selected diatomics (in parentheses): XΣ+2(CN ), XΠ2(NO ), aΠu3(C2), XΔ2(NiH ), XΔ3(TiO ), XΦ3(CoF ), and XΦ4(TiF ). States of Π symmetry are most affected by the deviation from axial symmetry.
Matsuki, S.; Higo, T.; Ohsawa, T.; Shiba, T.; Yanabu, Y.; Ogino, K.; Kadota, Y.; Haga, K.; Sakamoto, N.; Kume, K.; Matoba, M.
1983-11-07
The ground-state band up to the 4/sup +/ state in the even /sup 74approximately82/Se isotopes was studied by inelastic scattering of polarized protons at 65 MeV. Both the cross-section sigma(theta) and the analyzing-power A(theta) measurements leading to the 4/sup +/ state in the light /sup 74,76,78/Se isotopes show quite different shapes from those in the heavy /sup 80,82/Se isotopes. Coupled-channels analyses show that both the sigma(theta) and A(theta) distributions are well reproduced with a positive deformation parameter ..beta../sub 4/ in /sup 74,76,78/Se, but with a negative ..beta../sub 4/ in /sup 80,82/Se, indicating a hexadecapole-shape transition between /sup 78/Se and /sup 80/Se.
Search for the Tri-Axial Hexadecapole-Deformation Effects in Trans-Actinidae Nuclei
NASA Astrophysics Data System (ADS)
Dudek, J.; Mazurek, K.; Nerlo-Pomorska, B.
We have performed calculations of the nuclear potential energies in a 5-dimensional space of deformation parameters including α20, α22, α40, α42 and α44 multipole deformations by using the macroscopic-microscopic method. The energy expression contains the macroscopic term (in our case in the form of the Lublin Strasbourg Drop - LSD) and the microscopic terms of the Strutinsky shell energy and projected BCS pairing energy. The single-particle energies are obtained from the classical mean-field potential as well as from the correspondig Dirac relativistic realisation of the mean-field, both parametrised with the help of the deformed Woods-Saxon forms. Our resuls are compared to the selfconsistent Hartree Fock Bogolubov method with the D1S Gogny force.
Rotational structure of the odd-proton nuclide 171Tm: A projected shell model study
NASA Astrophysics Data System (ADS)
Liu, YanXin; Chen, FangQi; Yu, ShaoYing; Sun, Yang
2015-05-01
Deformed odd-mass nuclei are ideal examples where the interplay between single-particle and collective degrees of freedom can be studied. Inspired by the recent experimental high-spin data in the odd-proton nuclide 171Tm, we perform projected shell model (PSM) calculations to investigate structure of the ground band and other bands based on isomeric states. In addition to the usual quadrupole-quadrupole force in the Hamiltonian, we employ the hexadecapole-hexadecapole ( HH) interaction, in a self-consistent way with the hexadecapole deformation of the deformed basis. It is found that the known experimental data can be well described by the PSM calculation. The effect of the HH force on the quasiparticle isomeric states is discussed.
Senyuk, Bohdan; Puls, Owen; Tovkach, Oleh M.; Chernyshuk, Stanislav B.; Smalyukh, Ivan I.
2016-02-11
Outermost occupied electron shells of chemical elements can have symmetries resembling that of monopoles, dipoles, quadrupoles and octupoles corresponding to filled s-, p-, d- and forbitals. Theoretically, elements with hexadecapolar outer shells could also exist, but none of the known elements have filled g-orbitals. On the other hand, the research paradigm of ‘colloidal atoms’ displays complexity of particle behaviour exceeding that of atomic counterparts, which is driven by DNA functionalization, geometric shape and topology and weak external stimuli. We describe elastic hexadecapoles formed by polymer microspheres dispersed in a liquid crystal, a nematic fluid of orientationally ordered molecular rods. Because of conically degenerate boundary conditions, the solid microspheres locally perturb the alignment of the nematic host, inducing hexadecapolar distortions that drive anisotropic colloidal interactions. We uncover physical underpinnings of formation of colloidal elastic hexadecapoles and report the ensuing bonding inaccessible to elastic dipoles, quadrupoles and other nematic colloids studied previously.
Senyuk, Bohdan; Puls, Owen; Tovkach, Oleh M.; ...
2016-02-11
Outermost occupied electron shells of chemical elements can have symmetries resembling that of monopoles, dipoles, quadrupoles and octupoles corresponding to filled s-, p-, d- and forbitals. Theoretically, elements with hexadecapolar outer shells could also exist, but none of the known elements have filled g-orbitals. On the other hand, the research paradigm of ‘colloidal atoms’ displays complexity of particle behaviour exceeding that of atomic counterparts, which is driven by DNA functionalization, geometric shape and topology and weak external stimuli. We describe elastic hexadecapoles formed by polymer microspheres dispersed in a liquid crystal, a nematic fluid of orientationally ordered molecular rods. Becausemore » of conically degenerate boundary conditions, the solid microspheres locally perturb the alignment of the nematic host, inducing hexadecapolar distortions that drive anisotropic colloidal interactions. We uncover physical underpinnings of formation of colloidal elastic hexadecapoles and report the ensuing bonding inaccessible to elastic dipoles, quadrupoles and other nematic colloids studied previously.« less
Senyuk, Bohdan; Puls, Owen; Tovkach, Oleh M.; Chernyshuk, Stanislav B.; Smalyukh, Ivan I.
2016-01-01
Outermost occupied electron shells of chemical elements can have symmetries resembling that of monopoles, dipoles, quadrupoles and octupoles corresponding to filled s-, p-, d- and f-orbitals. Theoretically, elements with hexadecapolar outer shells could also exist, but none of the known elements have filled g-orbitals. On the other hand, the research paradigm of ‘colloidal atoms' displays complexity of particle behaviour exceeding that of atomic counterparts, which is driven by DNA functionalization, geometric shape and topology and weak external stimuli. Here we describe elastic hexadecapoles formed by polymer microspheres dispersed in a liquid crystal, a nematic fluid of orientationally ordered molecular rods. Because of conically degenerate boundary conditions, the solid microspheres locally perturb the alignment of the nematic host, inducing hexadecapolar distortions that drive anisotropic colloidal interactions. We uncover physical underpinnings of formation of colloidal elastic hexadecapoles and describe the ensuing bonding inaccessible to elastic dipoles, quadrupoles and other nematic colloids studied previously. PMID:26864184
NASA Astrophysics Data System (ADS)
Senyuk, Bohdan; Puls, Owen; Tovkach, Oleh M.; Chernyshuk, Stanislav B.; Smalyukh, Ivan I.
2016-02-01
Outermost occupied electron shells of chemical elements can have symmetries resembling that of monopoles, dipoles, quadrupoles and octupoles corresponding to filled s-, p-, d- and f-orbitals. Theoretically, elements with hexadecapolar outer shells could also exist, but none of the known elements have filled g-orbitals. On the other hand, the research paradigm of `colloidal atoms' displays complexity of particle behaviour exceeding that of atomic counterparts, which is driven by DNA functionalization, geometric shape and topology and weak external stimuli. Here we describe elastic hexadecapoles formed by polymer microspheres dispersed in a liquid crystal, a nematic fluid of orientationally ordered molecular rods. Because of conically degenerate boundary conditions, the solid microspheres locally perturb the alignment of the nematic host, inducing hexadecapolar distortions that drive anisotropic colloidal interactions. We uncover physical underpinnings of formation of colloidal elastic hexadecapoles and describe the ensuing bonding inaccessible to elastic dipoles, quadrupoles and other nematic colloids studied previously.
Structure of the K{sup {pi}} = 4{sup +} bands in {sup 186,188}Os
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.; Bettermann, L.; Braun, N.; Burke, D. G.; Faestermann, T.; Kruecken, R.; Wirth, H.-F.; Hertenberger, R.
2009-01-28
The structures of {sub 3}{sup +} states in Os have been debated over several decades. Based on measured B(E2) values they were interpreted in {sup 186-192}Os as K{sup {pi}} = 4{sup +} two-phonon vibrations, whereas inelastic scattering, and (t,{alpha}) work imply a hexadecapole phonon description. To clarify the nature of these K{sup {pi}} = 4{sup +} bands in {sup 186,188}Os, we performed a ({sup 3}He,d) reaction on {sup 185,187}Re targets using 30 MeV {sup 3}He beams and a Q3D spectrograph. Absolute cross sections were obtained for excited states up to 3 MeV at 9 angles from 5 deg. to 50 deg. Results indicate a significant (5/2){sup +}[402]{sub {pi}}+(3/2){sup +}[402]{sub {pi}} component in agreement with quasiparticle phonon model predictions for a single hexadecapole phonon structure.
a Survey of Giant Resonance Excitations with 200 Mev Protons
NASA Astrophysics Data System (ADS)
Tinsley, James Royce
The giant resonance region in ('60)Ni, ('90)Zr, ('120)Sn, and ('208)Pb has been studied using inelastic scattering of 200 MeV protons. Angular distributions were obtained for the giant quadrupole resonance, giant octupole resonance, and for the combined giant dipole and giant monopole resonance between 4 and 20 degrees. The 2(H/2PI)(omega) component of the giant hexadecapole resonance has been directly observed for the first time in ('208)Pb. In the other nuclei, upper limits on the amount of hexadecapole strength contained within the giant quadrupole resonance have been obtained. Peaks are observed in ('60)Ni and ('90)Zr that are consistent with recently reported M1 states. Discrepancies between sum rules extracted from this data and from previous work are discussed. Possible explanations include DWBA breakdown or difficulties in estimating the magnitude of the continuum. Systematics obtained for the giant resonances are compared to earlier work.
Study of mixed-symmetry excitations in 96Ru via inelastic proton-scattering
NASA Astrophysics Data System (ADS)
Hennig, A.; Spieker, M.; Werner, V.; Ahn, T.; Anagnostatou, V.; Cooper, N.; Derya, V.; Elvers, M.; Endres, J.; Goddard, P.; Heinz, A.; Hughes, R. O.; Ilie, G.; Mineva, M. N.; Pickstone, S. G.; Petkov, P.; Radeck, D.; Ross, T.; Savran, D.; Zilges, A.
