Abstract.
Recently, interacting boson model (IBM) calculations, in the O(6) basis up to the seniority quantum number v max= 40 , were made possible thanks to the availability of the SO(5) Clebsch-Gordan (CG) coefficients, computed in floating-point arithmetic (T.A. Welsh, unpublished (2008)). In this paper we have made use of these CG coefficients to extend the IBM to situations where triaxial deformation is present. Such a description has been considered in the algebraic collective model (ACM) which is an algebraic version of the Bohr model. To describe triaxiality in the ACM a term proportional to cos23\( \gamma\) must be included in the Hamiltonian. We show that, in the IBM, this can be achieved by including a term quadratic in (\( \hat{{Q}}\) ⊗ \( \hat{{Q}}\) ⊗ \( \hat{{Q}}\))0, which is an IBM image of the term cos23\( \gamma\) . Quadrupole shape invariants are used to investigate the \( \beta\) and \( \gamma\) rigidity of the states obtained with such a Hamiltonian and a comparison with the rigid asymmetric rotor model is presented. The staggering of \( \gamma\) -band level energies, obtained in the present approach, is analyzed and compared to the ones predicted by the geometrical models and by the IBM. A comparison between the experimental and calculated staggerings in 190Os and 192Os is shown.
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G. Thiamova, D.J. Rowe, Eur. Phys. J. A 41, 189 (2009)
F. Iachello, A. Arima, The Interacting Boson Model (Cambridge University Press, 1987)
A. Arima, F. Iachello, Ann. Phys. (N.Y.) 99, 253 (1976)
A. Arima, F. Iachello, Ann. Phys. (N.Y.) 111, 201 (1978)
A. Arima, F. Iachello, Ann. Phys. (N.Y.) 123, 468 (1979)
D.J. Rowe, P.S. Turner, J. Repka, J. Math. Phys. 45, 2761 (2004)
T.A. Welsh, unpublished (2008)
M.A. Caprio, D.J. Rowe, T.A. Welsh, Comput. Phys. Commun. 180, 1150 (2009)
D.J. Rowe, Nucl. Phys. A 735, 372 (2004)
D.J. Rowe, T.A. Welsh, M.A. Caprio, Phys. Rev. C 79, 054304 (2009)
D.J. Rowe, G. Thiamova, Nucl. Phys. A 760, 59 (2005)
D.J. Rowe, J. Phys. A: Math. Gen. 38, 10181 (2005)
P. Van Isacker, Phys. Rev. Lett. 83, 4269 (1999)
L. Wilets, M. Jean, Phys. Rev. 102, 788 (1956)
A.S. Davydov, G.F. Filippov, Nucl. Phys. 8, 237 (1958)
A.S. Davydov, A.A. Chaban, Nucl. Phys. 20, 499 (1960)
J.N. Ginocchio, M.W. Kirson, Phys. Rev. Lett. 44, 1744 (1980)
J.N. Ginocchio, M.W. Kirson, Nucl. Phys. A 350, 31 (1980)
A.E.L. Dieperink, O. Scholten, F. Iachello, Phys. Rev. Lett. 44, 1747 (1980)
A.E.L. Dieperink, R. Bijker, Phys. Lett. B 116, 77 (1982)
A.E.L. Dieperink, in Progress in Particle and Nuclear Physics, edited by D. Wilkinson, Vol. 9 (Plenum, New York, 1983) p. 121.
