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Sample records for hexadecapoles

  1. 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.

  2. Octupole and hexadecapole bands in 152Sm

    SciTech Connect

    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.

  3. Production and detection of atomic hexadecapole at Earth's magnetic field

    NASA Astrophysics Data System (ADS)

    Acosta, V. M.; Auzinsh, M.; Gawlik, W.; Grisins, P.; Higbie, J. M.; Jackson Kimball, D. F.; Krzemien, L.; Ledbetter, M. P.; Pustelny, S.; Rochester, S. M.; Yashchuk, V. V.; Budker, D.

    2008-07-01

    Anisotropy of atomic states is characterized by population differences and coherences between Zeeman sublevels. It can be efficiently created and probed via resonant interactions with light, the technique which is at the heart of modern atomic clocks and magnetometers. Recently, nonlinear magneto-optical techniques have been developed for selective production and detection of higher polarization moments, hexadecapole and hexacontatetrapole, in the ground states of the alkali atoms. Extension of these techniques into the range of geomagnetic fields is important for practical applications. This is because hexadecapole polarization corresponding to the $\\Delta M=4$ Zeeman coherence, with maximum possible $\\Delta M$ for electronic angular momentum $J=1/2$ and nuclear spin $I=3/2$, is insensitive to the nonlinear Zeeman effect (NLZ). This is of particular interest because NLZ normally leads to resonance splitting and systematic errors in atomic magnetometers. However, optical signals due to the hexadecapole moment decline sharply as a function of magnetic field. We report a novel method that allows selective creation of a macroscopic long-lived ground-state hexadecapole polarization. The immunity of the hexadecapole signal to NLZ is demonstrated with F=2 $^{87}$Rb atoms at Earth's field.

  4. Quadrupole and hexadecapole couplings for {sup 127}I in Li{sup 127}I

    SciTech Connect

    Thyssen, Jorn; Schwerdtfeger, Peter; Bender, Michael; Nazarewicz, Witold; Semmes, Paul B.

    2001-02-01

    The quadrupole and hexadecapole coupling constants for {sup 127}I in LiI were determined from relativistic Dirac-Fock electronic structure and self-consistent nuclear structure calculations. While the calculated quadrupole coupling constant agrees with the experimental value, the predicted hexadecapole coupling constant ranges between +6 and +20 mHz, which is of opposite sign and about three orders of magnitude smaller than the value deduced from recent high resolution radio-frequency molecular beam measurements [J. Cederberg, D. Olson, A. Nelson, D. Laine, P. Zimmer, M. Welge, M. Feig, T. Ho''ft, and N. London, J. Chem. Phys. 110, 2431 (1999)].

  5. Quadrupole and hexadecapole couplings for 127I in Li127I

    NASA Astrophysics Data System (ADS)

    Thyssen, Jørn; Schwerdtfeger, Peter; Bender, Michael; Nazarewicz, Witold; Semmes, Paul B.

    2001-02-01

    The quadrupole and hexadecapole coupling constants for 127I in LiI were determined from relativistic Dirac-Fock electronic structure and self-consistent nuclear structure calculations. While the calculated quadrupole coupling constant agrees with the experimental value, the predicted hexadecapole coupling constant ranges between +6 and +20 mHz, which is of opposite sign and about three orders of magnitude smaller than the value deduced from recent high resolution radio-frequency molecular beam measurements [J. Cederberg, D. Olson, A. Nelson, D. Laine, P. Zimmer, M. Welge, M. Feig, T. Höft, and N. London, J. Chem. Phys. 110, 2431 (1999)].

  6. 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.

  7. Elliptic and Hexadecapole Flow of Charged Hadrons in Au+Au Collisions at sNN=200GeV

    NASA Astrophysics Data System (ADS)

    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.; Csörgő, 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., Jr.; 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.-Å.; 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, Á.; 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.; Liška, 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.; Mikeš, 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.; Ružička, 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.; Slunečka, 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.; Tomášek, 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 (v2) and hexadecapole (v4) Fourier flow coefficients are reported for charged hadrons as a function of transverse momentum (pT) and collision centrality or number of participant nucleons (Npart) for Au+Au collisions at sNN=200GeV. The v2,4 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 v4(pT) are observed with a ratio v4(pT,Npart)/v22(pT,Npart)≈0.8 for 50≲Npart≲200, which is compatible with the combined effects of a finite viscosity and initial eccentricity fluctuations. For Npart≳200 this ratio increases up to 1.7 in the most central collisions.

  8. Elliptic and Hexadecapole Flow of Charged Hadrons in Au+Au Collisions at s_NN = 200 GeV

    SciTech Connect

    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.

  9. Elliptic and Hexadecapole Flow of Charged Hadrons in Au + Au Collisions at root s(NN)=GeV

    SciTech Connect

    Adare, A.; PHENIX Collaboration

    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}| {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 {approx}< N{sub part} {approx}< 200, which is compatible with the combined effects of a finite viscosity and initial eccentricity fluctuations. For N{sub part} {approx}> 200 this ratio increases up to 1.7 in the most central collisions.

  10. Elliptic and hexadecapole flow of charged hadrons in Au+Au collisions at sq.rt(s(NN))=200  GeV.

    PubMed

    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.

  11. Quadrupole, octopole, and hexadecapole electric moments of Sigma, Pi, Delta, and Phi electronic states: cylindrically asymmetric charge density distributions in linear molecules with nonzero electronic angular momentum.

    PubMed

    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

  12. Rotational enhancement of Doppler measurements of solar and stellar hexadecapole oscillations

    NASA Astrophysics Data System (ADS)

    Christensen-Dalsgaard, J.; Gough, D. O.