2015-02-01
Mixed-symmetry states of octupole (L = 3) and hexadecapole (L = 4) character have been recently proposed in the N = 52 isotones 92 Zr and 94Mo, based on strong M1 transitions to the lowest-lying 3- and 4+ states, respectively. In order to investigate similar excitations in the heaviest stable N = 52 isotone 96Ru, two inelastic proton-scattering experiments have been performed at the Wright Nuclear Structure Laboratory (WNSL), Yale University, USA and the Institute for Nuclear Physics, University of Cologne, Germany. From the combined data of both experiments, absolute E1, M1, and E2 transition strengths were extracted, allowing for the identification of candidates for MS octupole and hexadecapole states. The structure of the low-lying 4+ states is investigated by means of sdg-IBM-2 calculations.
Measuring Omega and the real correlation function from the redshift correlation function
NASA Technical Reports Server (NTRS)
Hamilton, A. J. S.
1992-01-01
Peculiar velocities distort the correlation function of galaxies in redshift space. In the linear regime, the distortion has a characteristic quadrupole plus hexadecapole form. The amplitude of the distortion depends on the cosmological density parameter Omega. Practical formulas are derived here which can be applied to redshift galaxy catalogs to measure Omega in the linear regime. The formulas also yield the real underlying correlation function in the linear regime, corrected for peculiar velocities.
Omega from the anisotropy of the redshift correlation function in the IRAS 2 Jansky survey
NASA Technical Reports Server (NTRS)
Hamilton, A. J. S.
1993-01-01
Peculiar velocities distort the correlation function of galaxies in redshift space. In the linear regime, the distortion has a characteristic quadrupole plus hexadecapole form, with amplitude depending on the cosmological density parameter Omega. I report here measurements of the anisotropy of the correlation function in the IRAS 2 Jy redshift survey. The inferred value of Omega is Omega = 0.5 + 0.5 or - 0.25.
Beam energy dependence of azimuthal anisotropy at RHIC-PHENIX
Taranenko, A.
2012-05-15
Recent PHENIX measurements of the elliptic ({upsilon}{sub 2}) and hexadecapole ({upsilon}{sub 4}) Fourier flow coefficients for charged hadrons as a function of transverse momentum (p{sub T}), collision centrality and particle species are presented and compared with results from the PHOBOS and STAR Collaborations respectively. The status of extensions to future PHENIX measurements at lower beam energies is also discussed.
Effective no-hair relations for neutron stars and quark stars: Relativistic results
NASA Astrophysics Data System (ADS)
Yagi, Kent; Kyutoku, Koutarou; Pappas, George; Yunes, Nicolás; Apostolatos, Theocharis A.
2014-06-01
Astrophysical charge-free black holes are known to satisfy no-hair relations through which all multipole moments can be specified in terms of just their mass and spin angular momentum. We here investigate the possible existence of no-hair-like relations among multipole moments for neutron stars and quark stars that are independent of their equation of state. We calculate the multipole moments of these stars up to hexadecapole order by constructing uniformly rotating and unmagnetized stellar solutions to the Einstein equations. For slowly rotating stars, we construct stellar solutions to quartic order in spin in a slow-rotation expansion, while for rapidly rotating stars, we solve the Einstein equations numerically with the LORENE and RNS codes. We find that the multipole moments extracted from these numerical solutions are consistent with each other and agree with the quartic-order slow-rotation approximation for spin frequencies below roughly 500 Hz. We also confirm that the current dipole is related to the mass quadrupole in an approximately equation-of-state-independent fashion, which does not break for rapidly rotating neutron stars or quark stars. We further find that the current-octupole and the mass-hexadecapole moments are related to the mass quadrupole in an approximately equation-of-state-independent way to roughly O(10%), worsening in the hexadecapole case. All of our findings are in good agreement with previous work that considered stellar solutions to leading order in a weak-field, Newtonian expansion. In fact, the hexadecapole-quadrupole relation agrees with the Newtonian one quite well even in moderately relativistic regimes. The quartic in spin, slowly rotating solutions found here allows us to estimate the systematic errors in the measurement of the neutron star's mass and radius with future x-ray observations, such as Neutron star Interior Composition ExploreR (NICER) and Large Observatory for X-ray Timing (LOFT). We find that the effect of these
Collective excitations of 96Ru by means of (p ,p'γ ) experiments
NASA Astrophysics Data System (ADS)
Hennig, A.; Ahn, T.; Anagnostatou, V.; Blazhev, A.; Cooper, N.; Derya, V.; Elvers, M.; Endres, J.; Goddard, P.; Heinz, A.; Hughes, R. O.; Ilie, G.; Mineva, M. N.; Petkov, P.; Pickstone, S. G.; Pietralla, N.; Radeck, D.; Ross, T. J.; Savran, D.; Spieker, M.; Werner, V.; Zilges, A.
2015-12-01
Background: One-phonon mixed-symmetry quadrupole excitations are a well-known feature of near-spherical, vibrational nuclei. Their interpretation as a fundamental building block of vibrational structures is supported by the identification of multiphonon states resulting from a coupling of fully-symmetric and mixed-symmetric quadrupole phonons. In addition, the observation of strong M 1 transitions between low-lying 3- and 4+ states has been interpreted as an evidence for one-phonon mixed-symmetry excitations of octupole and hexadecapole character. Purpose: The aim of the present study is to identify collective one- and two-phonon excitations in the heaviest stable N =52 isotone 96Ru based on a measurement of absolute M 1 , E 1 , and E 2 transition strengths. Methods: Inelastic proton-scattering experiments have been performed at the Wright Nuclear Structure Laboratory (WNSL), Yale University, and the Institute for Nuclear Physics (IKP), University of Cologne. From the acquired proton-γ and γ γ coincidence data we deduced spins of excited states, γ -decay branching ratios, and multipole mixing ratios, as well as lifetimes of excited states via the Doppler-shift attenuation method (DSAM). Results: Based on the new experimental data on absolute transition strengths, we identified the 2+ and 3+ members of the two-phonon mixed-symmetry quintuplet (21,ms +⊗21,s +) . Furthermore, we observed strong M 1 transitions between low-lying 3- and 4+ states suggesting one-phonon symmetric and mixed-symmetric octupole and hexadecapole components in their wave functions, respectively. The experimental results are compared to s d g -IBM-2 and shell-model calculations. Conclusions: Both the s d g -IBM-2 and the shell-model calculations are able to describe key features of mixed-symmetry excitations of 96Ru. Moreover, they support the one-phonon mixed-symmetry hexadecapole assignment of the experimental 42+ state.
NASA Technical Reports Server (NTRS)
Varanasi, P.; Sarangi, S.
1974-01-01
Collision-broadened line widths in CO-CO2 and CO-O2 collisions have been calculated by incorporating interactions due to octopoles and hexadecapoles and short-range repulsive interactions into Anderson's (1949) theory. It is shown how these higher-order interactions can be manipulated to yield good agreement with experimental data. A critical evaluation of this totally empirical manipulation suggests that a thorough revision of the theory is required for all but simple dipole-dipole interactions. In the process of the evaluation, the values of the multipole moments are discussed.
NASA Technical Reports Server (NTRS)
Varanasi, P.; Sarangi, S.
1974-01-01
Collision-broadened line widths in CO-CO2 and CO-O2 collisions have been calculated by incorporating interactions due to octopoles and hexadecapoles and short-range repulsive interactions into Anderson's (1949) theory. It is shown how these higher-order interactions can be manipulated to yield good agreement with experimental data. A critical evaluation of this totally empirical manipulation suggests that a thorough revision of the theory is required for all but simple dipole-dipole interactions. In the process of the evaluation, the values of the multipole moments are discussed.
Ternary fission of nuclei into comparable fragments
Karpeshin, F. F.
2015-07-15
The problem of nuclear fission into three comparable fragments is considered. A mechanism of true ternary fission is proposed. In contrast to sequential fission, where the three fragments arise upon two sequential events of binary fission, the mechanism in question relies on a scenario that originally involves fission into three fragments. This mechanism is driven by a hexadecapole deformation of the fissioning nucleus, in contrast to binary fission associated with quadrupole vibrations of the nuclear surface. The fragment-mass ratios are estimated. The dynamics of formation of collinear fragments and their subsequent motion in opposite directions is traced. The calculated probability of true ternary fission complies with observed values.
Realistic collective nuclear Hamiltonian
NASA Astrophysics Data System (ADS)
Dufour, Marianne; Zuker, Andrés P.
1996-10-01
The residual part of the realistic forces-obtained after extracting the monopole terms responsible for bulk properties-is strongly dominated by pairing and quadrupole interactions, with important στ.στ, octupole, and hexadecapole contributions. Their forms retain the simplicity of the traditional pairing plus multipole models, while eliminating their flaws through a normalization mechanism dictated by a universal A-1/3 scaling. Coupling strengths and effective charges are calculated and shown to agree with empirical values. Comparisons between different realistic interactions confirm the claim that they are very similar.
A Finite Field Method for Calculating Molecular Polarizability Tensors for Arbitrary Multipole Rank
Elking, Dennis M.; Perera, Lalith; Duke, Robert; Darden, Thomas; Pedersen, Lee G.
