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.
Mixed-symmetry octupole and hexadecapole excitations in N=52 isotones
NASA Astrophysics Data System (ADS)
Hennig, Andreas; Spieker, Mark; Werner, Volker; Ahn, Tan; Anagnostatou, Vassia; Cooper, Nathan; Derya, Vera; Elvers, Michael; Endres, Janis; Goddard, Phil; Heinz, Andreas; Hughes, Richard O.; Ilie, Gabriela; Mineva, Milena N.; Pickstone, Simon G.; Petkov, Pavel; Pietralla, Norbert; Radeck, Desirée; Ross, Tim J.; Savran, Deniz; Zilges, Andreas
2015-05-01
In addition to the well-established quadrupole mixed-symmetry states, octupole and hexadecapole excitations with mixed-symmetry character have been recently proposed for the N = 52 isotones 92Zr and 94Mo. We performed two inelastic proton-scattering experiments to study this kind of excitations in the heaviest stable N = 52 isotone 96Ru. From the combined experimental data of both experiments absolute transition strengths were extracted.
Sub-barrier backward quasielastic scattering: A probe of the hexadecapole deformation
NASA Astrophysics Data System (ADS)
Zhang, H. Q.; Lin, C. J.; Jia, H. M.; Yang, L.; Xu, X. X.; Yang, F.; Wu, Z. D.; Liu, Z. H.; Ma, N. R.; Sun, L. J.; Wang, D. X.
2016-05-01
The quasielastic scattering excitation functions for 16O + 152Sm,170Er and 174Yb were measured with high precision at a backward angle with small energy intervals at energies near the Coulomb barriers. The hexadecapole deformation (β4) of the target nuclei was extracted by using the lower-energy data and the obtained values agree with the available results reasonably well. This offers a sensitive method to extract β4. This method is especially meaningful for the radioactive nuclei considering the low beam intensities.
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.
Elliptic and hexadecapole flow of charged hadrons in Au+Au collisions at sq.rt(s(NN))=200 GeV.
Adare, A; Afanasiev, S; Aidala, C; Ajitanand, N N; Akiba, Y; Al-Bataineh, H; Alexander, J; Aoki, K; Aramaki, Y; Atomssa, E T; Averbeck, R; Awes, T C; Azmoun, B; Babintsev, V; Bai, M; Baksay, G; Baksay, L; Barish, K N; Bassalleck, B; Basye, A T; Bathe, S; Baublis, V; Baumann, C; Bazilevsky, A; Belikov, S; Belmont, R; Bennett, R; Berdnikov, A; Berdnikov, Y; Bickley, A A; Bok, J S; Boyle, K; Brooks, M L; Buesching, H; Bumazhnov, V; Bunce, G; Butsyk, S; Camacho, C M; Campbell, S; Chen, C-H; Chi, C Y; Chiu, M; Choi, I J; Choudhury, R K; Christiansen, P; Chujo, T; Chung, P; Chvala, O; Cianciolo, V; Citron, Z; Cole, B A; Connors, M; Constantin, P; Csanád, M; Csörgo, T; Dahms, T; Dairaku, S; Danchev, I; Das, K; Datta, A; David, G; Denisov, A; Deshpande, A; Desmond, E J; Dietzsch, O; Dion, A; Donadelli, M; Drapier, O; Drees, A; Drees, K A; Durham, J M; Durum, A; Dutta, D; Edwards, S; Efremenko, Y V; Ellinghaus, F; Engelmore, T; Enokizono, A; En'yo, H; Esumi, S; Fadem, B; Fields, D E; Finger, M; Finger, M; Fleuret, F; Fokin, S L; Fraenkel, Z; Frantz, J E; Franz, A; Frawley, A D; Fujiwara, K; Fukao, Y; Fusayasu, T; Garishvili, I; Glenn, A; Gong, H; Gonin, M; Goto, Y; Granier de Cassagnac, R; Grau, N; Greene, S V; Grosse Perdekamp, M; Gunji, T; Gustafsson, H-A; Haggerty, J S; Hahn, K I; Hamagaki, H; Hamblen, J; Hanks, J; Han, R; Hartouni, E P; Haslum, E; Hayano, R; Heffner, M; Hegyi, S; Hemmick, T K; Hester, T; He, X; Hill, J C; Hohlmann, M; Holzmann, W; Homma, K; Hong, B; Horaguchi, T; Hornback, D; Huang, S; Ichihara, T; Ichimiya, R; Ide, J; Ikeda, Y; Imai, K; Inaba, M; Isenhower, D; Ishihara, M; Isobe, T; Issah, M; Isupov, A; Ivanischev, D; Jacak, B V; Jia, J; Jin, J; Johnson, B M; Joo, K S; Jouan, D; Jumper, D S; Kajihara, F; Kametani, S; Kamihara, N; Kamin, J; Kang, J H; Kapustinsky, J; Karatsu, K; Kawall, D; Kawashima, M; Kazantsev, A V; Kempel, T; Khanzadeev, A; Kijima, K M; Kim, B I; Kim, D H; Kim, D J; Kim, E J; Kim, E; Kim, S H; Kim, Y J; Kinney, E; Kiriluk, K; Kiss, A; Kistenev, E; Kochenda, L; Komkov, B; Konno, M; Koster, J; Kotchetkov, D; Kozlov, A; Král, A; Kravitz, A; Kunde, G