    The possibility that rotational enhancement of the sensitivity of whole-disk Doppler observations of solar oscillations may permit the measurement of five-minute modes of degree l = 4 is considered. The method is applied to South Pole data. An analysis of superposed power spectra of artificial solar data suggests that estimations of power above the level of noise in the data of Palle et al. (1986) may provide confirmation of the rotational splitting noted by Duvall and Harvey (1984). It is pointed out that the present method extends the range of penetration depths of potentially detectable modes, adding substantially to the diagnostic power of the data to measure conditions in stellar cores.

  13. Microscopic study of low-lying yrast spectra in 100429108 Mo isotopes

    NASA Astrophysics Data System (ADS)

    Sawhney, Neeru; Bharti, Arun; Khosa, S. K.

    2002-10-01

    Variation-after-projection (VAP) calculations in conjunction with Hartree-Bogoliubov (HB) ansatz have been carried out for A=100-108 molybdenum (Mo) isotopes. In this framework, the yrast spectra with J_{max}(pi) ≥ 10(+) , B(E2) transition probabilities, quadrupole (bt_2) and hexadecapole (bt_4) deformation parameters, moment of inertia (I) and square of cranking frequency (om(2)) for even-even Mo isotopes have been obtained. The results of the calculation give an indication that it is important to include the hexadecapole-hexadecapole component of the two-body interaction for obtaining various nuclear structure quantities in these Mo isotopes.

  14. General formalism of collective motion for any deformed system

    NASA Astrophysics Data System (ADS)

    Guo, Jian-You

    2015-07-01

    Based on Bohr model, I have presented a general formalism describing the collective motion for any deformed system, in which the collective Hamiltonian is expressed as vibrations in the body-fixed frame, rotation of whole system around the laboratory frame, and coupling between vibrations and rotation. Under the condition of decoupling approximation, I have derived the quantized Hamiltonian operator. Based on the operator, I have calculated the rotational spectra for some special octupole and hexadecapole deformed systems and shown their dependencies on deformation. The result indicates that the contribution of octupole or hexadecapole deformations to the lowest band is regular, while that to higher bands is dramatic. These features reflecting octupole and hexadecapole deformations are helpful in recognizing the properties of real nuclei with octupole and/or hexadecapole deformations coexisting with quadrupole deformations.

  15. Reply to "Comment on two-phonon gamma-vibrational strength in osmium nuclei"

    SciTech Connect

    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.

  16. Study of mixed-symmetry excitations in 96Ru via inelastic proton-scattering

    NASA Astrophysics Data System (ADS)

    Hennig, A.; Spieker, M.; Werner, V.; Ahn, T.; Anagnostatou, V.; Cooper, N.; Derya, V.; Elvers, M.; Endres, J.; Goddard, P.; Heinz, A.; Hughes, R. O.; Ilie, G.; Mineva, M. N.; Pickstone, S. G.; Petkov, P.; Radeck, D.; Ross, T.; Savran, D.; Zilges, A.

    2015-02-01

    Mixed-symmetry states of octupole (L = 3) and hexadecapole (L = 4) character have been recently proposed in the N = 52 isotones 92 Zr and 94Mo, based on strong M1 transitions to the lowest-lying 3- and 4+ states, respectively. In order to investigate similar excitations in the heaviest stable N = 52 isotone 96Ru, two inelastic proton-scattering experiments have been performed at the Wright Nuclear Structure Laboratory (WNSL), Yale University, USA and the Institute for Nuclear Physics, University of Cologne, Germany. From the combined data of both experiments, absolute E1, M1, and E2 transition strengths were extracted, allowing for the identification of candidates for MS octupole and hexadecapole states. The structure of the low-lying 4+ states is investigated by means of sdg-IBM-2 calculations.

  17. Hexadecapolar Colloids

    DOE PAGESBeta

    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

  18. Structure of the K{sup {pi}} = 4{sup +} bands in {sup 186,188}Os

    SciTech Connect

    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.

  19. 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).

  20. Hexadecapolar colloids

    PubMed Central

    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

  1. 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.

  2. E4 properties in deformed nuclei and the sdg interacting boson model

    SciTech Connect

    Wu, H.C.; Dieperink, A.E.L.; Scholten, O.; Harakeh, M.N.; De Leo, R.; Pignanelli, M.; Morrison, I.

    1988-10-01

    The hexadecapole transition strength distribution is measured for the deformed nucleus /sup 150/Nd using the (p,p') reaction at E/sub p/ = 30 MeV. The experimental information on B(E4) values in this nucleus and in /sup 156/Gd is interpreted in the framework of the sdg interacting boson model. It is found that the main features of the experimental data are fairly well reproduced by a Hartree-Bose method plus Tamm-Dancoff approximation.

  3. Medium-energy hadron-nucleus scattering in the 1/[ital N] expansion formalism

    SciTech Connect

    Kuyucak, S. ); Morrison, I. )

    1993-08-01

    The algebraic-eikonal approach to the medium-energy hadron-nucleus scattering is generalized to arbitrary interactions and boson types using the 1/[ital N] expansion technique for the interacting boson model. The results are used in a comparative study of proton scattering from deformed nuclei in the [ital sd] and [ital sdg] boson models. The two models give almost identical results for a pure quadrupole interaction but widely differ when a hexadecapole interaction is included.

  4. Beam energy dependence of azimuthal anisotropy at RHIC-PHENIX

    SciTech Connect

    Taranenko, A.

    2012-05-15

    Recent PHENIX measurements of the elliptic ({upsilon}{sub 2}) and hexadecapole ({upsilon}{sub 4}) Fourier flow coefficients for charged hadrons as a function of transverse momentum (p{sub T}), collision centrality and particle species are presented and compared with results from the PHOBOS and STAR Collaborations respectively. The status of extensions to future PHENIX measurements at lower beam energies is also discussed.