2011-01-01
A finite field method for calculating spherical tensor molecular polarizability tensors αlm;l′m′ = ∂Δlm/∂ϕl′m′* by numerical derivatives of induced molecular multipole Δlm with respect to gradients of electrostatic potential ϕl′m′* is described for arbitrary multipole ranks l and l′. Inter-conversion formulae for transforming multipole moments and polarizability tensors between spherical and traceless Cartesian tensor conventions are derived. As an example, molecular polarizability tensors up to the hexadecapole-hexadecapole level are calculated for water at the HF, B3LYP, MP2, and CCSD levels. In addition, inter-molecular electrostatic and polarization energies calculated by molecular multipoles and polarizability tensors are compared to ab initio reference values calculated by the Reduced Variation Space (RVS) method for several randomly oriented small molecule dimers separated by a large distance. It is discussed how higher order molecular polarizability tensors can be used as a tool for testing and developing new polarization models for future force fields. PMID:21915883
Plattner, Nuria; Meuwly, Markus
2008-01-01
The influence of electrostatic multipole moments up to hexadecapole on the dynamics of photodissociated carbon monoxide (CO) in myoglobin is investigated. The CO electrostatic potential is expressed as an expansion into atomic multipole moments of increasing order up to octopole which are obtained from a distributed multipole analysis. Three models with increasingly accurate molecular multipoles (accurate quadrupole, octopole, and hexadecapole moments, respectively) are developed and used in molecular dynamics simulations. All models with a fluctuating quadrupole moment correctly describe the location of the B-state whereas the sign of the octopole moment differentiates between the Fe···CO and Fe···OC orientation. For the infrared spectrum of photodissociated CO, considerable differences between the three electrostatic models are found. The most detailed electrostatic model correctly reproduces the splitting, shift, and width of the CO spectrum in the B-state. From an analysis of the trajectories, the spectroscopic B1 and B2 states are assigned to the Fe···CO and Fe···OC substates, respectively. PMID:18178640
Special features of the K = 0 channel in nuclear fission
Barabanov, A. L.; Furman, W. I.
2009-08-15
The opinion that the K = 0 fission channel is completely closed if the spin J and the parity {pi} of the nucleus undergoing fission do not satisfy the condition (-1){sup J} = {pi} is widespread. On the basis of a detailed analysis of quantum numbers characterizing the rotational states of deformed nuclei, it is shown that this opinion is erroneous. In fact, the K = 0 channel may be partly open. Its suppression is caused by special features of fission barriers in the state being considered. It is also shown that factors that suppress the K = 0channel may exist even in states characterized by J and {pi} values such that they satisfy the condition (-1){sup J} = {pi}. More precise information about the contribution of the K = 0 channel may be obtained by measuring the hexadecapole component of the angular distribution of fragments originating from the slow-neutron-induced fission of aligned nuclei.
Polarisability and dispersion properties of SF 6
NASA Astrophysics Data System (ADS)
Fowler, P. W.; Kelly, H. M.; Steiner, E.
1993-02-01
Electric properties of the SF 6 molecule are surveyed. Coupled Hartree—Fock calculations of the dipole, dipole—octopole and quadrupole polarisabilities of SF 6 in a polarised basis given values of α = 27, E = 107, C = 229 and Δ C = 113 (all in au). Allowing for the large vibrational contribution to the experimental static polarisability, agreement is good, with CHF theory underestimating α by about 10%. The calculated hexadecapole moment of -25.7 e a40 is within the range of experimental estimates, but the calculated dipole—octopole polarisability E is smaller than previous model and estimated experimental values by an order of magnitude. A large vibrational contribution to E is predicted. Dispersion coefficients C6, C8 and Δ C8 are calculated for SF 6 paired with itself and rare gas atoms, and comparison is made with the sparse experimental data.
Investigation of phonon excitations in {sup 114}Cd with the (n,n{sup '}{gamma}) reaction
Bandyopadhyay, D.; Lesher, S. R.; Fransen, C.; Boukharouba, N.; McEllistrem, M. T.; Garrett, P. E.; Green, K. L.; Yates, S. W.
2007-11-15
Properties of low-spin states in {sup 114}Cd have been studied with the (n,n{sup '}{gamma}) reaction. Gamma-ray angular distributions and excitation functions have been used to characterize the decays of the excited levels. Level lifetimes have been obtained with the Doppler-shift attenuation method. Sixteen new levels and many new transitions have been suggested below 3.5 MeV in excitation energy. Levels belonging to the phonon multiplets have been proposed based on their decay patterns and collectivity, and the existing intruder structure has been extended. A two-phonon 1{sub ms}{sup +} state has been suggested. Excitation of the hexadecapole moment has been considered. Data have been compared with the theoretical calculations of the interacting boson model.
Structure of the K{sup {pi}=}4{sup +} bands in {sup 186,188}Os
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.; Lo Iudice, N.; Sushkov, A. V.; Bettermann, L.; Braun, N.; Burke, D. G.; Faestermann, T.; Kruecken, R.; Wirth, H.-F.; Hertenberger, R.
2010-09-15
The ({sup 3}He, d) single-proton stripping reaction has been performed on targets of {sup 185,187}Re to investigate the structures of the 4{sub 3}{sup +} states in {sup 186,188}Os. The experiment employed 30 MeV {sup 3}He beams, and the reaction products were analyzed with a Q3D spectrograph. Absolute cross sections were determined at nine angles between 5 deg. and 50 deg. for states up to approximately 3 MeV in excitation energy. Large (5/2){sup +}[402]{sub {pi}+}(3/2){sup +}[402]{sub {pi}}two-quasiparticle components are deduced for the 4{sub 3}{sup +} 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, {gamma}-{gamma} component in the 4{sub 3}{sup +}.
Nature of the K{sup {pi}} = 4{sup +} bands in the Os isotopes
Garrett, P. E.; Phillips, A. A.; Braun, N.; Demand, G. A.; Finlay, P.; Green, K. L.; Leach, K. G.; Schumaker, M. A.; Svensson, C. E.; Wong, J.; Bettermann, L.; Burke, D. G.; Faestermann, T.; Kruecken, R.; Wirth, H.-F.; Hertenberger, R.
2008-05-12
Levels in {sup 186,188}Os have been investigated using the ({sup 3}He,d) reaction with 30 MeV {sup 3}He beams. Absolute level-population cross sections have been determined, and angular distributions measured between 5 deg. and 50 deg. The 4{sub 3}{sup +} levels are observed to be some of the strongest populated states below 2 MeV excitation energy, and the magnitudes of the 5/2{sup +}[402]{sub {pi}}+3/2{sup +}[402]{sub {pi}} configuration extracted are in line with quasiparticle-phonon model predictions which state that the lowest-lying K{sup {pi}} = 4{sup +} band is predominantly a hexadecapole excitation.
Microscopic Calculations of 240Pu Fission
Younes, W; Gogny, D
2007-09-11
Hartree-Fock-Bogoliubov calculations have been performed with the Gogny finite-range effective interaction for {sup 240}Pu out to scission, using a new code developed at LLNL. A first set of calculations was performed with constrained quadrupole moment along the path of most probable fission, assuming axial symmetry but allowing for the spontaneous breaking of reflection symmetry of the nucleus. At a quadrupole moment of 345 b, the nucleus was found to spontaneously scission into two fragments. A second set of calculations, with all nuclear moments up to hexadecapole constrained, was performed to approach the scission configuration in a controlled manner. Calculated energies, moments, and representative plots of the total nuclear density are shown. The present calculations serve as a proof-of-principle, a blueprint, and starting-point solutions for a planned series of more comprehensive calculations to map out a large set of scission configurations, and the associated fission-fragment properties.
Global Calculations of Ground-State Axial Shape Asymmetry of Nuclei
Moeller, Peter; Bengtsson, Ragnar; Carlsson, B. Gillis; Olivius, Peter; Ichikawa, Takatoshi
2006-10-20
Important insight into the symmetry properties of the nuclear ground-state (gs) shape is obtained from the characteristics of low-lying collective energy-level spectra. In the 1950s, experimental and theoretical studies showed that in the gs many nuclei are spheroidal in shape rather than spherical. Later, a hexadecapole component of the gs shape was identified. In the 1970-1995 time frame, a consensus that reflection symmetry of the gs shape was broken for some nuclei emerged. Here we present the first calculation across the nuclear chart of axial symmetry breaking in the nuclear gs. We show that we fulfill a necessary condition: Where we calculate axial symmetry breaking, characteristic gamma bands are observed experimentally. Moreover, we find that, for those nuclei where axial asymmetry is found, a systematic deviation between calculated and measured masses is removed.
Microscopic structure of low-lying states in {sup 188,190,192}Os
Lo Iudice, N.; Sushkov, A. V.
2008-11-15
The phonon and quasiparticle structure of the low-lying states in {sup 188,190,192}Os is investigated within the microscopic quasiparticle-phonon model. An overall agreement with the data is obtained for energies and transitions. The properties of the 0{sup +} states are found to be correlated with the evolution of the nuclear shape toward the {gamma}-soft region. Special attention is devoted at the 4{sub 3}{sup +} state. This state is found to be composed of a large double-{gamma} phonon component coexisting with an even larger one-phonon hexadecapole piece. Such a mixed phonon structure explains the observed, apparently contradictory, properties of the 4{sub 3}{sup +} states in Os isotopes.
Effect of coupling in the 28Si+154Sm reaction studied by quasi-elastic scattering
NASA Astrophysics Data System (ADS)
Kaur, Gurpreet; Behera, B. R.; Jhingan, A.; Nayak, B. K.; Dubey, R.; Sharma, Priya; Thakur, Meenu; Mahajan, Ruchi; Saneesh, N.; Banerjee, Tathagata; Khushboo, Kumar, A.; Mandal, S.; Saxena, A.; Sugathan, P.; Rowley, N.
2016-09-01
The study of the coupling to collective states of the 28Si projectile and 154Sm target in fusion mechanism is reported. Understanding such couplings is important as they influence the barrier height and the formation probability of the compound nuclei, which in turn may be related to the synthesis of superheavy elements in heavier systems. In the present work, before performing the coupled-channel calculations, we wish to obtain an experimental signature of coupling to projectile and target excitation through barrier distribution (BD) study. To this end, the BDs of the 28Si+154Sm and 16O+154Sm systems have been compared using existing fusion data, scaled to compensate for the differences between the nominal Coulomb barriers and the respective coupling strengths. However, the large error bars on the high-energy side of the fusion BD prevent any definite identification of such signatures. We have, therefore, performed a quasi-elastic (QE) scattering experiment for the heavier 28Si+154Sm system and compared its results with existing QE data for the 16O projectile. Since QE BDs are precise at higher energies, the comparison has shown that the BD of 28Si+154Sm is similar to that of 16O+154Sm to a large extent except for a peaklike structure on the higher energy side. The similarity shows that the 154Sm deformation plays a major role in the fusion mechanism of 28Si+154Sm system. The peaklike structure is attributed to 28Si excitation. In contrast with previous studies, it is found that a coupled-channel calculation with vibrational coupling to the first 2+ state of 28Si reproduces this structure rather well. However, an almost identical result is found with the rotational coupling scheme if one considers the large positive hexadecapole deformation of the projectile. A value around that given by Möller and Nix (β4≈0.25 ) leads to a strong cancellation in the re-orientation term that couples the 2+ state back to itself, making that state look vibrational in this
Polarizable atomic multipole X-ray refinement: application to peptide crystals
Schnieders, Michael J.; Fenn, Timothy D.; Pande, Vijay S.; Brunger, Axel T.