J; Kurita, K; Kurosawa, M; Kwon, Y; Kyle, G S; Lacey, R; Lai, Y S; Lajoie, J G; Lebedev, A; Lee, D M; Lee, J; Lee, K B; Lee, K; Lee, K S; Leitch, M J; Leite, M A L; Leitner, E; Lenzi, B; Liebing, P; Linden Levy, L A; Liska, T; Litvinenko, A; Liu, H; Liu, M X; Li, X; Love, B; Luechtenborg, R; Lynch, D; Maguire, C F; Makdisi, Y I; Malakhov, A; Malik, M D; Manko, V I; Mannel, E; Mao, Y; Masui, H; Matathias, F; McCumber, M; McGaughey, P L; Means, N; Meredith, B; Miake, Y; Mignerey, A C; Mikes, P; Miki, K; Milov, A; Mishra, M; Mitchell, J T; Mohanty, A K; Morino, Y; Morreale, A; Morrison, D P; Moukhanova, T V; Murata, J; Nagamiya, S; Nagle, J L; Naglis, M; Nagy, M I; Nakagawa, I; Nakamiya, Y; Nakamura, T; Nakano, K; Newby, J; Nguyen, M; Nouicer, R; Nyanin, A S; O'Brien, E; Oda, S X; Ogilvie, C A; Okada, K; Oka, M; Onuki, Y; Oskarsson, A; Ouchida, M; Ozawa, K; Pak, R; Pantuev, V; Papavassiliou, V; Park, I H; Park, J; Park, S K; Park, W J; Pate, S F; Pei, H; Peng, J-C; Pereira, H; Peresedov, V; Peressounko, D Yu; Pinkenburg, C; Pisani, R P; Proissl, M; Purschke, M L; Purwar, A K; Qu, H; Rak, J; Rakotozafindrabe, A; Ravinovich, I; Read, K F; Reygers, K; Riabov, V; Riabov, Y; Richardson, E; Roach, D; Roche, G; Rolnick, S D; Rosati, M; Rosen, C A; Rosendahl, S S E; Rosnet, P; Rukoyatkin, P; Ruzicka, P; Sahlmueller, B; Saito, N; Sakaguchi, T; Sakashita, K; Samsonov, V; Sano, S; Sato, T; Sawada, S; Sedgwick, K; Seele, J; Seidl, R; Semenov, A Yu; Seto, R; Sharma, D; Shein, I; Shibata, T-A; Shigaki, K; Shimomura, M; Shoji, K; Shukla, P; Sickles, A; Silva, C L; Silvermyr, D; Silvestre, C; Sim, K S; Singh, B K; Singh, C P; Singh, V; Slunecka, M; Soltz, R A; Sondheim, W E; Sorensen, S P; Sourikova, I V; Sparks, N A; Stankus, P W; Stenlund, E; Stoll, S P; Sugitate, T; Sukhanov, A; Sziklai, J; Takagui, E M; Taketani, A; Tanabe, R; Tanaka, Y; Tanida, K; Tannenbaum, M J; Tarafdar, S; Taranenko, A; Tarján, P; Themann, H; Thomas, T L; Togawa, M; Toia, A; Tomásek, L; Torii, H; Towell, R S; Tserruya, I; Tsuchimoto, Y; Vale, C; Valle, H; van Hecke, H W; Vazquez-Zambrano, E; Veicht, A; Velkovska, J; Vértesi, R; Vinogradov, A A; Virius, M; Vrba, V; Vznuzdaev, E; Wang, X R; Watanabe, D; Watanabe, K; Watanabe, Y; Wei, F; Wei, R; Wessels, J; White, S N; Winter, D; Wood, J P; Woody, C L; Wright, R M; Wysocki, M; Xie, W; Yamaguchi, Y L; Yamaura, K; Yang, R; Yanovich, A; Ying, J; Yokkaichi, S; Young, G R; Younus, I; You, Z; Yushmanov, I E; Zajc, W A; Zhang, C; Zhou, S; Zolin, L
2010-08-01
Differential measurements of the elliptic (v(2)) and hexadecapole (v(4)) Fourier flow coefficients are reported for charged hadrons as a function of transverse momentum (p(T)) and collision centrality or number of participant nucleons (N(part)) for Au+Au collisions at sq.rt(s(NN))=200 GeV. The v(2,4) measurements at pseudorapidity |η|≤0.35, obtained with four separate reaction-plane detectors positioned in the range 1.0<|η|<3.9, show good agreement, indicating the absence of significant Δη-dependent nonflow correlations. Sizable values for v(4)(p(T)) are observed with a ratio v(4)(p(T),N(part))/v(2)(2)(p(T),N(part))≈0.8 for 50≲N(part)≲200, which is compatible with the combined effects of a finite viscosity and initial eccentricity fluctuations. For N(part)≳200 this ratio increases up to 1.7 in the most central collisions. PMID:20867976
Adare, A.; Bickley, A. A.; Ellinghaus, F.; Glenn, A.; Kinney, E.; Kiriluk, K.; Linden Levy, L. A.; Nagle, J. L.; Rosen, C. A.; Seele, J.; Wysocki, M.; Afanasiev, S.; Isupov, A.; Litvinenko, A.; Malakhov, A.; Peresedov, V.; Rukoyatkin, P.; Zolin, L.; Aidala, C.; Datta, A.
2010-08-06
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}|{<=}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_equal}0.8 for 50 < or approx. IN{sub part} < or approx. 200, which is compatible with the combined effects of a finite viscosity and initial eccentricity fluctuations. For N{sub part} > or approx. 200 this ratio increases up to 1.7 in the most central collisions.