  5. 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.

  6. Ternary fission of nuclei into comparable fragments

    SciTech Connect

    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.

  7. 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.

  8. Ternary fission of nuclei into comparable fragments

    NASA Astrophysics Data System (ADS)

    Karpeshin, F. F.

    2015-07-01

    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.

  9. Description of strong M1 transitions between 4^+ states at N=52 within the sdg-IBM-2

    NASA Astrophysics Data System (ADS)

    Casperson, R. J.; Werner, V.; Heinze, S.

    2009-10-01

    The interplay between collective and single-particle degrees of freedom for nuclei near the N=50 shell closure have recently been under investigation. In Molybdenum and Ruthenium nuclei, collective symmetric and mixed-symmetric structures have been identified, while in Zirconium, underlying shell-structure plays an enhanced role. The one-phonon 2^+ mixed-symmetry state was identified from its strong M1 transition to the 2^+1 state. Similar transitions were observed between 4^+ states in ^94Mo and ^92Zr, and shell model calculations indicate that hexadecapole excitations play a role. These phenomena will be investigated within the sdg-Interacting Boson Model-2 in order to gain a better understanding about the structure of the states involved, and to which extent the hexadecapole degree of freedom is important at relatively low energies. First calculations within this model, using an F-spin conserving Hamiltonian to disentangle symmetric and mixed- symmetric structures, will be presented and compared to data.

  10. Phase transitions in the sdg interacting boson model

    NASA Astrophysics Data System (ADS)

    Van Isacker, P.; Bouldjedri, A.; Zerguine, S.

    2010-05-01

    A geometric analysis of the sdg interacting boson model is performed. A coherent state is used in terms of three types of deformation: axial quadrupole ( β), axial hexadecapole ( β) and triaxial ( γ). The phase-transitional structure is established for a schematic sdg Hamiltonian which is intermediate between four dynamical symmetries of U(15), namely the spherical U(5)⊗U(9), the (prolate and oblate) deformed SU(3) and the γ-soft SO(15) limits. For realistic choices of the Hamiltonian parameters the resulting phase diagram has properties close to what is obtained in the sd version of the model and, in particular, no transition towards a stable triaxial shape is found.

  11. Triaxial rotor model description of E2 properties in Os186,188,190,192

    NASA Astrophysics Data System (ADS)

    Allmond, J. M.; Zaballa, R.; Oros-Peusquens, A. M.; Kulp, W. D.; Wood, J. L.

    2008-07-01

    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 Os186,188,190,192. Most large and medium transition E2 matrix elements can be reproduced to within ~10%, and most diagonal elements to within ~30%. Most small transition matrix elements can be reproduced to within ~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 Os190,192 indicate significant admixtures of K=4 components. Attention is given to the Kπ=4+ bands in these nuclei and the controversial issue of whether they are of quadrupole or hexadecapole nature.

  12. Microscopic structure of low-lying states in {sup 188,190,192}Os

    SciTech Connect

    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.

  13. Structure of the K{sup {pi}=}4{sup +} bands in {sup 186,188}Os

    SciTech Connect

    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 +}.

  14. Nature of the K{sup {pi}} = 4{sup +} bands in the Os isotopes

    SciTech Connect

    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.

  15. Global Calculations of Ground-State Axial Shape Asymmetry of Nuclei

    SciTech Connect

    Moeller, Peter; Bengtsson, Ragnar; Carlsson, B. Gillis; Olivius, Peter; Ichikawa, Takatoshi

    2006-10-20

    Important insight into the symmetry properties of the nuclear ground-state (gs) shape is obtained from the characteristics of low-lying collective energy-level spectra. In the 1950s, experimental and theoretical studies showed that in the gs many nuclei are spheroidal in shape rather than spherical. Later, a hexadecapole component of the gs shape was identified. In the 1970-1995 time frame, a consensus that reflection symmetry of the gs shape was broken for some nuclei emerged. Here we present the first calculation across the nuclear chart of axial symmetry breaking in the nuclear gs. We show that we fulfill a necessary condition: Where we calculate axial symmetry breaking, characteristic gamma bands are observed experimentally. Moreover, we find that, for those nuclei where axial asymmetry is found, a systematic deviation between calculated and measured masses is removed.

  16. Nuclear charge radii and electric quadrupole moments of even-even isotopes

    SciTech Connect

    Nerlo-Pomorska, B.; Mach, B.

    1995-07-01

    Isotope shifts of the charge mean-square radii and electric quadrupole moments of even-even nuclei with 20{le}{Zeta}{le}98 are calculated using a dynamical microscopic model. A single-particle Nilsson potential with the Seo set of correction terms, pairing forces in the BCS formalism, and a long-range interaction in the local approximation are used. A collective Hamiltionian is obtained using a generator coordinate method with the Gaussian overlap approximation. The potential energy of the nucleus consists of a microscopic-macroscopic Strutinsky energy and a zero-point vibrational term. A liquid droplet model is used for the macroscopic part of the potential. A BCS wave function is taken as a generator function, and two collective variables, quadrupole and hexadecapole deformations, serve as the generator coordinates. In general, good agreement between the theory and experimental data is achieved. 16 refs., 8 figs., 1 tab.

  17. Microscopic Calculations of 240Pu Fission

    SciTech Connect

    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.

  18. Electromagnetic Properties of the I π = 11/2‑ isomers in the cadmium isotopes: What can we learn from them?

    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.