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 Gaussian 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.
NASA Astrophysics Data System (ADS)
Zhao, Gong-Bo; Wang, Yuting; Saito, Shun; Wang, Dandan; Ross, Ashley J.; Beutler, Florian; Grieb, Jan Niklas; Chuang, Chia-Hsun; Kitaura, Francisco-Shu; Rodriguez-Torres, Sergio; Percival, Will J.; Brownstein, Joel R.; Cuesta, Antonio J.; Eisenstein, Daniel J.; Gil-Marín, Héctor; Kneib, Jean-Paul; Nichol, Robert C.; Olmstead, Matthew D.; Prada, Francisco; Rossi, Graziano; Salazar-Albornoz, Salvador; Samushia, Lado; Sánchez, Ariel G.; Thomas, Daniel; Tinker, Jeremy L.; Tojeiro, Rita; Weinberg, David H.; Zhu, Fangzhou
2017-04-01
We perform a tomographic baryon acoustic oscillations (BAO) analysis using the monopole, quadrupole and hexadecapole of the redshift-space galaxy power spectrum measured from the pre-reconstructed combined galaxy sample of the completed Sloan Digital Sky Survey Baryon Oscillation Spectroscopic Survey (BOSS) Data Release12 covering the redshift range of 0.20 < z < 0.75. By allowing for overlap between neighbouring redshift slices, we successfully obtained the isotropic and anisotropic BAO distance measurements within nine redshift slices to a precision of 1.5-3.4 per cent for DV/rd, 1.8-4.2 per cent for DA/rd and 3.7-7.5 per cent for H rd, depending on effective redshifts. We provide our BAO measurement of DA/rd and H rd with the full covariance matrix, which can be used for cosmological implications. Our measurements are consistent with those presented in Alam et al., in which the BAO distances are measured at three effective redshifts. We constrain dark energy parameters using our measurements and find an improvement of the Figure-of-Merit of dark energy in general due to the temporal BAO information resolved. This paper is a part of a set that analyses the final galaxy clustering data set from BOSS.
NASA Astrophysics Data System (ADS)
Beutler, Florian; Seo, Hee-Jong; Saito, Shun; Chuang, Chia-Hsun; Cuesta, Antonio J.; Eisenstein, Daniel J.; Gil-Marín, Héctor; Grieb, Jan Niklas; Hand, Nick; Kitaura, Francisco-Shu; Modi, Chirag; Nichol, Robert C.; Olmstead, Matthew D.; Percival, Will J.; Prada, Francisco; Sánchez, Ariel G.; Rodriguez-Torres, Sergio; Ross, Ashley J.; Ross, Nicholas P.; Schneider, Donald P.; Tinker, Jeremy; Tojeiro, Rita; Vargas-Magaña, Mariana
2017-04-01
We investigate the anisotropic clustering of the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 12 sample, which consists of 1198 006 galaxies in the redshift range 0.2 < z < 0.75 and a sky coverage of 10 252 deg2. We analyse this data set in Fourier space, using the power-spectrum multipoles to measure redshift-space distortions simultaneously with the Alcock-Paczynski effect and the baryon acoustic oscillation scale. We include the power-spectrum monopole, quadrupole and hexadecapole in our analysis and compare our measurements with a perturbation-theory-based model, while properly accounting for the survey window function. To evaluate the reliability of our analysis pipeline, we participate in a mock challenge, which results in systematic uncertainties significantly smaller than the statistical uncertainties. While the high-redshift constraint on fσ8 at zeff = 0.61 indicates a small (∼1.4σ) deviation from the prediction of the Planck ΛCDM (Λ cold dark matter) model, the low-redshift constraint is in good agreement with Planck ΛCDM. This paper is part of a set that analyses the final galaxy clustering data set from BOSS. The measurements and likelihoods presented here are combined with others in Alam et al. to produce the final cosmological constraints from BOSS.
Direct inelastic scattering of N/sub 2/ from Ag(111). I. Rotational populations and alignment
Sitz, G.O.; Kummel, A.C.; Zare, R.N.
1988-08-15
The rotational state populations and the quadrupole and hexadecapole alignment moments of N/sub 2/ scattered off clean Ag(111) are determined by resonance enhanced multiphoton ionization (REMPI). The scattered N/sub 2/ is found to be highly aligned with its rotational angular momentum vector J parallel to the surface. The degree of alignment is found to increase with increasing rotational excitation. We see less than perfect alignment at intermediate J values indicating that the surface is not completely flat. The alignment is relatively insensitive to incident energy, incident angle, or surface temperature T/sub s/. However, the rotational state population distributions show pronounced rainbows for higher incident energy and/or more grazing exit angle. The rotational state distributions are found to depend strongly on the final scattering angle at low T/sub s/; this effect is markedly reduced at higher T/sub s/. Time-of-flight measurements are used to determine the average velocity of the scattered N/sub 2/ as a function of rotational level. It is found that higher rotational excitation correlates with lower average velocity and that the incident molecules lose 20%--30% of their translational energy to the solid. No correlation is found between velocity and alignment. A comparison is made with published results for the NO/Ag(111) system and a variety of theoretical models found in the literature.
Multiproperty empirical isotropic interatomic potentials for CH4-inert gas mixtures.
El-Kader, M S A
2013-11-01
An approximate empirical isotropic interatomic potentials for CH4-inert gas mixtures are developed by simultaneously fitting the Exponential-Spline-Morse-Spline-van der Waals (ESMSV) potential form to viscosity, thermal conductivity, thermal diffusion factors, diffusion coefficient, interaction second pressure virial coefficient and scattering cross-section data. Quantum mechanical lineshapes of collision-induced absorption (CIA) at different temperatures for CH4-He and at T = 87 K for CH4-Ar are computed using theoretical values for overlap, octopole and hexadecapole mechanisms and interaction potential as input. Also, the quantum mechanical lineshapes of collision-induced light scattering (CILS) for the mixtures CH4-Ar and CH4-Xe at room temperature are calculated. The spectra of scattering consist essentially of an intense, purely translational component which includes scattering due to free pairs and bound dimers, and the other is due to the induced rotational scattering. These spectra have been interpreted by means of pair-polarizability terms, which arise from a long-range dipole-induced-dipole (DID) with small dispersion corrections and a short-range interaction mechanism involving higher-order dipole-quadrupole A and dipole-octopole E multipole polarizabilities. Good agreement between computed and experimental lineshapes of both absorption and scattering is obtained when the models of potential, interaction-induced dipole and polarizability components are used.
Systematic study of deformation effects on fusion cross-sections using various proximity potentials
NASA Astrophysics Data System (ADS)
Rajbongshi, Tapan; Kalita, Kushal
2014-06-01
The influence of static quadrupole and hexadecapole (positive & negative) deformation of targets are studied using eleven different versions of nuclear potentials. The height and position of the interaction barrier for the reactions induced by spherical projectile (16O) on the deformed targets such as 166Er, 154Sm and 176Yb have been estimated. It is found that the nucleus-nucleus potential strongly depends on the value of the deformation parameters and orientation of the target. The experimental fusion cross-section of the reactions 16O + 176Yb, 16O +166Er and 16O +154Sm are investigated by applyingWong's formula using various parameterizations of the proximity potential as well as an assessment of the results of a multi-dimensional barrier penetration model (BPM). The fusion cross-sections by Prox 77, Prox 88, Prox 00, Prox 00DP, Denisov DP, Bass 80, CW 76 and AW 95 potentials are found to be better than the rest in comparison to experimental data.
Asai, M.; Tsukada, K.; Ishii, Y.; Toyoshima, A.; Ishii, T.; Nagame, Y.; Nishinaka, I.; Haba, H.; Ichikawa, T.; Kojima, Y.; Sueki, K.
2011-01-15
Excited states in {sup 251}Fm populated via the {alpha} decay of {sup 255}No are studied in detail through {alpha}-{gamma} coincidence and {alpha} fine-structure measurements. Five excited states reported previously in {sup 251}Fm are firmly established through the {alpha}-{gamma} coincidence measurement, and rotational bands built on one-quasiparticle states are newly established through the {alpha} fine-structure measurement. Spin-parities and neutron configurations of the excited states in {sup 251}Fm as well as the ground state of {sup 255}No are definitely identified on the basis of deduced internal conversion coefficients, lifetimes of {gamma} transitions, rotational-band energies built on one-quasiparticle states, and hindrance factors of {alpha} transitions. It is found that the excitation energy of the 1/2{sup +}[620] state in N=151 isotones increases with the atomic number, especially at Z{>=}100, while that of the 1/2{sup +}[631] state decreases at Z=100. Ground-state deformations and energies of neutron one-quasiparticle states in the N=151 isotones are calculated using a macroscopic-microscopic model, and the energy systematics of the one-quasiparticle states in the isotones are discussed in terms of the evolution of nuclear deformation involving the hexadecapole ({beta}{sub 4}) and hexacontatetrapole ({beta}{sub 6}) deformations.
Recent developments in the tidal deformability of spinning compact objects
NASA Astrophysics Data System (ADS)
Pani, Paolo; Gualtieri, Leonardo; Maselli, Andrea; Ferrari, Valeria
2016-04-01
We review recent work on the theory of tidal deformability and the tidal Love numbers of a slowly spinning compact object within general relativity. Angular momentum introduces couplings between distortions of different parity and new classes of spin-induced, tidal Love numbers emerge. Due to spin-tidal effects, a rotating object immersed in a quadrupolar, electric tidal field can acquire some induced mass, spin, quadrupole, octupole and hexadecapole moments to second-order in the spin. The tidal Love numbers depend strongly on the object’s internal structure. All tidal Love numbers of a Kerr black hole (BH) were proved to be exactly zero to first-order in the spin and also to second-order in the spin, at least in the axisymmetric case. For a binary system close to the merger, various components of the tidal field become relevant. Preliminary results suggest that spin-tidal couplings can introduce important corrections to the gravitational waveforms of spinning neutron star (NS) binaries approaching the merger.