Bruna, Pablo J; Grein, Friedrich
2007-08-21
The number of independent components, n, of traceless electric 2(l)-multipole moments is determined for C(infinity v) molecules in Sigma(+/-), Pi, Delta, and Phi electronic states (Lambda=0,1,2,3). Each 2(l) pole is defined by a rank-l irreducible tensor with (2l+1) components P(m)((l)) proportional to the solid spherical harmonic r(l)Y(m)(l)(theta,phi). Here we focus our attention on 2(l) poles with l=2,3,4 (quadrupole Theta, octopole Omega, and hexadecapole Phi). 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 Lambda. For Sigma(+/-)(Lambda=0) states, all 2(l) poles have one independent parameter (n=1). For spatially degenerate states--Pi, Delta, and Phi (Lambda=1,2,3)--the general rule reads n=1 for l<2/Lambda/ (when the 2(l)-pole rank lies below 2/Lambda/ but n=2 for higher 2(l) poles with l>or=2/Lambda/. The second nonzero term is the off-diagonal matrix element [formula: see text]. Thus, a Pi(Lambda=1) state has one dipole (mu(z)) but two independent 2(l) poles for l>or=2--starting with the quadrupole [Theta(zz),(Theta(xx)-Theta(yy))]. A Delta(Lambda=2) state has n=1 for 2((1,2,3)) poles (mu(z),Theta(zz),Omega(zzz)) but n=2 for higher 2((l>or=4)) poles--from the hexadecapole Phi up. For Phi(Lambda=3) states, it holds that n=1 for 2(1) to 2(5) poles but n=2 for all 2((l>or=6)) poles. In short, what is usually stated in the literature--that n=1 for all possible 2(l) poles of linear molecules--only applies to Sigma(+/-) states. For degenerate states with n=2, all Cartesian 2(l)-pole components (l>or=2/Lambda/) can be expressed as linear combinations of two irreducible multipoles, P(m=0)((l)) and P/m/=2 Lambda)((l)) [parallel (z axis) and anisotropy (xy plane)]. Our predictions are exemplified by the Theta, Omega, and Phi moments calculated for Lambda=0-3 states of selected diatomics (in parentheses): X (2)Sigma(+)(CN), X (2)Pi(NO), a (3)Pi(u)(C(2)), X (2)Delta(NiH), X (3)Delta(TiO), X
NASA Astrophysics Data System (ADS)
Roy, Victor; Mohanty, Bedangadas; Chaudhuri, A. K.
2013-06-01
The experimentally measured elliptic (v2) and hexadecapole (v4) flow of charged particles as a function of transverse momentum (pT) at midrapidity in Pb-Pb collisions at \\sqrt{s_{{N}N}} = 2.76 TeV is compared with the relativistic viscous hydrodynamic model simulations. The simulations are carried out for two different initial energy density profiles obtained from (i) the Glauber model, and (ii) the color glass condensate (CGC) model. A comparison to experimental data for 10-20% to 40-50% centrality shows that a centrality dependent shear viscosity to entropy density (η/s) ratio with values ranging between 0.0 to 0.12 is needed to explain the v2 data for simulations with the Glauber based initial condition, whereas for the CGC based initial conditions a slightly higher value of η/s is preferred, around 0.08 to 0.16. From the comparison of the v4 simulated results to the corresponding experimental measurements we observe that for the centralities 20-30% to 40-50% the η/s values lie between 0.0 to 0.12 for both the initial conditions studied. The η/s values obtained from our studies for Pb-Pb collisions at \\sqrt{s_{{N}N}} = 2.76 TeV are compared to other studies which use both transport and hydrodynamic approaches.
Reply to "Comment on two-phonon gamma-vibrational strength in osmium nuclei"
Wu, C.Y.; Cline, D.; Hayes, A.B.; Simon, M.W.; Krueken, R.; Cooper, J.R.; Barton, C.J.; Beausang, C.W.; Bialik, C.; Caprio, M.A.; Casten, R.F.; Hecht, A.A.; Newman, H.; Novak, J.; Pietralla, N.; Zyromski, K.; Zamfir, N.V.
2002-09-03
The claim that the two-phonon gamma-vibrational configuration constitutes a major component for the I=4+ states in osmium nuclei is based on solid experimental evidence. A non-negligible two-quasiparticle or hexadecapole component must also exist in order to explain the data.
Effects of angular dependence of surface diffuseness in deformed nuclei on Coulomb barrier
NASA Astrophysics Data System (ADS)
Adamian, G. G.; Antonenko, N. V.; Malov, L. A.; Scamps, G.; Lacroix, D.
2014-09-01
The angular dependence of surface diffuseness is further discussed. The results of self-consistent calculations are compared with those obtained with the phenomenological mean-field potential. The rather simple parametrizations are suggested. The effects of surface polarization and hexadecapole deformation on the height of the Coulomb barrier are revealed.
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. 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
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.
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
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.
{ital g} boson and systematics of the {ital M}1 scissors mode
Davis, E.D.; Diallo, A.F.; Barrett, B.R.
1996-06-01
We discuss systematics of the {ital M}1 scissors mode within the interacting boson model when the {ital g}-boson degree of freedom is included explicitly and microscopically motivated choices of model parameters are adopted. We try to relate the {ital M}1 centroid energy to the energetics of deformation. We conclude that, with the introduction of a hexadecapole-hexadecapole interaction and a {ital g}-boson admixture in the ground state of only a few percent, we can obtain reasonable estimates of the {ital M}1 centroid energy, without invoking a Majorana interaction. If one takes seriously variations in microscopic estimates of boson {ital g} factors, then the summed {ital M}1 strength near midshell can be interpreted in terms of boson occupation numbers which saturate. {copyright} {ital 1996 The American Physical Society.}
A note on the electric quadrupole and higher electric moments of ozone (O3)
NASA Astrophysics Data System (ADS)
Maroulis, George
2012-02-01
We have obtained accurate ab initio and density functional theory values for the quadrupole, octopole and hexadecapole electric moments of the cyclic and open forms of ozone. Our best values have been calculated at the coupled cluster level of theory with molecule-specific basis sets. For the quadrupole moment (Θαβ/ea02) they are Θyy = -1.366 (cyclic), Θxx = -1.202, Θyy = 1.426 and Θxx = -0.223 (open). For the octopole (Ωαβγ/ea03) and hexadecapole (Φαβγδ/ea04) moments our best results are Ωzzz = 2.25, Φyyyy = 19.53 (cyclic), Ωxxz = 3.28, Ωzzz = -2.97, Φxxxx = -6.00, Φyyyy = -3.90 and Φzzzz = -3.54 (open).