M.A. Caprio, F. Iachello, Ann. Phys. (N.Y.) 318, 454 (2005)
K. Heyde, P. Van Isacker, M. Waroquier, G. Wenes, Y. Gigase, J. Stachel, Nucl. Phys. A 398, 235 (1983)
S. Kuyucak, I. Morrison, Phys. Lett. B 255, 305 (1991)
S. Kuyucak, V.-S. Lac, I. Morrison, B.R. Barret, Phys. Lett. B 263, 347 (1991)
P. Van Isacker, J.Q. Chen, Phys. Rev. C 24, 684 (1981)
K. Heyde, P. Van Isacker, M. Waroquier, J. Moreau, Phys. Rev. C 29, 1420 (1984)
R.F. Casten, P. Von Brentano, K. Heyde, P. Van Isacker, J. Jolie, Nucl. Phys. A 439, 289 (1985)
Y.F. Smirnov, N.A. Smirnova, P. Van Isacker, Phys. Rev. C 61, 041302(R) (2000)
F. Iachello, in Dronten Nuclear Structure Summer School, edited by C. Abrahams, K. Allaart, A.E.L. Dieperink (Plenum, New York, 1982) p. 53
O. Castaños, A. Frank, P. Van Isacker, Phys. Rev. Lett. 52, 263 (1976)
R.F. Casten, A. Aprahamian, D.D. Warner, unpublished
A. Bohr, B.R. Mottelson, Nuclear Structure: Nuclear Deformations, Vol. 2 (World Scientific, Singapore, 1998)
E. Chacon, M. Moshinsky, R.T. Sharp, J. Math. Phys. 17, 668 (1976)
E. Chacon, M. Moshinsky, J. Math. Phys. 18, 870 (1978)
J.P. Elliott, J.A. Evans, J. Phys. A: Math. Gen. 38, 5507 (2005)
D.J. Rowe, Prog. Part. Nucl. Phys. 37, 265 (1996)
K. Kumar, Phys. Rev. Lett. 28, 249 (1972)
D. Cline, Annu. Rev. Nucl. Part. Sci. 36, 683 (1986)
G. Rosensteel, D.J. Rowe, Ann. Phys. (N.Y.) 104, 134 (1977)
V. Werner, N. Pietralla, P. von Brentano, R.F. Casten, R.V. Jolos, Phys. Rev. C 61, 021301(R) (2000)
G. Thiamova, P. Cejnar, Nucl. Phys. A 765, 97 (2006)
D. Bonatsos, E.A. McCutchan, R.F. Casten, R.J. Casperson, Phys. Rev. Lett. 100, 142501 (2008)
F. Iachello, N.V. Zamfir, Phys. Rev. Lett. 92, 212501 (2004)
Feng Pan, Y. Zhang, J.P. Draayer, J. Phys. G 31, 1039 (2005)
D.J. Rowe, Phys. Rev. Lett. 93, 122502 (2004)
D. Bonatsos, E.A. McCutchan, R.F. Casten, Phys. Rev. Lett. 104, 022502 (2010)
P. Van Isacker, A. Bouldjedri, S. Zerguine, arXiv: 0910.0829v1 (nucl-th) (2009)
J. Meyer-ter-Vehn, Nucl. Phys. A 249, 111 (1975)
S.W. Yates, J.C. Cunnane, P.J. Daly, R. Thompson, R.K. Sheline, Nucl. Phys. A 222, 276 (1974)
A.G. Sitenko, V.K. Tartakovskii, Lectures on the Theory of the Nucleus (Pergamon Press, 1975)
E.A. McCutchan, D. Bonatsos, N.V. Zamfir, R.F. Casten, Phys. Rev. C 76, 024306 (2007)
N.V. Zamfir, R.F. Casten, Phys. Lett. B 260, 024306 (1991)
G. Puddu, O. Scholten, T. Otsuka, Nucl. Phys. A 348, 109 (1980)
N.V. Zamfir, R.F. Casten, Phys. Lett. B 152, 22 (1985)
L. Fortunato, S. De Baerdemacker, K. Heyde, Phys. Rev. C 74, 014310 (2006)
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Thiamova, G. The IBM description of triaxial nuclei. Eur. Phys. J. A 45, 81–90 (2010). https://doi.org/10.1140/epja/i2010-10982-2
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DOI: https://doi.org/10.1140/epja/i2010-10982-2