NASA Astrophysics Data System (ADS)
Möller, P.; Sierk, A. J.; Bengtsson, R.; Sagawa, H.; Ichikawa, T.
2012-03-01
We calculate potential-energy surfaces as functions of spheroidal (ɛ2), hexadecapole (ɛ4), and axial-asymmetry (γ) shape coordinates for 7206 nuclei from A=31 to A=290. We tabulate the deformations and energies of all minima deeper than 0.2 MeV and of the saddles between all pairs of minima. The tabulation is terminated at N=160. Our study is based on the FRLDM macroscopic-microscopic model defined in ATOMIC DATA AND NUCLEAR DATA TABLES [P. Möller, J.R. Nix, W.D. Myers, W.J. Swiatecki, At. Data Nucl. Data Tables 59 (1995) 185]. We also present potential-energy contour plots versus ɛ2 and γ for 1224 even-even nuclei in the region studied. We can identify nuclei for which a necessary condition for shape isomers occurs, namely multiple minima in the calculated potential-energy surface. We find that the vast majority of nuclear shape isomers occur in the A=80 region, the A=100 region, and in a more extended region centered around 208Pb. A calculated region of shape isomers that has so far not been extensively explored is the region of neutron-deficient actinides "north-east" of 208Pb.
Cluster radioactivity with effects of deformations and orientations of nuclei included
Arun, Sham K.; Gupta, Raj K.; Kanwar, Shefali; Singh, BirBikram; Sharma, Manoj K.
2009-09-15
Based on the preformed cluster model (PCM) of Gupta and collaborators, we have extended our recent study on ground-state cluster decays to parent nuclei resulting in daughters other than spherical {sup 208}Pb, i.e., to deformed daughters, and the very new cases of {sup 14}C and {sup 15}N decays of {sup 223}Ac, and {sup 34}Si decay of {sup 238}U, taking nuclei as spherical, quadrupole deformed ({beta}{sub 2}) alone, and with higher multipole deformations up to hexadecapole ({beta}{sub 2}, {beta}{sub 3}, {beta}{sub 4}) together with the 'optimum' orientations of cold decay process. Except for {sup 14}C decays of {sup 221}Fr, {sup 221-224,226}Ra, and {sup 225}Ac where higher multipole deformations up to {beta}{sub 4} are found essential, the quadrupole deformation {beta}{sub 2} alone is found good enough to fit the experimental data. Because the PCM treats the cluster-decay process as the tunneling of a preformed cluster, the deformations and orientations of nuclei modify both the preformation probability P{sub 0} and tunneling probability P, and hence the decay half-life, considerably.
NASA Astrophysics Data System (ADS)
Matsumura, Takeshi; Michimura, Shinji; Inami, Toshiya; Hayashi, Yuya; Fushiya, Kengo; Matsuda, Tatsuma D.; Higashinaka, Ryuji; Aoki, Yuji; Sugawara, Hitoshi
2014-04-01
The antiferromagnetic ordered phase in SmRu4P12 below the metal-insulator transition at TMI=16.5 K with an unresolved transition at T*˜14 K has been studied by resonant and nonresonant x-ray diffraction in magnetic fields. In the intermediate phase, a nonresonant Thomson scattering with q =(1,0,0) is induced by applying a magnetic field, which is presumably caused by atomic displacements reflecting the charge order in the p band, as predicted theoretically [R. Shiina, J. Phys. Soc. Jpn. 82, 083713 (2013), 10.7566/JPSJ.82.083713]. Simultaneously, the antiferromagnetic moment of Sm is enhanced along the field direction, which is considered to reflect the staggered ordering of the Γ7-Γ8 crystal-field states (scalar or hexadecapole order). The present results show that the orbital-dependent p-f hybridization in association with the nesting instability in the p band gives rise to the unconventional charge order similarly with PrRu4P12 and PrFe4P12.
Avramopoulos, A; Papadopoulos, M G; Reis, H
2007-03-15
A discrete model based on the multipolar expansion including terms up to hexadecapoles was employed to describe the electrostatic interactions in liquid acetonitrile. Liquid structures obtained form molecular dynamics simulations with different classical, nonpolarizable potentials were used to analyze the electrostatic interactions. The computed average local field was employed for the determination of the environmental effects on the linear and nonlinear electrical molecular properties. Dipole-dipole interactions yield the dominant contribution to the local field, whereas higher multipolar contributions are small but not negligible. Using the effective in-phase properties, macroscopic linear and nonlinear susceptibilities of the liquid were computed. Depending on the partial charges describing the Coulomb interactions of the force field employed, either the linear properties (refractive index and dielectric constant) were reproduced in good agreement with experiment or the nonlinear properties [third-harmonic generation (THG) and electric field induced second-harmonic (EFISH) generation] and the bulk density but never both sets of properties together. It is concluded that the partial charges of the force fields investigated are not suitable for reliable dielectric properties. New methods are probably necessary for the determination of partial charges, which should take into account the collective and long-range nature of electrostatic interactions more precisely.
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.
HPAM: Hirshfeld Partitioned Atomic Multipoles
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
Molecular multipole moments of water molecules in ice Ih
NASA Astrophysics Data System (ADS)
Batista, Enrique R.; Xantheas, Sotiris S.; Jónsson, Hannes
1998-09-01
We have used an induction model including dipole, dipole-quadrupole, quadrupole-quadrupole polarizability and first hyperpolarizability as well as fixed octopole and hexadecapole moments to study the electric field in ice. The self-consistent induction calculations gave an average total dipole moment of 3.09 D, a 67% increase over the dipole moment of an isolated water molecule. A previous, more approximate induction model study by Coulson and Eisenberg [Proc. R. Soc. Lond. A 291, 445 (1966)] suggested a significantly smaller average value of 2.6 D. This value has been used extensively in recent years as a reference point in the development of various polarizable interaction potentials for water as well as for assessment of the convergence of water cluster properties to those of bulk. The reason for this difference is not due to approximations made in the computational scheme of Coulson and Eisenberg but rather due to the use of less accurate values for the molecular multipoles in these earlier calculations.
Universal correlations of nuclear observables and the structure of exotic nuclei
Casten, R.F.; Zamfir, N.V. |||
1996-12-31
Despite the apparent complexity of nuclear structural evolution, recent work has shown a remarkable underlying simplicity that is unexpected, global, and which leads to new signatures for structure based on the easiest-to-obtain data. As such they will be extremely valuable for use in the experiments with low intensity radioactive beams. Beautiful correlations based either on extrinsic variables such as N{sub p}N{sub n} or the P-factor or correlations between collective observables themselves have been discovered. Examples to be discussed include a tri-partite classification of structural evolution, leading to a new paradigm that discloses certain specific classes of nuclei, universal trajectories for B(E2: w{sub 1}{sup +} {r_arrow} 0{sub 1}{sup +}) values and their use in extracting hexadecapole deformations from this observable alone, the use of these B(E2) values to identify shell gaps and magic numbers in exotic nuclei, the relationship of {beta} and {gamma} deformations, and single nucleon separation energies. Predictions for nuclei far off stability by interpolation will also be discussed.
Investigation of {sup 152}Sm by Complementary Reactions
Garrett, P. E.; Kulp, W. D.; Wood, J. L.; Allmond, J. M.; Bandyopadhyay, D.; Choudry, S. N.; Kumar, A.; Lesher, S. R.; McEllistrem, M. T.; Mynk, M. G.; McKay, C. J.; Orce, J. N.; Christen, S.; Dewald, A.; Fitzler, A.; Fransen, C.; Jessen, K.; Jolie, J.; Kloezer, A.; Kudejova, P.
2009-01-28
Understanding the nuclear structure of {sup 152}Sm, along with other N = 90 isotones, has long posed a challenge. A rapid transition in shape between the spherical N = 88 {sup 150}Sm and well-deformed N = 92 {sup 154}Sm is observed, along with strong evidence for shape coexistence. Competing ideas have been put forward over the decades, with the most recent being that N = 90 is at the critical point of a shape phase transition. Until recently, the lack of high-precision data has not allowed the competing models to be extensively tested. In a coordinated program of investigation, a series of complementary experiments, which include high-statistics {beta} decay, multi-step Coulomb excitation, the {sup 150}Nd({alpha},2n) reaction, and the (n,n'{gamma}) reaction, have been performed for {sup 152}Sm. These experiments have revealed the existence of a pairing-isomer band, a hexadecapole band, the lack of multi-phonon {beta} vibrational bands, and the repetition of structures built on the first excited K{sup {pi}} = 0{sup +} as built on the ground state. The status of these coordinated studies is examined.
Precision modeling of redshift-space distortions from a multipoint propagator expansion
NASA Astrophysics Data System (ADS)
Taruya, Atsushi; Nishimichi, Takahiro; Bernardeau, Francis
2013-04-01
Using a full implementation of resummed perturbation theory (PT) from a multipoint propagator expansion, we put forward new theoretical predictions for the two-point statistics of matter fluctuations in redshift space. The predictions consistently include PT corrections up to the two-loop order and are based on an improved prescription of the redshift-space distortions that properly takes into account their non-Gaussian impact from a systematic low-k expansion. In contrast to the previous studies that partly used standard PT calculations, the present treatment is able to provide a consistent prediction for both power spectra and correlation functions. These results are compared with N-body simulations with which a very good agreement is found up to the quadrupole moment. However, the theoretical predictions for the hexadecapole moment of the power spectra are found to significantly depart from the numerical results at low redshift. We examine this issue and find it to be likely related to an improper modeling of the redshift-space distortions damping effects on which this moment shows large dependence.