Constraining halo occupation distribution and cosmic growth rate using multipole power spectrum
NASA Astrophysics Data System (ADS)
Hikage, Chiaki
2014-06-01
We propose a new method of measuring halo occupation distribution (HOD) together with cosmic growth rate using multipole components of galaxy power spectrum Pl(k). The non-linear redshift-space distortion due to the random motion of satellite galaxies, i.e. Fingers-of-God, generates high-l multipole anisotropy in galaxy clustering, such as the hexadecapole (l = 4) and tetra-hexadecapole (l = 6), which are sensitive to the fraction and the velocity dispersion of satellite galaxies. Using simulated samples following the HOD of luminous red galaxies, we find that the input HOD parameters are successfully reproduced from Pl(k), and that high-l multipole information help to break the degeneracy among HOD parameters. We also show that the measurements of the cosmic growth rate as well as the satellite fraction and velocity dispersions are significantly improved by adding the small-scale information of high-l multipoles.
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
Deformation effects on sub-barrier fusion cross sections in 16O+174,176Yb
NASA Astrophysics Data System (ADS)
Rajbongshi, Tapan; Kalita, K.; Nath, S.; Gehlot, J.; Banerjee, Tathagata; Mukul, Ish; Dubey, R.; Madhavan, N.; Lin, C. J.; Shamlath, A.; Laveen, P. V.; Shareef, M.; Kumar, Neeraj; Jisha, P.; Sharma, P.
2016-05-01
Background: Couplings with various reaction channels are known to enhance sub-barrier fusion cross sections by several orders in magnitude. However, a few open questions still remain. For example, the influence of higher order static deformations on sub-barrier fusion cross sections is yet to be comprehensively understood. Purpose: We study the role of hexadecapole nuclear deformation effect on sub-barrier fusion cross sections. Also, this work aims to extract hexadecapole deformation (β4) in nuclei in the lanthanide region. Method: The evaporation residue (ER) excitation functions for 16O+174,176Yb were measured at laboratory beam energies (Elab) in the range of 64.6-103.6 MeV. Measurements were carried out by employing the recoil mass spectrometer Heavy Ion Reaction Analyzer (HIRA) at IUAC, New Delhi. Fusion barrier distributions (BDs) were extracted from data. Results from the experiment were subjected to coupled-channels analysis, in which β4 was varied as a free parameter. Results: Experimental fusion cross sections at energies below the barrier expectedly showed strong enhancement compared to the predictions from the one-dimensional barrier penetration model. Data were satisfactorily reproduced after inclusion of negative β4 for both the targets in the coupled-channels calculation. Conclusions: The significant role of hexadecapole deformation was observed in the sub-barrier fusion of 16O+174,176Yb. The proposed value of β4 reproduced the measured fusion excitation function reasonably well. The BDs from these data were also extracted but no definitive conclusions could be drawn from them.
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.
First-principles theory of multipolar order in neptunium dioxide
NASA Astrophysics Data System (ADS)
Suzuki, M.-T.; Magnani, N.; Oppeneer, P. M.
2010-12-01
We provide a first-principles, materials-specific theory of multipolar order and superexchange in NpO2 by means of a noncollinear local-density approximation +U (LDA+U) method. Our calculations offer a precise microscopic description of the triple- q antiferro ordered phase in the absence of any dipolar moment. We find that, while the most common nondipolar degrees of freedom (e.g., electric quadrupoles and magnetic octupoles) are active in the ordered phase, both the usually neglected higher-order multipoles (electric hexadecapoles and magnetic triakontadipoles) have at least an equally significant effect.
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.
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.
Realistic collective nuclear Hamiltonian
Dufour, M.; Zuker, A.P.
1996-10-01
The residual part of the realistic forces{emdash}obtained after extracting the monopole terms responsible for bulk properties{emdash}is strongly dominated by pairing and quadrupole interactions, with important {sigma}{tau}{center_dot}{sigma}{tau}, 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 {ital A}{sup {minus}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. {copyright} {ital 1996 The American Physical Society.}
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
2011-11-30
A finite field method for calculating spherical tensor molecular polarizability tensors α(lm;l'm') = ∂Δ(lm)/∂ϕ(l'm')* by numerical derivatives of induced molecular multipole Δ(lm) with respect to gradients of electrostatic potential ϕ(l'm')* is described for arbitrary multipole ranks l and l'. Interconversion 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 using the following ab initio methods: Hartree-Fock (HF), Becke three-parameter Lee-Yang-Parr exchange-correlation functional (B3LYP), Møller-Plesset perturbation theory up to second order (MP2), and Coupled Cluster theory with single and double excitations (CCSD). In addition, intermolecular electrostatic and polarization energies calculated by molecular multipoles and polarizability tensors are compared with ab initio reference values calculated by the Reduced Variation Space 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
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
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.
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.
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 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.
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 +}.
Luo, W.D.; Bouguettoucha, A.; Dobaczewski, J.; Dudek, J.; Li, X.
1995-12-01
Microscopic analysis of the quantum (shell) effects related to the presence of the hexadecapole ({ital Y}{sub 4{mu}}; {mu}=0,2,4) components in the nuclear mean field is performed for the superdeformed nuclei in the mass {ital A} {similar_to} 150 region using the deformed Woods-Saxon potential. No shell effects favoring the {ital C}{sub 4}-symmetry are found. The calculations indicate, however, the existence of the {alpha}{sub 44}-deformation driving orbitals whose occupation might induce an {alpha}{sub 44}-polarization effect. For {sup 149}Gd and {sup 153}Dy nuclei, in which the existence of the {ital C}{sub 4}-symmetry effects is suspected, properties of several excited particle-hole configuration are analyzed.
NASA Astrophysics Data System (ADS)
Lei, Y.; Pittel, S.; Jiang, H.
2016-07-01
The electromagnetic features of the 11/2‑ isomers in the odd-mass Cd isotopes are shown to exhibit an an anomaly near N = 70. We report shell-model calculations of these isotopes aimed at describing these properties. We find a sudden phase change in the hexadecapole component of the wave functions precisely at N = 70, which gives rise to different linear relations between the Q and μ values before and after N = 70, as needed to reproduce the experimental data. The particle-hole transformation properties associated with a strong subshell closure at N = 70 followed by fairly close-lying neutron orbitals from N = 70 ‑ 82 is suggested as a possible explanation for this phase change.