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

    NASA Astrophysics Data System (ADS)

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

    2004-01-01

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

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

    PubMed

    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

  1. Effect of coupling in the 28Si+154Sm reaction studied by quasi-elastic scattering

    NASA Astrophysics Data System (ADS)

    Kaur, Gurpreet; Behera, B. R.; Jhingan, A.; Nayak, B. K.; Dubey, R.; Sharma, Priya; Thakur, Meenu; Mahajan, Ruchi; Saneesh, N.; Banerjee, Tathagata; Khushboo, Kumar, A.; Mandal, S.; Saxena, A.; Sugathan, P.; Rowley, N.

    2016-09-01

    The study of the coupling to collective states of the 28Si projectile and 154Sm target in fusion mechanism is reported. Understanding such couplings is important as they influence the barrier height and the formation probability of the compound nuclei, which in turn may be related to the synthesis of superheavy elements in heavier systems. In the present work, before performing the coupled-channel calculations, we wish to obtain an experimental signature of coupling to projectile and target excitation through barrier distribution (BD) study. To this end, the BDs of the 28Si+154Sm and 16O+154Sm systems have been compared using existing fusion data, scaled to compensate for the differences between the nominal Coulomb barriers and the respective coupling strengths. However, the large error bars on the high-energy side of the fusion BD prevent any definite identification of such signatures. We have, therefore, performed a quasi-elastic (QE) scattering experiment for the heavier 28Si+154Sm system and compared its results with existing QE data for the 16O projectile. Since QE BDs are precise at higher energies, the comparison has shown that the BD of 28Si+154Sm is similar to that of 16O+154Sm to a large extent except for a peaklike structure on the higher energy side. The similarity shows that the 154Sm deformation plays a major role in the fusion mechanism of 28Si+154Sm system. The peaklike structure is attributed to 28Si excitation. In contrast with previous studies, it is found that a coupled-channel calculation with vibrational coupling to the first 2+ state of 28Si reproduces this structure rather well. However, an almost identical result is found with the rotational coupling scheme if one considers the large positive hexadecapole deformation of the projectile. A value around that given by Möller and Nix (β4≈0.25 ) leads to a strong cancellation in the re-orientation term that couples the 2+ state back to itself, making that state look vibrational in this

  2. HPAM: Hirshfeld Partitioned Atomic Multipoles.

    PubMed

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

    2012-02-01

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

  3. Investigation of 152Sm by Complementary Reactions

    NASA Astrophysics Data System (ADS)

    Garrett, P. E.; Kulp, W. D.; Wood, J. L.; Allmond, J. M.; Bandyopadhyay, D.; Christen, S.; Choudry, S. N.; Cline, D.; Dashdorj, D.; Dewald, A.; Fitzler, A.; Fransen, C.; Hayes, A. B.; Hua, H.; Jessen, K.; Jolie, J.; Kloezer, A.; Kudejova, P.; Kumar, A.; Lesher, S. R.; Linnemann, A.; Lisetskiy, A.; Martin, D.; Masur, M.; McEllistrem, M. T.; Möller, O.; Mynk, M. G.; McKay, C. J.; Orce, J. N.; Pejovic, P.; Pissulla, T.; Regis, J.-M.; Schiller, A.; Teng, R.; Tonev, D.; Wu, C. Y.; Yates, S. W.

    2009-01-01

    Understanding the nuclear structure of 152Sm, along with other N = 90 isotones, has long posed a challenge. A rapid transition in shape between the spherical N = 88 150Sm and well-deformed N = 92 154Sm is observed, along with strong evidence for shape coexistence. Competing ideas have been put forward over the decades, with the most recent being that N = 90 is at the critical point of a shape phase transition. Until recently, the lack of high-precision data has not allowed the competing models to be extensively tested. In a coordinated program of investigation, a series of complementary experiments, which include high-statistics β decay, multi-step Coulomb excitation, the 150Nd(α,2n) reaction, and the (n,n'γ) reaction, have been performed for 152Sm. These experiments have revealed the existence of a pairing-isomer band, a hexadecapole band, the lack of multi-phonon β vibrational bands, and the repetition of structures built on the first excited Kπ = 0+ as built on the ground state. The status of these coordinated studies is examined.

  4. Investigation of {sup 152}Sm by Complementary Reactions

    SciTech Connect

    Garrett, P. E.; Kulp, W. D.; Wood, J. L.; Allmond, J. M.; Bandyopadhyay, D.; Choudry, S. N.; Kumar, A.; Lesher, S. R.; McEllistrem, M. T.; Mynk, M. G.; McKay, C. J.; Orce, J. N.; Christen, S.; Dewald, A.; Fitzler, A.; Fransen, C.; Jessen, K.; Jolie, J.; Kloezer, A.; Kudejova, P.

    2009-01-28

    Understanding the nuclear structure of {sup 152}Sm, along with other N = 90 isotones, has long posed a challenge. A rapid transition in shape between the spherical N = 88 {sup 150}Sm and well-deformed N = 92 {sup 154}Sm is observed, along with strong evidence for shape coexistence. Competing ideas have been put forward over the decades, with the most recent being that N = 90 is at the critical point of a shape phase transition. Until recently, the lack of high-precision data has not allowed the competing models to be extensively tested. In a coordinated program of investigation, a series of complementary experiments, which include high-statistics {beta} decay, multi-step Coulomb excitation, the {sup 150}Nd({alpha},2n) reaction, and the (n,n'{gamma}) reaction, have been performed for {sup 152}Sm. These experiments have revealed the existence of a pairing-isomer band, a hexadecapole band, the lack of multi-phonon {beta} vibrational bands, and the repetition of structures built on the first excited K{sup {pi}} = 0{sup +} as built on the ground state. The status of these coordinated studies is examined.