Tidal deformations of a spinning compact object
NASA Astrophysics Data System (ADS)
Pani, Paolo; Gualtieri, Leonardo; Maselli, Andrea; Ferrari, Valeria
2015-07-01
The deformability of a compact object induced by a perturbing tidal field is encoded in the tidal Love numbers, which depend sensibly on the object's internal structure. These numbers are known only for static, spherically-symmetric objects. As a first step to compute the tidal Love numbers of a spinning compact star, here we extend powerful perturbative techniques to compute the exterior geometry of a spinning object distorted by an axisymmetric tidal field to second order in the angular momentum. The spin of the object introduces couplings between electric and magnetic deformations and new classes of induced Love numbers emerge. For example, a spinning object immersed in a quadrupolar, electric tidal field can acquire some induced mass, spin, quadrupole, octupole and hexadecapole moments to second order in the spin. The deformations are encoded in a set of inhomogeneous differential equations which, remarkably, can be solved analytically in vacuum. We discuss certain subtleties in defining the tidal Love numbers in general relativity, which are due to the difficulty in separating the tidal field from the linear response of the object in the solution, even in the static case. By extending the standard procedure to identify the linear response in the static case, we prove analytically that the Love numbers of a Kerr black hole remain zero to second order in the spin. As a by-product, we provide the explicit form for a slowly-rotating, tidally-deformed Kerr black hole to quadratic order in the spin, and discuss its geodesic and geometrical properties.
Triaxial rotor model description of E2 properties in {sup 186,188,190,192}Os
Allmond, J. M.; Zaballa, R.; Oros-Peusquens, A. M.; Kulp, W. D.; Wood, J. L.
2008-07-15
The triaxial rotor model with independent inertia and electric quadrupole tensors is applied to the description of the extensive set of E2 matrix elements available for {sup 186,188,190,192}Os. Most large and medium transition E2 matrix elements can be reproduced to within {approx}10%, and most diagonal elements to within {approx}30%. Most small transition matrix elements can be reproduced to within {approx}30%, and they support the interference effect exhibited by the model between the inertia and E2 tensors: this is a new feature of quantum rotor models. The diagonal E2 matrix elements at higher spins in the K=2 band are extremely sensitive to admixtures of higher K values: the low experimental values in {sup 190,192}Os indicate significant admixtures of K=4 components. Attention is given to the K{sup {pi}}=4{sup +} bands in these nuclei and the controversial issue of whether they are of quadrupole or hexadecapole nature.
Impacts of satellite galaxies on the redshift-space distortions
Hikage, Chiaki; Yamamoto, Kazuhiro E-mail: kazuhiro@hiroshima-u.ac.jp
2013-08-01
We study the impacts of the satellite galaxies on the redshift-space distortions. In our multipole power spectrum analysis of the luminous red galaxies (LRGs) samples of the Sloan digital sky survey (SDSS), we have clearly detected the non-zero signature of the hexadecapole and tetrahexadecapole spectrum, which almost disappears in the power spectrum with the sample of the brightest LRGs only. We thus demonstrate that the satellite LRGs in multiple systems make a significant contribution to the multipole power spectrum though its fraction is small. The behavior can be understood by a simple halo model, in which the one-halo term, describing the Finger of God (FoG) effect from the satellite galaxies, makes the dominant contribution to the higher multipole spectra. We demonstrate that the small-scale information of higher multipole spectrum is useful for calibrating the satellite FoG effect and improves the measurement of the cosmic growth rate dramatically. We further demonstrate that the fiber collision in the galaxy survey influences the one-halo term and the higher multipole spectra, because the number of satellite galaxies in the halo occupation distribution (HOD) is changed. We also discuss about the impact of satellite galaxies on future high-redshift surveys targeting the H-alpha emitters.
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.
Kandathil, Shaun M; Fletcher, Timothy L; Yuan, Yongna; Knowles, Joshua; Popelier, Paul L A
2013-08-05
We propose a generic method to model polarization in the context of high-rank multipolar electrostatics. This method involves the machine learning technique kriging, here used to capture the response of an atomic multipole moment of a given atom to a change in the positions of the atoms surrounding this atom. The atoms are malleable boxes with sharp boundaries, they do not overlap and exhaust space. The method is applied to histidine where it is able to predict atomic multipole moments (up to hexadecapole) for unseen configurations, after training on 600 geometries distorted using normal modes of each of its 24 local energy minima at B3LYP/apc-1 level. The quality of the predictions is assessed by calculating the Coulomb energy between an atom for which the moments have been predicted and the surrounding atoms (having exact moments). Only interactions between atoms separated by three or more bonds ("1, 4 and higher" interactions) are included in this energy error. This energy is compared with that of a central atom with exact multipole moments interacting with the same environment. The resulting energy discrepancies are summed for 328 atom-atom interactions, for each of the 29 atoms of histidine being a central atom in turn. For 80% of the 539 test configurations (outside the training set), this summed energy deviates by less than 1 kcal mol(-1). Copyright © 2013 Wiley Periodicals, Inc.
/sup 74,76,78,80,82/Se by inelastic scattering of 64. 8 MeV protons
Ogino, K.
1986-01-01
The inelastic scattering of 64.8 MeV protons has been studied on the stable even XU YSSe isotopes. The inelastically scattered protons were momentum analyzed in a magnetic spectrograph with a resulting energy resolution of approximately 20 keV. Levels up to the excitation energy of about 5 MeV were investigated. Many new levels were observed for the isotopes studied. The angular distributions obtained were compared with the predictions of distorted-wave Born approximation and coupled-channels calculations and a number of new spin assignments were proposed. Several 4 states with comparable strengths were found at about E/sub x/ = 2.0--5.0 MeV, showing large fragmentation of octupole and hexadecapole transition strengths, in contrast to the case of Zn isotopes. The distributions of the transition strengths for the 2 , 3 , and 4 states were compared with the theoretical calculations based on the random-phase-approximation model for spherical nuclei.
NASA Astrophysics Data System (ADS)
Kulp, W. D.; Wood, J. L.; Garrett, P. E.
2004-10-01
The N=90 region has long been a focus of collective nuclear model investigations. We report on a program of study which involves both systematic investigations (of ^150Nd, ^152Sm, ^154Gd, and ^156Dy to date) and multi-spectroscopy investigations (radioactive decay, (n,n'γ), (α, 2nγ) and multi-Coulex) of ^152Sm. These studies provide both ``horizontal'' and ``vertical'' extensions of our spectroscopic knowledge of these widely-studied nuclei. We report on the identification of the systematic occurrence of a low-energy 0^+ ``pairing isomer'' band [1], a K^π = 2^+ ``βγ'' band, a ``hexadecapole'' band, and a broad family of ``octupole'' bands. The radioactive decay studies have been done using the 8π spectrometer (both at LBNL and TRIUMF-ISAC). The multi-Coulex studies have been made using Gammasphere-CHICO (at LBNL). The (α, 2nγ) studies have been carried out at the University of Cologne tandem. The (n,n'γ) studies were made at the University of Kentucky Van de Graaff. [1] W. D. Kulp et al., Phys. Rev. Lett. 91, 102501 (2003).
NASA Astrophysics Data System (ADS)
Predoi-Cross, Adriana; Holladay, Christopher; Heung, Henry; Bouanich, Jean-Pierre; Mellau, Georg Ch.; Keller, Reimund; Hurtmans, Daniel R.
2008-09-01
We report measurements for N 2-broadening, pressure-shift and line mixing coefficients for 55 oxygen transitions in the A-band retrieved using a multispectrum fitting technique. Nineteen laboratory absorption spectra were recorded at 0.02 cm -1 resolution using a multi-pass absorption cell with path length of 1636.9 cm and the IFS 120 Fourier transform spectrometer located at Justus-Liebig-University in Giessen, Germany. The total sample pressures ranged from 8.8 to 3004.5 Torr with oxygen volume mixing ratios in nitrogen ranging between 0.057 and 0.62. An Exponential Power Gap (EPG) scaling law was used to calculate the N 2-broadening and N 2-line mixing coefficients. The line broadening and shift coefficients for the A-band of oxygen self-perturbed and perturbed by N 2 are modeled using semiclassical calculations based on the Robert-Bonamy formalism and two intermolecular potentials. These potentials involve electrostatic contributions including the hexadecapole moment of the molecules and (a) a simple dispersion contribution with one adjustable parameter to fit the broadening coefficients or (b) the atom-atom Lennard-Jones model without such adjustable parameters. The first potential leads to very weak broadening coefficients for high J transitions whereas the second potential gives much more improved results at medium and large J values, in reasonable agreement with the experimental data. For the line shifts which mainly arise in our calculation from the electronic state dependence of the isotropic potential, their general trends with increasing J values can be well predicted, especially from the first potential. From the theoretical results, we have derived air-broadening and air-induced shift coefficients with an agreement comparable to that obtained for O 2-O 2 and O 2-N 2.
Measurement of the dipole in the cross-correlation function of galaxies
NASA Astrophysics Data System (ADS)
Gaztanaga, Enrique; Bonvin, Camille; Hui, Lam
2017-01-01
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 that 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.
NASA Astrophysics Data System (ADS)
Chopra, Sahila; Kaur, Arshdeep; Hemdeep, Gupta, Raj K.
2016-04-01
The product PCNPsurv of compound nucleus (CN) fusion probability PCN and survival probability Psurv is calculated to determine the reduced evaporation residue cross section σER/σfusion , denoted σERreduced, with (total) fusion cross section σfusion given as a sum of CN-formation cross section σCN and non-CN cross section σnCN for each reaction, where σCN is the sum of evaporation residue cross section σER and fusion-fission cross section σff and σnCN, if not measured, is estimated empirically as the difference between measured and calculated σfusion. Our calculations of PCN and Psurv, based on the dynamical cluster-decay model, were successfully made for some 17 "hot" fusion reactions, forming different CN of mass numbers ACN˜100 -300 , with deformations of nuclei up to hexadecapole deformations and "compact" orientations for both coplanar (Φc=0∘ ) and noncoplanar (Φc≠0∘ ) configurations, using various different nuclear interaction potentials. Interesting variations of σERreduced with CN excitation energy E*, fissility parameter χ , CN mass ACN, and Coulomb parameter Z1Z2 show that, independent of entrance channel, different isotopes of CN, and nuclear interaction potentials used, the dominant quantity in the product is Psurv, which classifies all the studied CN into three groups of weakly fissioning, radioactive, and strongly fissioning superheavy nuclei, with relative magnitudes of σERreduced˜1 , ˜10-6 , and ˜10-11 , which, like for PCN, get further grouped in two dependencies of (i) weakly fissioning and strongly fissioning superheavy nuclei decreasing with increasing E* and (ii) radioactive nuclei increasing with increasing E*.