NASA Astrophysics Data System (ADS)
Sagui, Celeste; Pedersen, Lee G.; Darden, Thomas A.
2004-01-01
The accurate simulation of biologically active macromolecules faces serious limitations that originate in the treatment of electrostatics in the empirical force fields. The current use of "partial charges" is a significant source of errors, since these vary widely with different conformations. By contrast, the molecular electrostatic potential (MEP) obtained through the use of a distributed multipole moment description, has been shown to converge to the quantum MEP outside the van der Waals surface, when higher order multipoles are used. However, in spite of the considerable improvement to the representation of the electronic cloud, higher order multipoles are not part of current classical biomolecular force fields due to the excessive computational cost. In this paper we present an efficient formalism for the treatment of higher order multipoles in Cartesian tensor formalism. The Ewald "direct sum" is evaluated through a McMurchie-Davidson formalism [L. McMurchie and E. Davidson, J. Comput. Phys. 26, 218 (1978)]. The "reciprocal sum" has been implemented in three different ways: using an Ewald scheme, a particle mesh Ewald (PME) method, and a multigrid-based approach. We find that even though the use of the McMurchie-Davidson formalism considerably reduces the cost of the calculation with respect to the standard matrix implementation of multipole interactions, the calculation in direct space remains expensive. When most of the calculation is moved to reciprocal space via the PME method, the cost of a calculation where all multipolar interactions (up to hexadecapole-hexadecapole) are included is only about 8.5 times more expensive than a regular AMBER 7 [D. A. Pearlman et al., Comput. Phys. Commun. 91, 1 (1995)] implementation with only charge-charge interactions. The multigrid implementation is slower but shows very promising results for parallelization. It provides a natural way to interface with continuous, Gaussian-based electrostatics in the future. It is
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.
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. PMID:25685458
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.
Effect of deformations on the binding energy of centrally depressed nuclei
NASA Astrophysics Data System (ADS)
Ismail, M.; Ellithi, A. Y.; Adel, A.; Abdulghany, A. R.
2015-07-01
The energy density formalism is implemented to study the binding energy of some heavy, superheavy and hyperheavy nuclei. The macroscopic contribution of binding energy is derived in the presence of a depression parameter in the nuclear density distribution, and the total energy is obtained by adding the shell and pairing correction to the macroscopic part. Total energy is studied with the variation of quadrupole {{β }2} and hexadecapole {{β }4} deformation parameters using different values of depression parameter. The addition of the shell and pairing corrections affects the behavior of the total energy especially the minimum position at specific deformation parameters, a second minimum in some cases are close to the first one, suggesting the possible existence of shape isomers. We minimized the total energy with respect to deformation and density depression parameters and obtained the binding energy of 208Pb, 238U, 252Cf, 280Cn, 285-289Fl, 298Fl, 306120, 320126, 339136, 500174 and 700226. The binding energies obtained are in good agreement with the available experimental data. The difference between the binding energies obtained by this simple method and experimental ones is less than 0.13%.
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.
Excitation of the ground state rotational band in 20Ne by 0.8 GeV protons
NASA Astrophysics Data System (ADS)
Blanpied, G. S.; Balchin, G. A.; Langston, G. E.; Ritchie, B. G.; Barlett, M. L.; Hoffmann, G. W.; McGill, J. A.; Franey, M. A.; Gazzaly, M.; Wildenthal, B. H.
1984-10-01
Angular distributions for the scattering of 0.8 GeV polarized protons from the ground state rotational band in 20Ne are reported. Cross sections and analyzing powers for protons exciting these states were measured with a high resolution spectrometer. Coupled channels and distorted wave Born approximation analyses of scattering data for the 0+, 2+, 4+, and experimentally unresolved 6+ states are presented. The observed cross section data for the 0+, 2+, and 4+ states are reproduced quite well with the coupled channels calculations, and the large hexadecapole deformation reported previously is confirmed. The distorted wave Born approximation results are equally good for the 0+ angular distribution, but are a significantly poorer representation of the cross section data for the 2+ and 4+ states. Both calculations do equally well in explaining the 0+ analyzing power data and both fail to explain the 4+ analyzing power data past the region of the first maximum. The coupled channels results do a better job in explaining the 2+ analyzing power data. The multipole moments of the deformed optical potential used in the coupled channels calculations are related to those of the matter distributions by Satchler's theorem. These are compared to the moments found using other hadronic probes, those of the charge distribution determined by electromagnetic measurements, and to moments from shell model and Hartree-Fock calculations.
Minimizing the 1/r(2) perturbation for ideal fluence detectors in small source γ-irradiation fields.
Bielajew, Alex F
2014-08-21
A technique for analyzing the effect of the geometrical shape of a source or a detector, using a quadrupole expansion, is described herein. It is shown that this method may be exploited to predict, optimize the geometry of a source, or a measurement device, and nearly eliminate, the departure from the 1/r(2) fall-off characteristic due to irradiation from small sources. We have investigated several simple shapes that have a vanishing Q2 quadrupole moment: a right circular cylinder with a diameter to depth ratio of √[2], a cone with a radius to height ratio of unity, and an oblate ellipsoid with a diameter to depth ratio of √[3/2]. These ideal shapes produce optimally small departures in a 1/r(2) field, nearly mimicking a point-like detector. We have also found a rotationally symmetric shape, intermediate to the other three, that has additionally, a vanishing Q4, the hexadecapole moment. This geometry further improves the 1/r(2)-perturbation characteristics and has an additional free parameter that may be adjusted to model the ideal cylinder, cone or oblate spheroid. PMID:25054611
Solvent effects on the relative stability of the PdCl2(H2O)n and PdHCl(H2O)n cis and trans isomers
NASA Astrophysics Data System (ADS)
Siegbahn, Per E. M.