  5. Collision-induced rotovibrational spectra of H/sub 2/-He pairs from first principles

    SciTech Connect

    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 associated with the fundamental band (v = 0..-->..v' = 1) are obtained as functions of separation R of the collisional pair for the isotropic and anisotropic overlap induction components (lambdaL = 01 and 21), and the quadrupole- and hexadecapole-induced parts (lambdaL = 23 and 45). From these induced dipole components and Meyer, Hariharan, and Kutzelnigg's isotropic part of the ab initio potential surface, we compute in the (forbidden) fundamental band of hydrogen the collision-induced absorption spectra of the collisional complex of hydrogen (H/sub 2/) and helium from an exact quantum formalism. Both the shape of the computed spectral profiles and the theoretical absolute intensity agree closely with existing measurements at temperatures from 18 to 300 K. The fact that these spectra, and presumably the analogous overtone and ''hot'' (v>0) bands of the H/sub 2/-He complex which are not known from measurements, can be accurately obtained from basic principles is significant for research related to the atmospheres of the giant planets and late-type stars.

  6. Cluster radioactivity with effects of deformations and orientations of nuclei included

    SciTech Connect

    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.

  7. Signature for g bosons from medium energy proton scattering experiments

    SciTech Connect

    Kuyucak, S.

    1993-10-01

    We apply the recently developed algebraic (1/N expansion) scattering formalism to medium energy proton scattering from {sup 154}Sm and {sup 176}Yb. The nuclear structure effects in this formalism are described by the interacting boson model generalized to arbitrary interactions and types of bosons i.e. s,d,g, etc. We find that, in the sd boson model, a consistent description of cross sections is possible only for the 0{sup +} and 2{sup +} states. The failure of the model with regard to the 4{sup +} states indicates that the effective hexadecapole operator used in the sd model is inadequate. In contrast, the data for scattering to the 0{sup +}, 2{sup +} and 4{sup +} states could be consistently described in the sdg boson model. The spectroscopic data for the low-lying levels usually can not distinguish between the sd and sdg models due to renormalization of parameters, and one has to look at high spin or energy data for evidence of g bosons. The inelastic proton scattering experiments, on the other hand, directly probe the wave functions, and hence could provide a signature for g bosons even in the ground band states.

  8. Impacts of satellite galaxies on the redshift-space distortions

    SciTech Connect

    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.

  9. Multipole plasmon resonances in self-assembled metal hollow-nanospheres.

    PubMed

    Yin, Jun; Zang, Yashu; Xu, Binbin; Li, Shuping; Kang, Junyong; Fang, Yanyan; Wu, Zhihao; Li, Jing

    2014-04-21

    Recently, multipole plasmonic mode resonances in metal hollow structures, such as dipole, quadrupole, and octupole modes, have been widely investigated by researchers with the aim for potential applications in bio-sensing, fluorescence, nanolasers or nonlinear nano-photonics. Here, in this work, the multipole plasmon resonances in self-assembled metal hollow-nanospheres (HNSs) are theoretically and experimentally demonstrated and the hot spots originating from the higher order mode plasmonic resonance and interparticle coupling effect are proposed to be used for Raman scattering enhancements. Dipole, quadrupole, octupole and hexadecapole mode plasmonic resonances were clearly resolved in the extinction spectra of these Ag HNS arrays showing good agreement with the theoretical simulation results. Strong regular hot spots were obtained around the surface and in the gaps of the Ag HNSs through the higher order mode plasmonic resonances and corresponding interparticle coupling effect between the HNSs. Maximum local field intensity was accomplished by optimizing the size of as well as the coupling distance between the HNSs and then it was applied to SERS sensing. Raman mapping also demonstrated these self-assembled plasmonic cavity arrays to be a stable and uniform SERS-active substrate.

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

    SciTech Connect

    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.

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

    NASA Astrophysics Data System (ADS)

    Szmytkowski, Radosław; Łukasik, Grzegorz

    2016-09-01

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

  12. Neutron one-quasiparticle states in {sup 251}Fm{sub 151} populated via the {alpha} decay of {sup 255}No

    SciTech Connect

    Asai, M.; Tsukada, K.; Ishii, Y.; Toyoshima, A.; Ishii, T.; Nagame, Y.; Nishinaka, I.; Haba, H.; Ichikawa, T.; Kojima, Y.; Sueki, K.

    2011-01-15

    Excited states in {sup 251}Fm populated via the {alpha} decay of {sup 255}No are studied in detail through {alpha}-{gamma} coincidence and {alpha} fine-structure measurements. Five excited states reported previously in {sup 251}Fm are firmly established through the {alpha}-{gamma} coincidence measurement, and rotational bands built on one-quasiparticle states are newly established through the {alpha} fine-structure measurement. Spin-parities and neutron configurations of the excited states in {sup 251}Fm as well as the ground state of {sup 255}No are definitely identified on the basis of deduced internal conversion coefficients, lifetimes of {gamma} transitions, rotational-band energies built on one-quasiparticle states, and hindrance factors of {alpha} transitions. It is found that the excitation energy of the 1/2{sup +}[620] state in N=151 isotones increases with the atomic number, especially at Z{>=}100, while that of the 1/2{sup +}[631] state decreases at Z=100. Ground-state deformations and energies of neutron one-quasiparticle states in the N=151 isotones are calculated using a macroscopic-microscopic model, and the energy systematics of the one-quasiparticle states in the isotones are discussed in terms of the evolution of nuclear deformation involving the hexadecapole ({beta}{sub 4}) and hexacontatetrapole ({beta}{sub 6}) deformations.

  13. Stability of {sup 248–254}Cf isotopes against alpha and cluster radioactivity

    SciTech Connect

    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.

  14. {alpha}-Decay half-lives, {alpha}-capture, and {alpha}-nucleus potential

    SciTech Connect

    Denisov, V. Yu. Khudenko, A.A.