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.
Role of higher-multipole deformations in exotic {sup 14}C cluster radioactivity
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}) and {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.
Properties of Th4+ and Th3+ from rf spectroscopy of high-L thorium Rydberg ions
NASA Astrophysics Data System (ADS)
Keele, Julie Adel
Several properties of radon-like Th4+ and francium-like Th3+ were determined from measurements of high-L Rydberg fine structure in Th3+ and Th2+ ions. The measurements were carried out using the resonant excitation Stark ionization spectroscopy (RESIS) technique to detect rf transitions between levels in the same n. The measured Rydberg fine structures were then fit to an effective potential model, and the properties of the ions were extracted. Properties of the 1S0 ground state of Th4+ extracted from the measurements of the n=37 Th3+ Rydberg fine structure were the scalar dipole polarizability, alpha D,0=7.702(6)a.u. and the scalar quadrupole polarizability, alphaQ,0=29.1(1.6) a.u. The Th2+ Rydberg fine structure is much more complex since the ground state of Th3+ is a 2 F5/2, and the presence of low-lying excited states cause non-adiabatic effects in the fine structure which are not well described by the effective potential. To extract the properties, non-adiabatic corrections had to be calculated. The properties of Th3+ extracted were the permanent quadrupole moment, Q=0.5931(14)a.u. , the scalar and tensor dipole polarizabilities, alpha D,0=15.224(33)a.u. and alpha D,2=--5.30(11)a.u., the permanent hexadecapole moment, pi=--0.69(28)a.u., and the reduced dipole and octupole matrix elements coupling the ground state to the 6 d 2D3/2 state, |
Nuclear energy surfaces at high-spin in the A{approximately}180 mass region
Chasman, R.R.; Egido, J.L.; Robledo, L.M.
1995-08-01
We are studying nuclear energy surfaces at high spin, with an emphasis on very deformed shapes using two complementary methods: (1) the Strutinsky method for making surveys of mass regions and (2) Hartree-Fock calculations using a Gogny interaction to study specific nuclei that appear to be particularly interesting from the Strutinsky method calculations. The great advantage of the Strutinsky method is that one can study the energy surfaces of many nuclides ({approximately}300) with a single set of calculations. Although the Hartree-Fock calculations are quite time-consuming relative to the Strutinsky calculations, they determine the shape at a minimum without being limited to a few deformation modes. We completed a study of {sup 182}Os using both approaches. In our cranked Strutinsky calculations, which incorporate a necking mode deformation in addition to quadrupole and hexadecapole deformations, we found three well-separated, deep, strongly deformed minima. The first is characterized by nuclear shapes with axis ratios of 1.5:1; the second by axis ratios of 2.2:1 and the third by axis ratios of 2.9:1. We also studied this nuclide with the density-dependent Gogny interaction at I = 60 using the Hartree-Fock method and found minima characterized by shapes with axis ratios of 1.5:1 and 2.2:1. A comparison of the shapes at these minima, generated in the two calculations, shows that the necking mode of deformation is extremely useful for generating nuclear shapes at large deformation that minimize the energy. The Hartree-Fock calculations are being extended to larger deformations in order to further explore the energy surface in the region of the 2.9:1 minimum.
Zielinski, François; Popelier, Paul L A
2014-07-01
The point-charge approximation, typically used by classical molecular mechanics force-fields, can be overcome by a multipolar expansion. For decades multipole moments were only used in the context of the rigid body approximation but recently it has become possible to combine multipolar electrostatics with molecular flexibility. The program DL_MULTI, which is derived from DL_POLY_2, includes efficient multipolar Ewald functionality up to the hexadecapole moment but the code is restricted to rigid bodies. The incorporation of flexibility into DL_MULTI would cause too large an impact on its architecture whereas the package DL_POLY_4 offers a more attractive and sustainable route to handle multipolar electrostatics. This package inherently handles molecular flexibility, which warrants sufficiently transferable atoms or atoms that are "knowledgeable" about their chemical environment (as made possible by quantum chemical topology and machine learning). DL_MULTI uses the spherical multipole formalism, which is mathematically more involved than the Cartesian one but which is more compact. DL_POLY_4 uses the computationally efficient method of smooth particle mesh Ewald (SPME) summation, which has also been parallellized by others. Therefore, combining the strengths of DL_POLY_4 and DL_MULTI poses the challenge of merging SPME with multipolar electrostatics by spherical multipole. In an effort to recast as clearly as possible the principles behind DL_MULTI, its key equations have been reformulated by the more streamlined route involving the algebra of complex numbers, and some of these equations' peculiarities clarified. This article explores theoretically the repercussions of the merging of SPME with spherical multipole electrostatics (as implemented in DL_MULTI). Difficulties in design and implementation of possible future code are discussed.
Deformation electron-density distributions of tetraazathiapentalenes with hypervalent SN bonds
NASA Astrophysics Data System (ADS)
Iwasaki, Fujiko; Yoshida, Satoshi; Kakuma, Seiji; Watanabe, Toshiya; Yasui, Masanori
1995-06-01
3,4-Dimethyl-2,5-diphenyl-3,4-dihydro-3a-thia-1,3,4,6-tetraazapentalene ( 1) and 2,3,4,5-tetrahydro-1,6-diphenyl-3,4-propano-6a-thia-1,3,4,6-tetraazapentalene-2,5-dione ( 2) are typical hypervalent sulfur compounds with SN bonds of 1.90-1.96 Å, which are longer than the normal single SN bond (1.74 Å) by about 10%. The electron-density distributions of these compounds were investigated in order to shed light on the character of hypervalent S ··· N bonds. Intensity data of X-ray diffraction were measured at 143 K and the structure refinements were performed using multipole expansion atomic scattering factors up to the hexadecapole expansion for the S atom. Crystal data are: 1, orthorhombic, Pbcn, a = 14.433(3), b = 9.220(2), c = 11.236(2) Å, Z = 4, R = 0.037 for 6398 reflections; 2, orthorhombic, Iba 2, a = 20.313(3), b = 21.365(2), c = 7.472(2) Å, Z = 8, R = 0.036 for 6617 reflections. In the model deformation maps of 1 and 2 electron densities along the SN bonds are observed near the nitrogen atoms, not in the center of the bonds. The net atomic charges derived from the multipole refinement suggest a polarized character of the SN bond. Lone-pair electron densities of hypervalent sulfur atoms, observed on the up and down sides of the pentalene plane, suggest a coupling of lone pair with pπ and non-bonding d or p electrons.
Kumar, Raj; Bansal, Manie; Arun, Sham K.; Gupta, Raj K.
2009-09-15
Using the capture cross-section data from {sup 48}Ca+{sup 238}U, {sup 48}Ca+{sup 244}Pu, and {sup 48}Ca+{sup 248}Cm reactions in the superheavy mass region, and fusion-evaporation cross sections from {sup 58}Ni+{sup 58}Ni, {sup 64}Ni+{sup 64}Ni, and {sup 64}Ni+{sup 100}Mo reactions known for fusion hindrance phenomenon in coupled-channels calculations, the Wong formula is assessed for its angular momentum and barrier-modification effects at sub-barrier energies. The simple, l=0 barrier-based Wong formula is shown to ignore the modifications of the barrier due to its inbuilt l dependence via l summation, which is found to be adequate enough to explain the capture cross sections for all the three above-mentioned {sup 48}Ca-based reactions forming superheavy systems. For the capture (equivalently, quasifission) reactions, the complete l-summed Wong formula is shown to be the same as the dynamical cluster-decay model expression, of one of us (R.K.G.) and collaborators, with the condition of fragment preformation probability P{sub 0}{sup l}=1 for all the angular momentum l values. In the case of fusion-evaporation cross sections, however, a further modification of barriers is required for below-barrier energies, affected in terms of either the barrier 'lowering' or barrier 'narrowing' via the curvature constant. Calculations are made for use of nuclear proximity potential, with effects of multipole deformations included up to hexadecapole, and orientation degrees of freedom integrated for both the coplanar and noncoplanar configurations.
Adiabatic fission barriers in superheavy nuclei
NASA Astrophysics Data System (ADS)
Jachimowicz, P.; Kowal, M.; Skalski, J.
2017-01-01
Using the microscopic-macroscopic model based on the deformed Woods-Saxon single-particle potential and the Yukawa-plus-exponential macroscopic energy, we calculated static fission barriers Bf for 1305 heavy and superheavy nuclei 98 ≤Z ≤126 , including even-even, odd-even, even-odd and odd-odd systems. For odd and odd-odd nuclei, adiabatic potential-energy surfaces were calculated by a minimization over configurations with one blocked neutron or/and proton on a level from the 10th below to the 10th above the Fermi level. The parameters of the model that have been fixed previously by a fit to masses of even-even heavy nuclei were kept unchanged. A search for saddle points has been performed by the "imaginary water flow" method on a basic five-dimensional deformation grid, including triaxiality. Two auxiliary grids were used for checking the effects of the mass asymmetry and hexadecapole nonaxiality. The ground states (g.s.) were found by energy minimization over configurations and deformations. We find that the nonaxiality significantly changes first and second fission saddle in many nuclei. The effect of the mass asymmetry, known to lower the second, very deformed saddles in actinides, in the heaviest nuclei appears at the less deformed saddles in more than 100 nuclei. It happens for those saddles in which the triaxiality does not play any role, which suggests a decoupling between effects of the mass asymmetry and triaxiality. We studied also the influence of the pairing interaction strength on the staggering of Bf for odd- and even-particle numbers. Finally, we provide a comparison of our results with other theoretical fission barrier evaluations and with available experimental estimates.