The relative stability of the cis and trans isomers of the PdCl2(H2O)n and PdHCl(H2O)n complexes with up to six water ligands has been studied. Optimized geometries are discussed with particular emphasis on the positions taken by the second sphere water ligands. It is found that the empty coordination site above palladium is not as attractive for the second sphere ligands as might have been anticipated. Two types of hydrogen bonds, of O-H...Pd and O-H...H-Pd were found, which have only recently been detected experimentally. The effect of a water solvent on the complexes was then studied using a model with a spherical cavity surrounded by a dielectric continuum. Since the cis forms of the complexes have large dipole moments, the dipole term of the solvent reaction field strongly favours these structures. However, it is found that the quadrupolar terms have an almost equally large effect in the opposite direction, favouring the trans isomer. Even the octapole and hexadecapole moments make non-negligible contributions to the relative stabilities.
Stability of {sup 248–254}Cf isotopes against alpha and cluster radioactivity
Santhosh, K.P. Biju, R.K.
2013-07-15
Stability of {sup 248–254}Cf nuclei against alpha and cluster emissions is studied within our Coulomb and proximity potential model (CPPM). It is found that these nuclei are stable against light clusters (except alpha particles) and unstable against heavy cluster (A{sub 2}≥40) emissions. For heavy cluster emissions the daughter nuclei lead to doubly magic {sup 208}Pb or the neighbouring one. The effects of quadrupole and hexadecapole deformations of parent nuclei, daughter nuclei and emitted cluster on half lives are also studied. The computed alpha decay half life values (including quadrupole deformation β{sub 2}) are in close agreement with experimental data. Inclusion of quadrupole deformation reduces the height and width of the barrier (increases the barrier penetrability) and hence half life decreases. -- Highlights: •{sup 248–254}Cf parents are stable against light clusters (except alpha particles) and are unstable against heavy clusters ({sup 46}Ar, {sup 48,50}Ca etc.). •For the case of heavy cluster emissions the daughter nuclei are doubly magic {sup 208}Pb or neighbouring one. •The alpha decay half lives are in agreement with experimental data. •The cluster decay half lives decrease with the inclusion of quadrupole deformation.
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).
GAMMASPHERE+FMA : a journey beyond the proton drip-line.
Seweryniak, D.; Woods, P. J.; Ressler, J. J.; Davids, C. N.; Heinz, A.; Sonzogni, A. A.; Uusitalo, J.; Walters, W. B.; Caggiano, J. A.; Carpenter, M. P.; Cizewski, J. A.; Davinson, T.; Ding, K. Y.; Fotiades, N.; Garg, U.; Janssens, R. V. F.; Khoo, T. L.; Kondev, F. G.; Lauritsen, T.; Lister, C. J.; Reiter, P.; Shergur, J.; Wiedenhover, I.
2000-11-30
The majority of experiments performed during the 2-year long stay of GAMMAS-PHERE at the Argonne National Laboratory aimed to study proton-rich nuclei far from the line of stability at and beyond the proton drip-line. A high reaction channel selectivity was required to assign in-beam {gamma}-ray transitions to weakly populated exotic nuclei in the presence of background from strong reaction channels. In many of the experiments this was achieved by using the Argonne fragment mass analyzer to separate heavy-ion fusion-evaporation reaction products from scattered beam and disperse them according to their mass-over-charge-state ratio. For medium mass and heavy a and proton emitters the Recoil-Decay Tagging method was implemented. In-beam {gamma}-ray transitions were observed in several proton emitters between Z=50 and Z=82. Among others, rotational bands were assigned to {sup 141}Ho and {sup 131}Eu. A quadruple deformation of {beta}=0.25(4) was deduced for the ground state in {sup 141}Ho from the extracted dynamic moment of inertia. Based on observed band crossings and signature splittings the 7/2{sup {minus}} [523] and 1/2{sup +}[411] configurations were proposed for the ground state and the isomeric state, respectively. Comparison with particle-rotor calculations indicates, however, that {sup 141}Ho may have significant hexadecapole deformation and could be triaxial.
Collision-induced rotovibrational spectra of H/sub 2/-He pairs from first principles
Frommhold, L.; Meyer, W.
1987-01-15
A previous study of the collision-induced dipole moment has treated the H/sub 2/-He complex as a molecule in self-consistent-field and size-consistent coupled-electron-pair approximation (Meyer and Frommhold, Phys. Rev. A 34, 2771 (1986)). Based on that work, the vibrational dipole transition elements
NASA Astrophysics Data System (ADS)
Szmytkowski, Radosław; Łukasik, Grzegorz
2016-09-01
We present tabulated data for several families of static electric and magnetic multipole susceptibilities for hydrogenic atoms with nuclear charge numbers from the range 1 ⩽ Z ⩽ 137. Atomic nuclei are assumed to be point-like and spinless. The susceptibilities considered include the multipole electric polarizabilities α E L → E L and magnetizabilities (magnetic susceptibilities) χ M L → M L with 1 ⩽ L ⩽ 4 (i.e., the dipole, quadrupole, octupole and hexadecapole ones), the electric-to-magnetic cross-susceptibilities α E L → M(L - 1) with 2 ⩽ L ⩽ 5 and α E L → M(L + 1) with 1 ⩽ L ⩽ 4, the magnetic-to-electric cross-susceptibilities χ M L → E(L - 1) with 2 ⩽ L ⩽ 5 and χ M L → E(L + 1) with 1 ⩽ L ⩽ 4 (it holds that χ M L → E(L ∓ 1) =α E(L ∓ 1) → M L), and the electric-to-toroidal-magnetic cross-susceptibilities α E L → T L with 1 ⩽ L ⩽ 4. Numerical values are computed from general exact analytical formulas, derived by us elsewhere within the framework of the Dirac relativistic quantum mechanics, and involving generalized hypergeometric functions 3F2 of the unit argument.