    2009-11-15

    {alpha}-Decay half-lives and {alpha}-capture cross sections are evaluated in the framework of a unified model for {alpha}-decay and {alpha}-capture. In this model {alpha}-decay and {alpha}-capture are considered as penetration of the {alpha}-particle through the potential barrier formed by the nuclear, Coulomb, and centrifugal interactions between the {alpha}-particle and nucleus. The spins and parities of the parent and daughter nuclei as well as the quadrupole and hexadecapole deformations of the daughter nuclei are taken into account for evaluation of the {alpha}-decay half-lives. The {alpha}-decay half-lives for 344 nuclei and the {alpha}-capture cross sections of {sup 40}Ca, {sup 44}Ca, {sup 59}Co, {sup 208}Pb, and {sup 209}Bi agree well with the experimental data. The evaluated {alpha}-decay half-lives within the range of 10{sup -9}{<=}T{sub 1/2}{<=}10{sup 38} s for 1246 {alpha}-emitters are tabulated.

  15. 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.

  16. 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.

  17. Minimizing the 1/r(2) perturbation for ideal fluence detectors in small source γ-irradiation fields.

    PubMed

    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

  18. Higher-multipole deformations and compactness of hot fusion reactions

    SciTech Connect

    Manhas, Monika; Gupta, Raj K.; Li, Qingfeng; Greiner, Walter; Patra, S. K.

    2006-09-15

    The effect of adding the higher-multipole deformations {beta}{sub 6} and {beta}{sub 8}, and the octupole deformation {beta}{sub 3} (in addition to quadrupole and hexadecapole deformations {beta}{sub 2} and {beta}{sub 4}), on the distribution of barriers in orientation degrees of freedom is studied for a ''compact'' configuration of spherical-plus-deformed or deformed-plus-deformed nuclei in hot fusion reactions. Though {beta}{sub 3} is known to be nonzero for only a few nuclei, its role toward compactness of hot fusion reactions is found to be as important as that of {beta}{sub 4}. With {beta}{sub 3} included, depending on its sign and magnitude, the belly-to-belly compact, bbc (or equatorial compact, ec), configuration due to {beta}{sub 4} changes to not-belly-to-belly compact, nbbc (or not-equatorial compact, nec), and vice versa. Similarly, {beta}{sub 6} is found to be as important as {beta}{sub 3} and/or {beta}{sub 4} for spherical-plus-deformed nuclei, but is rather insignificant for collisions involving deformed-plus-deformed nuclei. On the other hand, the addition of {beta}{sub 8} is shown to be insignificant also for spherical-plus-deformed nuclei.

  19. Triaxial rotor model description of E2 properties in {sup 186,188,190,192}Os

    SciTech Connect

    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.

  20. 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.

  1. Quadrupole Polarizabilities in A ~150 Superdeformed Bands

    NASA Astrophysics Data System (ADS)

    Satula, Wojciech; Nazarewicz, Witold; Dobaczewski, Jacek; Dudek, Jerzy

    1996-10-01

    In this study, the quadrupole and hexadecapole moments of superdeformed (SD) bands in the A ~150 mass region have been analyzed in the cranking Skyrme-Hartree-Fock model. The analysis shows that the relative quadrupole moments, δ Q_20(X_A)≡ Q_20(X_A)-Q_20(^152Dy;yrast), follow experimental trends rather well and that they can be written as a sum of independent contributions from the single-particle/hole states around the doubly-magic SD core of ^152Dy with a surpisingly high accuracy. For more than 90% of the SD bands considered, the deviation |δ Q_20 ( X_A) - sum_Nn_zΛδ q^[Nn_zΛ]| is less than 0.04 b. It suggests that the SD high-spin bands around ^152Dy are excellent examples of an almost undisturbed single-particle motion, i.e., can be described by the extreme shell model.

  2. Quantum Chemical Analysis of MHC-Peptide Interactions for Vaccine Design

    PubMed Central

    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

  3. 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.

  4. 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.

  5. Universal correlations of nuclear observables and the structure of exotic nuclei

    SciTech Connect

    Casten, R.F.; Zamfir, N.V. |||

    1996-12-31

    Despite the apparent complexity of nuclear structural evolution, recent work has shown a remarkable underlying simplicity that is unexpected, global, and which leads to new signatures for structure based on the easiest-to-obtain data. As such they will be extremely valuable for use in the experiments with low intensity radioactive beams. Beautiful correlations based either on extrinsic variables such as N{sub p}N{sub n} or the P-factor or correlations between collective observables themselves have been discovered. Examples to be discussed include a tri-partite classification of structural evolution, leading to a new paradigm that discloses certain specific classes of nuclei, universal trajectories for B(E2: w{sub 1}{sup +} {r_arrow} 0{sub 1}{sup +}) values and their use in extracting hexadecapole deformations from this observable alone, the use of these B(E2) values to identify shell gaps and magic numbers in exotic nuclei, the relationship of {beta} and {gamma} deformations, and single nucleon separation energies. Predictions for nuclei far off stability by interpolation will also be discussed.