Dudek, J.
1987-01-01
Mechanisms influencing the behavior of superdeformed nuclei are studied using several well established nuclear structure techniques. In particular: pairing, thermal excitation, shell and liquid-drop mechanisms are considered. The effects of quadrupole and hexadecapole (both axial and non-axial), and octupole deformation degrees of freedom are studied. Most of the results are illustrated using the case of /sup 152/Dy nucleus in which a superdeformed band extending up to I approx. 60 h-bar has been found in experiment. Some comparisons between /sup 152/Dy and the nuclei in the neighborhood are given. Calculations show that pairing ''de-aligns'' typically 6 to 8 units of angular momentum, as compared to the corresponding rigid rotation. This takes place for spins extending up to the highest limit, and thus diminishes the effective moments of inertia. Predicted octupole shape susceptibility is extremely large, significantly stronger than the susceptibilities known in the ground-states of many Actinide nuclei. Consequences of this result for the near-constancy of the dynamical moments of inertia are pointed out. Nuclear level densities calculated in function of spin, excitation energy and deformation explain the ''unusual'' side feeding pattern of the /sup 152/Dy superdeformed states. Predictions of super-superdeformed nuclear states (axis ratio varying between 2:1 and 3:1 or more) are given and exemplified for Erbium nuclei. Finally, the problem of superdeformation stability and the influence of increased collective inertia on a barrier penetration are examined. An analytical expression for the effective inertia parameter is obtained and its derivation outlined. 35 refs., 9 figs.
NASA Astrophysics Data System (ADS)
Chopra, Sahila; Kaur, Arshdeep; Gupta, Raj K.
2015-03-01
After a successful attempt to define and determine recently the compound nucleus (CN) fusion/ formation probability PCN within the dynamical cluster-decay model (DCM), we introduce and estimate here for the first time the survival probability Psurv of CN against fission, again within the DCM. Calculated as the dynamical fragmentation process, Psurv is defined as the ratio of the evaporation residue (ER) cross section σER and the sum of σER and fusion-fission (ff) cross section σff, the CN formation cross section σCN, where each contributing fragmentation cross section is determined in terms of its formation and barrier penetration probabilities P0 and P . In DCM, the deformations up to hexadecapole and "compact" orientations for both in-plane (coplanar) and out-of-plane (noncoplanar) configurations are allowed. Some 16 "hot" fusion reactions, forming a CN of mass number ACN˜100 to superheavy nuclei, are analyzed for various different nuclear interaction potentials, and the variation of Psurv on CN excitation energy E*, fissility parameter χ , CN mass ACN, and Coulomb parameter Z1Z2 is investigated. Interesting results are that three groups, namely, weakly fissioning, radioactive, and strongly fissioning superheavy nuclei, are identified with Psurv, respectively, ˜1 ,˜10-6 , and ˜10-10 . For the weakly fissioning group (100
NASA Astrophysics Data System (ADS)
Szmytkowski, Radosław; Łukasik, Grzegorz
2016-06-01
The ground state of the Dirac one-electron atom, placed in a weak, static electric field of definite 2L polarity, is studied within the framework of the first-order perturbation theory. The Sturmian expansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B: At. Mol. Opt. Phys. 30, 825 (1997), 10.1088/0953-4075/30/4/007; erratum R. Szmytkowski, J. Phys. B: At. Mol. Opt. Phys. 30, 2747 (1997), 10.1088/0953-4075/30/11/023] is used to derive closed-form analytical expressions for various far-field and near-nucleus static electric multipole susceptibilities of the atom. The far-field multipole susceptibilities—the polarizabilities αL, the electric-to-magnetic cross susceptibilities αE L →M (L ∓1 ), and the electric-to-toroidal-magnetic cross susceptibilities αE L →T L —are found to be expressible in terms of one or two nonterminating generalized hypergeometric functions F2 with the unit argument. Counterpart formulas for the near-nucleus multipole susceptibilities—the electric nuclear shielding constants σEL→E L, the near-nucleus electric-to-magnetic cross susceptibilities σE L →M (L ∓1 ), and the near-nucleus electric-to-toroidal-magnetic cross susceptibilities σE L →T L —involve one or two terminating F2(1 ) series and for each L may be rewritten in terms of elementary functions. Numerical values of the far-field dipole, quadrupole, octupole, and hexadecapole susceptibilities are provided for selected hydrogenic ions. The effect of a declared uncertainty in the CODATA 2014 recommended value of the fine-structure constant α on the accuracy of numerical results is investigated. Analytical quasirelativistic approximations, valid to the second order in α Z , where Z is the nuclear charge number, are also derived for all types of the far-field and near-nucleus susceptibilities considered in the paper.
NASA Astrophysics Data System (ADS)
Niyti; Gupta, Raj K.; Hess, Peter Otto
2015-06-01
The dynamical cluster-decay model (DCM), with deformation and orientation effects included, is used to calculate the fusion evaporation residue cross-sections σxn for x = 1, 2, 3 and 4 neutrons emission in a fusion reaction 206Pb + 48Ca → 254No* at various 48Ca-beam energies Elab = 212.7- 242.5 MeV (equivalently, E* = 19.8- 43.9 MeV). Considering the higher multipole deformations up to hexadecapole deformation β4i and the sticking moment-of-inertia IS, the DCM with pocket formula for nuclear proximity potential is shown to give a good description of the measured individual light-particle (here neutrons) decay channels for configurations of "hot, compact" orientations θci, within one parameter fitting of the neck-length ΔR. A check on some of the variables involved in DCM shows that (i) spherical configurations give nearly the same result as above for deformed and oriented ones; (ii) the non-sticking moment-of-inertia INS gives unphysical results; and (iii) configurations of "cold, elongated" orientations do not fit the data at all. Furthermore, for the four different isotopes of 204,206,207,208Pb-based reactions, the dependence of, say, the 2n-emission yield σ2n on the isotopic composition of the compound nucleus is also studied within the DCM for "hot" fusion process. Of all the four Pb-isotopes and three excitation energies E* considered, at each E*, the ΔR is largest for compound system 256No*, followed by 255No*, 254No* and smallest for 252No*, which means to suggest that the neutrons emission occur earliest for 256No*, then for 255No*, 254No* and finally by 252No*, in complete agreement with experimental data according to which compound system 256No* has the highest cross-section and 252No* the lowest with 255No* and 254No* lying in between. This result is related to the double magicity of both the target (208Pb) and projectile (48Ca) nuclei, as well as to the experimentally known result of projectile with a larger number of neutrons (here the target
Matta, Chérif F
2010-04-30
except when inadequate basis sets were used by today's standards. Extensive tabulation of molecular and atomic properties at the three theoretical levels is available in the Supporting Information, including optimized geometries, molecular energies, virial ratios, molecular electrostatic moments up to and including hexadecapoles, atomic populations, atomic volumes, atomic electrostatic moments up to and including the quadrupoles, and atomic energies.
Geometry and dynamics of a tidally deformed black hole
Poisson, Eric; Vlasov, Igor
2010-01-15
The metric of a nonrotating black hole deformed by a tidal interaction is calculated and expressed as an expansion in the strength of the tidal coupling. The expansion parameter is the inverse length scale R{sup -1}, where R is the radius of curvature of the external spacetime in which the black hole moves. The expansion begins at order R{sup -2}, and it is carried out through order R{sup -4}. The metric is parametrized by a number of tidal multipole moments, which specify the black hole's tidal environment. The tidal moments are freely-specifiable functions of time that are related to the Weyl tensor of the external spacetime. At order R{sup -2} the metric involves the tidal quadrupole moments E{sub ab} and B{sub ab}. At order R{sup -3} it involves the time derivative of the quadrupole moments and the tidal octupole moments E{sub abc} and B{sub abc}. At order R{sup -4} the metric involves the second time derivative of the quadrupole moments, the first time derivative of the octupole moments, the tidal hexadecapole moments E{sub abcd} and B{sub abcd}, and bilinear combinations of the quadrupole moments. The metric is presented in a light-cone coordinate system that possesses a clear geometrical meaning: The advanced-time coordinate v is constant on past light cones that converge toward the black hole; the angles {theta} and {phi} are constant on the null generators of each light cone; and the radial coordinate r is an affine parameter on each generator, which decreases as the light cones converge toward the black hole. The coordinates are well-behaved on the black-hole horizon, and they are adjusted so that the coordinate description of the horizon is the same as in the Schwarzschild geometry: r=2M+O(R{sup -5}). At the order of accuracy maintained in this work, the horizon is a stationary null hypersurface foliated by apparent horizons; it is an isolated horizon in the sense of Ashtekar and Krishnan. As an application of our results we examine the induced geometry
HPAM: Hirshfeld partitioned atomic multipoles
NASA Astrophysics Data System (ADS)
Elking, Dennis M.; Perera, Lalith; Pedersen, Lee G.
2012-02-01
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 l 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 l=0 (atomic charges) to l=4 (atomic hexadecapoles). Both HD and HD-I atomic multipoles up to rank l are shown to exactly reproduce ab initio molecular multipole moments of rank L for L⩽l. In addition, molecular dipole moments calculated by HD, HD-I, and ChelpG atomic charges only ( l=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. Program summaryProgram title: HPAM Catalogue identifier: AEKP_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKP_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License v2 No. of lines in distributed program, including test data, etc.: 500 809 No. of bytes in distributed program, including test data, etc.: 13 424 494 Distribution format: tar.gz Programming language: C Computer: Any Operating system: Linux RAM: Typically, a few hundred megabytes Classification: 16.13 External routines: The program requires 'formatted checkpoint' files obtained from the Gaussian 03 or Gaussian 09 quantum chemistry program. Nature of problem: An ab initio
Distribution function approach to redshift space distortions. Part II: N-body simulations
Okumura, Teppei; Seljak, Uroš; McDonald, Patrick; Desjacques, Vincent E-mail: useljak@berkeley.edu E-mail: dvince@physik.uzh.ch
2012-02-01
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. We 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 breaks down
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