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.
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.
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
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.
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.
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.
Multiproperty empirical isotropic interatomic potentials for CH4–inert gas mixtures
El-Kader, M.S.A.
2012-01-01
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. PMID:25685458
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.
Polarizable atomic multipole X-ray refinement: application to peptide crystals
Schnieders, Michael J.; Fenn, Timothy D.; Pande, Vijay S.; Brunger, Axel T.
2009-01-01
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 free by 20–40% relative to the original spherically symmetric scattering model. PMID:19690373
Quantum Chemical Analysis of MHC-Peptide Interactions for Vaccine Design
Agudelo, W.A; Patarroyo, M.E
2010-01-01
The development of an adequate immune response against pathogens is mediated by molecular interactions between different cell types. Among them, binding of antigenic peptides to the Major Histocompatibility Complex (MHC) molecule expressed on the membrane of antigen presenting cells (APCs), and their subsequent recognition by the T cell receptor have been demonstrated to be crucial for developing an adequate immune response. The present review compiles computational quantum chemistry studies about the electrostatic potential variations induced on the MHC binding region by peptide’s amino acids, carried out with the aim of describing MHC–peptide binding interactions. The global idea is that the electrostatic potential can be represented in terms of a series expansion (charge, dipole, quadrupole, hexadecapole, etc.) whose three first terms provide a good local approximation to the molecular electrostatic ‘landscape’ and to the variations induced on such landscape by targeted modifications on the residues of the antigenic peptide. Studies carried out in four MHC class II human allele molecules, which are the most representative alleles of their corresponding haplotypes, showed that each of these molecules have conserved as well as specific electrostatic characteristics, which can be correlated at a good extent with the peptide binding profiles reported experimentally for these molecules. The information provided by such characteristics would help increase our knowledge about antigen binding and presentation, and could ultimately contribute to developing a logical and rational methodology for designing chemically synthesized, multi-antigenic, subunit-based vaccines, through the application of quantum chemistry methods. PMID:20394575
Geometric biases in power-spectrum measurements
NASA Astrophysics Data System (ADS)
Samushia, L.; Branchini, E.; Percival, W. J.
2015-10-01
The observed distribution of galaxies has local transverse isotropy around the line of sight (LOS) with respect to the observer. The difference in the statistical clustering signal along and across the LOS encodes important information about the geometry of the Universe, its expansion rate and the rate of growth of structure within it. Because the LOS varies across a survey, the standard fast Fourier transform (FFT) based methods of measuring the anisotropic power spectrum (APS) cannot be used for surveys with wide observational footprint, other than to measure the monopole moment. We derive a simple analytic formula to quantify the bias for higher order Legendre moments, and we demonstrate that it is scale independent for a simple survey model, and depends only on the observed area. We derive a similar numerical correction formula for recently proposed alternative estimators of the APS that are based on summing over galaxies rather than using an FFT, and can therefore incorporate a varying LOS. We demonstrate that their bias depends on scale but not on the observed area. For a quadrupole the bias is always less than 1 per cent for k > 0.01 h Mpc^{-1} at z > 0.32. For a hexadecapole the bias is below 5 per cent for k > 0.05 h Mpc^{-1} at z > 0.32.
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.
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, |
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.
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.
The charge density of urea from synchrotron diffraction data.
Birkedal, Henrik; Madsen, Dennis; Mathiesen, Ragnvald H; Knudsen, Kenneth; Weber, Hans-Peter; Pattison, Philip; Schwarzenbach, Dieter
2004-09-01
The charge density of urea is studied using very high precision single-crystal synchrotron-radiation diffraction data collected at the Swiss-Norwegian Beam Lines at ESRF. An unprecedented resolution of 1.44 A(-1) in sin theta;/lambda is obtained at 123 K. The optimization of the experiment for charge-density studies is discussed. The high precision of the data allowed the refinement of a multipole model extending to hexadecapoles and quadrupoles on the heavy and H atoms, respectively, as well as a liberal treatment of radial functions. The topological properties of the resulting electron density are analysed and compared with earlier experimental results as well as with periodic Hartree-Fock calculations. The properties of the strongly polarized C-O bond agree with trends derived from previous experimental results while the ab initio calculations differ significantly. The results indicate that the description of the C-O bond requires more flexible basis sets in the theoretical calculations. The calculated integrated atomic charges are much larger than the observed ones. It is suggested that the present experimental results provide new target values for validation of future ab initio calculations. The molecular dipole moment derived from the integrated atomic properties is the same as the one obtained from the multipole model even though the individual atomic contributions differ. Comparison with literature data for urea in solution and the gas phase yields a dipole enhancement in the solid of about 1.5 D. The thermal expansion of urea is determined using synchrotron powder diffraction data. With decreasing temperature, an increasing anisotropic strain is observed. PMID:15477674
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.
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*.
{sup 208}Pb-daughter cluster radioactivity and the deformations and orientations of nuclei
Arun, Sham K.; Gupta, Raj K.; Singh, BirBikram; Kanwar, Shefali; Sharma, Manoj K.
2009-06-15
The role of deformations and orientations of nuclei is studied for the first time in cluster decays of various radioactive nuclei, particularly those decaying to doubly closed shell, spherical {sup 208}Pb daughter nucleus. Also, the significance of using the correct Q-value of the decay process is pointed out. The model used is the preformed cluster model (PCM) of Gupta and collaborators [R. K. Gupta et al., Proc. Int. Conf. on Nuclear Reactions Mechanisms, Varenna, 1988, p. 416; Phys. Rev. C 39, 1992 (1989); 55, 218 (1997); Heavy Elements and Related New Phenomena, edited by W. Greiner and R. K. Gupta, World Sc. 1999, Vol. II, p. 731]. In this model, cluster emission is treated as a tunneling of the confining interaction barrier by a cluster considered already preformed with a relative probability P{sub 0}. Since both the scattering potential and potential energy surface due to the fragmentation process in the ground state of the parent nucleus change significantly with the inclusion of deformation and orientation effects, both the penetrability P and preformation probability P{sub 0} of clusters change accordingly. The calculated decay half-lives for all the cluster decays investigated here are generally in good agreement with measured values for the calculation performed with quadrupole deformations {beta}{sub 2} alone and 'optimum' orientations of cold elongated configurations. In some cases, particularly for {sup 14}C decay of Ra nuclei, the inclusion of multipole deformations up to hexadecapole {beta}{sub 4} is found to be essential for a comparison with data. However, the available {beta}{sub 4}-values, particularly for nuclei in the mass region 16{<=}A{<=}26, need be used with caution.