  6. Application of charge density methods to a protein model compound: Calculation of Coulombic intermolecular interaction energies from the experimental charge density

    PubMed Central

    Li, Xue; Wu, Guang; Abramov, Yuriy A.; Volkov, Anatoliy V.; Coppens, Philip

    2002-01-01

    A combined experimental and theoretical charge density study of the pentapeptide Boc-Gln-d-Iva-Hyp-Ala-Phol (Boc, butoxycarbonyl; Gln, glutamine; Iva, isovaline; Hyp, hydroxyproline; Ala, ethylalanine; Phol, phenylalaninol) is described. The experimental analysis, based on synchrotron x-ray data collected at 20 K, is combined with ab initio theoretical calculations. The topologies of the experimental and theoretical densities are analyzed in terms of the atoms in molecules quantum theory. Topological parameters, including atomic charges and higher moments integrated over the atomic basins, have been evaluated with the program topxd and are used to calculate the electrostatic interactions between the molecules in the crystal. The interaction energies obtained after adding dispersive and repulsive van der Waals contributions agree quite well with those based on M-B3LYP/6–31G** dimer calculations for two of the three dimers in the crystal, whereas for the third a larger stabilization is obtained than predicted by the calculation. The agreement with theory is significantly better than that obtained with multipole moments derived directly from the aspherical atom refinement. The convergence of the interaction as a function of addition of successively higher moments up to and including hexadecapoles (l = 4) is found to be within 2–3 kJ/mol. Although shortcomings of both the theoretical and experimental procedures are pointed out, the agreement obtained supports the potential of the experimental method for the evaluation of interactions in larger biologically relevant molecules. PMID:12221293

  7. Application of charge density methods to a protein model compound: calculation of Coulombic intermolecular interaction energies from the experimental charge density.

    PubMed

    Li, Xue; Wu, Guang; Abramov, Yuriy A; Volkov, Anatoliy V; Coppens, Philip

    2002-09-17

    A combined experimental and theoretical charge density study of the pentapeptide Boc-Gln-d-Iva-Hyp-Ala-Phol (Boc, butoxycarbonyl; Gln, glutamine; Iva, isovaline; Hyp, hydroxyproline; Ala, ethylalanine; Phol, phenylalaninol) is described. The experimental analysis, based on synchrotron x-ray data collected at 20 K, is combined with ab initio theoretical calculations. The topologies of the experimental and theoretical densities are analyzed in terms of the atoms in molecules quantum theory. Topological parameters, including atomic charges and higher moments integrated over the atomic basins, have been evaluated with the program topxd and are used to calculate the electrostatic interactions between the molecules in the crystal. The interaction energies obtained after adding dispersive and repulsive van der Waals contributions agree quite well with those based on M-B3LYP/6-31G** dimer calculations for two of the three dimers in the crystal, whereas for the third a larger stabilization is obtained than predicted by the calculation. The agreement with theory is significantly better than that obtained with multipole moments derived directly from the aspherical atom refinement. The convergence of the interaction as a function of addition of successively higher moments up to and including hexadecapoles (l = 4) is found to be within 2-3 kJ/mol. Although shortcomings of both the theoretical and experimental procedures are pointed out, the agreement obtained supports the potential of the experimental method for the evaluation of interactions in larger biologically relevant molecules. PMID:12221293

  8. Direct inelastic scattering of N/sub 2/ from Ag(111). I. Rotational populations and alignment

    SciTech Connect

    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.

  9. 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, ||=1.436(2) a.u. and ||=3.3(1.1) a.u.

  10. Nitrogen-broadened lineshapes in the oxygen A-band: Experimental results and theoretical calculations

    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.

  11. Product PCNPsurv or the "reduced" evaporation residue cross section σER/σfusion for "hot" fusion reactions studied with the dynamical cluster-decay model

    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*.

  12. Spherical tensor multipolar electrostatics and smooth particle mesh Ewald summation: a theoretical study.

    PubMed

    Zielinski, François; Popelier, Paul L A

    2014-07-01

    The point-charge approximation, typically used by classical molecular mechanics force-fields, can be overcome by a multipolar expansion. For decades multipole moments were only used in the context of the rigid body approximation but recently it has become possible to combine multipolar electrostatics with molecular flexibility. The program DL_MULTI, which is derived from DL_POLY_2, includes efficient multipolar Ewald functionality up to the hexadecapole moment but the code is restricted to rigid bodies. The incorporation of flexibility into DL_MULTI would cause too large an impact on its architecture whereas the package DL_POLY_4 offers a more attractive and sustainable route to handle multipolar electrostatics. This package inherently handles molecular flexibility, which warrants sufficiently transferable atoms or atoms that are "knowledgeable" about their chemical environment (as made possible by quantum chemical topology and machine learning). DL_MULTI uses the spherical multipole formalism, which is mathematically more involved than the Cartesian one but which is more compact. DL_POLY_4 uses the computationally efficient method of smooth particle mesh Ewald (SPME) summation, which has also been parallellized by others. Therefore, combining the strengths of DL_POLY_4 and DL_MULTI poses the challenge of merging SPME with multipolar electrostatics by spherical multipole. In an effort to recast as clearly as possible the principles behind DL_MULTI, its key equations have been reformulated by the more streamlined route involving the algebra of complex numbers, and some of these equations' peculiarities clarified. This article explores theoretically the repercussions of the merging of SPME with spherical multipole electrostatics (as implemented in DL_MULTI). Difficulties in design and implementation of possible future code are discussed.

  13. Nuclear energy surfaces at high-spin in the A{approximately}180 mass region

    SciTech Connect

    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.