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.
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)
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)
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)
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
Accurate electric multipole moment, static polarizability and hyperpolarizability derivatives for N2
NASA Astrophysics Data System (ADS)
Maroulis, George
2003-02-01
We report accurate values of the electric moments, static polarizabilities, hyperpolarizabilities and their respective derivatives for N2. Our values have been extracted from finite-field Møller-Pleset perturbation theory and coupled cluster calculations performed with carefully designed basis sets. A large [15s12p9d7f] basis set consisting of 290 CGTF is expected to provide reference self-consistent-field values of near-Hartree-Fock quality for all properties. The Hartree-Fock limit for the mean hyperpolarizability is estimated at γ¯=715±4e4a04Eh-3 at the experimental bond length Re=2.074 32a0. Accurate estimates of the electron correlation effects were obtained with a [10s7p6d4f] basis set. Our best values are Θ=-1.1258ea02 for the quadrupole and Φ=-6.75ea04 for the hexadecapole moment, ᾱ=11.7709 and Δα=4.6074e2a02Eh-1 for the mean and the anisotropy of the dipole polarizability, C¯=41.63e2a04Eh-1 for the mean quadrupole polarizability and γ¯=927e4a04Eh-3 for the dipole hyperpolarizability. The latter value is quite close to Shelton's experimental estimate of 917±5e4a04Eh-3 [D. P. Shelton, Phys. Rev. A 42, 2578 (1990)]. The R dependence of all properties has been calculated with a [7s5p4d2f] basis set. At the CCSD(T) level of theory the dipole polarizability varies around Re as ᾱ(R)/e2a02Eh-1=11.8483+6.1758(R-Re)+0.9191(R-Re)2-0.8212(R-Re)3-0.0006(R-Re)4, Δα(R)/e2a02Eh-1=4.6032+7.0301(R-Re)+1.9340(R-Re)2-0.5708(R-Re)3+0.1949(R-Re)4. For the Cartesian components and the mean of γαβγδ, (dγzzzz/dR)e=1398, (dγxxxx/dR)e=867, (dγxxzz/dR)e=317, and (dγ¯/dR)e=994e4a03Eh-3. For the quadrupole polarizability Cαβ,γδ, we report (dCzz,zz/dR)e=19.20, (dCxz,xz/dR)e=16.55, (dCxx,xx/dR)e=10.20, and (dC¯/dR)e=23.31e2a03Eh-1. At the MP2 level of theory the components of the dipole-octopole polarizability (Eα,βγδ) and the mean dipole-dipole-octopole hyperpolarizability B¯ we have obtained (dEz,zzz/dR)e=36.71, (dEx,xxx/dR)e=-12.94e2a03Eh-1, and
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
NASA Astrophysics Data System (ADS)
Maroulis, George
1998-04-01
The electric multipole moments, dipole and quadrupole polarizability and hyperpolarizability of hydrogen chloride have been determined from an extensive and systematic study based on finite-field fourth-order many-body perturbation theory and coupled-cluster calculations. Our best values for the dipole, quadrupole, octopole and hexadecapole moment at the experimental internuclear separation of Re=2.408645a0 are μ=0.4238ea0, Θ=2.67ea02, Ω=3.94ea03, and Φ=13.37ea04, respectively. For the mean and the anisotropy of the dipole polarizability ααβ we recommend ᾱ=17.41±0.02 and Δα=1.60±0.03e2a02Eh-1. For the mean value of the first dipole hyperpolarizability βαβγ we advance β¯=-6.8±0.3e3a03Eh-2. Extensive calculations with a [8s6p6d3f/5s4p2d1f] basis set at the CCSD(T) level of theory yield the R-dependence of the Cartesian components and the mean of the second dipole hyperpolarizability γαβγδ(R)/e4a04Eh-3 around Re as γzzzz(R)=1907+1326(R-Re)+570(R-Re)2+10(R-Re)3-40(R-Re)4, γxxxx(R)=3900+747(R-Re)-65(R-Re)2-38(R-Re)3-7(R-Re)4, γxxzz(R)=962+222(R-Re)+88(R-Re)2+49(R-Re)3+5(R-Re)4, γ¯(R)=3230+841(R-Re)+151(R-Re)2+21(R-Re)3-9(R-Re)4, with z as the molecular axis. The present investigation suggests an estimate of (26.7±0.3)×102e4a04Eh-3 for the Hartree-Fock limit of the mean value γ¯ at Re. CCSD(T) calculations with basis sets of [8s6p6d3f/5s4p2d1f] and [9s7p5d4f/6s5p4d1f] size and MP4 calculations with the even larger [15s12p7d3f/12s7p2d1f] give (7.0±0.3)×102e4a04Eh-3 for the electron correlation effects for this property, thus leading to a recommended value of γ¯=(33.7±0.6)×102e4a04Eh-3. For the quadrupole polarizability Cαβ,γδ/e2a04Eh-1 at Re our best values are Czz,zz=41.68, Cxz,xz=26.11, and Cxx,xx=35.38, calculated with the [9s7p5d4f/6s5p4d1f] basis set at the CCSD(T) level of theory. The following CCSD(T) values were obtained with [8s6p6d3f/5s4p2d1f] at Re: dipole-quadrupole polarizability Aα,βγ/e2a03Eh-1, Az,zz=14.0, and