  14. Deformation electron-density distributions of tetraazathiapentalenes with hypervalent SN bonds

    NASA Astrophysics Data System (ADS)

    Iwasaki, Fujiko; Yoshida, Satoshi; Kakuma, Seiji; Watanabe, Toshiya; Yasui, Masanori

    1995-06-01

    3,4-Dimethyl-2,5-diphenyl-3,4-dihydro-3a-thia-1,3,4,6-tetraazapentalene ( 1) and 2,3,4,5-tetrahydro-1,6-diphenyl-3,4-propano-6a-thia-1,3,4,6-tetraazapentalene-2,5-dione ( 2) are typical hypervalent sulfur compounds with SN bonds of 1.90-1.96 Å, which are longer than the normal single SN bond (1.74 Å) by about 10%. The electron-density distributions of these compounds were investigated in order to shed light on the character of hypervalent S ··· N bonds. Intensity data of X-ray diffraction were measured at 143 K and the structure refinements were performed using multipole expansion atomic scattering factors up to the hexadecapole expansion for the S atom. Crystal data are: 1, orthorhombic, Pbcn, a = 14.433(3), b = 9.220(2), c = 11.236(2) Å, Z = 4, R = 0.037 for 6398 reflections; 2, orthorhombic, Iba 2, a = 20.313(3), b = 21.365(2), c = 7.472(2) Å, Z = 8, R = 0.036 for 6617 reflections. In the model deformation maps of 1 and 2 electron densities along the SN bonds are observed near the nitrogen atoms, not in the center of the bonds. The net atomic charges derived from the multipole refinement suggest a polarized character of the SN bond. Lone-pair electron densities of hypervalent sulfur atoms, observed on the up and down sides of the pentalene plane, suggest a coupling of lone pair with pπ and non-bonding d or p electrons.

  15. Superdeformed nuclei: Shells-vs-liquid drop, pairing-vs-thermal excitations, triaxial-vs-octupole shapes, super-superdeformation

    SciTech Connect

    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.

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

    SciTech Connect

    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.

  17. Angular momentum partitioning and hexacontatetrapoles in impulsively excited argon ions

    NASA Astrophysics Data System (ADS)

    Al-Khateeb, Hasan Mousa

    We have studied simultaneous ionization and excitation of argon atoms by transversely-polarized electron impact. We measured the integrated Stokes parameters of the light emitted along the direction of the electron polarization from the excited ions without detecting the scattered electrons. The excited states under investigation, 2F7/2, 2F 5/2, 2D5/2, and 2P3/2 , have a 3p4 (1D) core and the 4p outer electron. With the exception of the 2P3/2 state, which has a 12% 3P core component, they are well-LS coupled. Our experiment can measure two normalized integrated state multipoles for the total angular momentum J: t 11 (J) and t20 ( J). These multipoles are called the magnetic dipole and the electric quadrupole moments and they are related to the integrated Stokes parameters P3 and P1 respectively. The other integrated Stokes parameter P2 is consistent with zero for all the states under investigation, which means that inelastic Mott scattering is not occurring. We showed that the Rubin-Bederson hypothesis holds for these well-LS coupled states for L and S multipoles. We determine the state multipoles for the 1D core and the 4p outer electron by using the formalism of irreducible tensor multipole moments. We have made the first experimental measurements of the an orbital multipole moment of rank 4 (hexadecapole moment) for the 1D core. Furthermore, it is possible to determine the orbital multipole of rank 6 (hexacontatetrapole moment) accurately for the 2F states.

  18. Static electric multipole susceptibilities of the relativistic hydrogenlike atom in the ground state: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function

    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.

  19. Determination of the compound nucleus survival probability Psurv for various "hot" fusion reactions based on the dynamical cluster-decay model

    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

  20. Evaporation residue cross-section in the decay of 254No* formed in 206Pb + 48Ca and its isotopic dependence using other Pb targets within the dynamical cluster-decay model

    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

  1. How dependent are molecular and atomic properties on the electronic structure method? Comparison of Hartree-Fock, DFT, and MP2 on a biologically relevant set of molecules.

    PubMed

    Matta, Chérif F

    2010-04-30

    except when inadequate basis sets were used by today's standards. Extensive tabulation of molecular and atomic properties at the three theoretical levels is available in the Supporting Information, including optimized geometries, molecular energies, virial ratios, molecular electrostatic moments up to and including hexadecapoles, atomic populations, atomic volumes, atomic electrostatic moments up to and including the quadrupoles, and atomic energies.

  2. Distribution function approach to redshift space distortions. Part II: N-body simulations

    SciTech Connect

    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

  3. 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

  4. HPAM: Hirshfeld partitioned atomic multipoles

    NASA Astrophysics Data System (ADS)

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

    2012-02-01

    An implementation of the Hirshfeld (HD) and Hirshfeld-Iterated (HD-I) atomic charge density partitioning schemes is described. Atomic charges and atomic multipoles are calculated from the HD and HD-I atomic charge densities for arbitrary atomic multipole rank l on molecules of arbitrary shape and size. The HD and HD-I atomic charges/multipoles are tested by comparing molecular multipole moments and the electrostatic potential (ESP) surrounding a molecule with their reference ab initio values. In general, the HD-I atomic charges/multipoles are found to better reproduce ab initio electrostatic properties over HD atomic charges/multipoles. A systematic increase in precision for reproducing ab initio electrostatic properties is demonstrated by increasing the atomic multipole rank from l=0 (atomic charges) to l=4 (atomic hexadecapoles). Both HD and HD-I atomic multipoles up to rank l are shown to exactly reproduce ab initio molecular multipole moments of rank L for L⩽l. In addition, molecular dipole moments calculated by HD, HD-I, and ChelpG atomic charges only ( l=0) are compared with reference ab initio values. Significant errors in reproducing ab initio molecular dipole moments are found if only HD or HD-I atomic charges used. Program summaryProgram title: HPAM Catalogue identifier: AEKP_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKP_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License v2 No. of lines in distributed program, including test data, etc.: 500 809 No. of bytes in distributed program, including test data, etc.: 13 424 494 Distribution format: tar.gz Programming language: C Computer: Any Operating system: Linux RAM: Typically, a few hundred megabytes Classification: 16.13 External routines: The program requires 'formatted checkpoint' files obtained from the Gaussian 03 or Gaussian 09 quantum chemistry program. Nature of problem: An ab initio

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

    NASA Astrophysics Data System (ADS)

    Maroulis, George

    1998-04-01

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