Abstract
An algebraic framework for carrying out detailed shell model calculations in a SU(3) basis is introduced and applied to various sets of ds-shell valence nucleons bound in a shell model mean-field with residual quadrupole–quadrupole and pairing interactions. Binding energies, experimentally known low-lying positive parity energy levels as well as electric quadrupole moments, magnetic dipole moments, B(E2) and B(M1) values of \(^{17-22}\)O and \(^{17}\)F, \(^{18}\)Ne, \(^{19}\)Na, \(^{20}\)Mg, \(^{21}\)Al, \(^{22}\)Si are fit and compared to the corresponding experimental results. It is shown that the binding energies of these nuclei are fit well by the model with the quality of the fit to the low-lying energy levels similar to that of the shell model using the USD interaction. It is also shown that the overall data pattern of the results fits to the known electric quadrupole moments, magnetic dipole moments, B(E2) and B(M1) values follow that of the experimental data with only a few exceptions. In addition, the ground-state dynamic shape of these nuclei is estimated with the correspondence between the Bohr \((\beta ,\gamma )\) variables and the SU(3) irreducible representation \((\lambda \,\mu )\). The results show that the nuclei in the ds-shell approaching the neutron or proton drip line tend to be triaxially unstable with relatively stronger pairing interactions.
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References
P. Ring, P. Schuck, The Nuclear Many-Body Problem (Springer, Berlin, 1980)
I. Talmi, Simple Models of Complex Nuclei: The Shell Model and Interacting Boson Model (Springer, Berlin, 1993)
B.A. Brown, Prog. Part. Nucl. Phys. 47, 517 (2001)
E. Caurier, G. Martínez-Pinedo, F. Nowacki, A. Poves, A.P. Zuker, Rev. Mod. Phys. 77, 427 (2005)
J.P. Draayer, T. Dytrych, K.D. Launey, D. Langr, Prog. Part. Nucl. Phys. 67, 516 (2012)
B.R. Barrett, P. Navrátil, J.P. Vary, Prog. Part. Nucl. Phys. 69, 131 (2013)
K.D. Launey, T. Dytrych, J.P. Draayer, Prog. Part. Nucl. Phys. 89, 101 (2016)
P. Sternberg, E.G. Ng, C. Yang, P. Maris, J.P. Vary, M. Sosonkina, H.V. Le, Accelerating configuration interaction calculations for nuclear structure, in The Proceedings of the 2008 ACM/IEEE Conference on Supercomputing (Austin, Texas, Nov. 15-21), Conference on High Performance Networking and Computing (IEEE Press, 2008)
B.A. Brown, W.D.M. Rae, Nucl. Data Sheets 120, 115 (2014)
C.W. Johnson, W.E. Ormand, K.S. McElvain, H. Shan, arXiv:1801.08432 (2018)
N. Shimizu, T. Mizusaki, T. Utsuno, Y. Tsunoda, Comput. Phys. Commun. 244, 372 (2019)
J.P. Elliott, Proc. R. Soc. A 245, 128–562 (1958)
J.P. Elliott, M. Harvey, Proc. R. Soc. A 272, 557 (1963)
M. Moshinsky, E. Chacón, J. Flores, M. de Liano, P.A. Mello, Group Theory and the Many-Body Problem (Gordon and Breach, Science Publishers Inc., New York, 1968)
D. Braunschweig, Comput. Phys. Commun. 14, 109 (1978)
D. Braunschweig, Comput. Phys. Commun. 15, 259 (1978)
C. Bahri, J.P. Draayer, Comput. Phys. Commun. 83, 59 (1994)
D.R. Bes, R.A. Sorensen, The pairing-plus-quadrupole model, in Advances in Nuclear Physics, vol. 2, ed. by M. Baranger, E. Vogt (Plenum Press, New York, 1969)
M. Dufour, A.P. Zuker, Phys. Rev. C 54, 1641 (1996)
J.-Q. Chen, Group Representation Theory For Physicists (World Scientific, Singapore, 1989)
J.-Q. Chen, M.-J. Gao, Y.-J. Shi, M. Vallieres, D.-H. Feng, Nucl. Phys. A 419, 77 (1984)
J.P. Draayer, Y. Leschber, S.C. Park, R. Lopez, Comput. Phys. Commun. 56, 279 (1989)
K.V.K. Brahman, R.D.R. Raju, At. Data Nucl. Data Tables 16, 165 (1975)
E.M. Ibrahim, Royal Society Mathematical Tables, vol. 1 (Cambridge University Press, Cambridge, 1950)
S.G. Nilsson, I. Ragnarsson, Shapes and Shells in Nuclear Structure (Cambridge University Press, Cambridge, 1995)
B.G. Wybourne, Classical Groups for Physicists (Wiley, New York, 1974)
G.B. de Robinson, Representation Theory of the Symmetric Group (University of Toronto Press, Toronto, 1961)
Y. Akiyama, Nucl. Data Sheets A 2, 403 (1966)
Y. Akiyama, J.P. Draayer, Comput. Phys. Commun. 5, 405 (1973)
J.P. Draayer, Y. Akiyama, J. Math. Phys. 14, 1904 (1973)
F. Pan, S. Yuan, K.D. Launey, J.P. Draayer, Nucl. Phys. A 952, 70 (2016)
L.C. Biedenharn, J.D. Louck, Angular Momentum in Quantum Physics, Theory and Application (Addison-Wesley, Reading, 1981)
B.A. Brown, B.H. Wildenthal, Annu. Rev. Nucl. Part. Sci. 38, 29 (1988)
G.K. Tobin, M.C. Ferriss, K.D. Launey, T. Dytrych, J.P. Draayer, A.C. Dreyfuss, C. Bahri, Phys. Rev. C 89, 034312 (2014)
A.C. Dreyfuss, K.D. Launey, T. Dytrych, J.P. Draayer, R.B. Baker, C.M. Deibel, C. Bahri, Phys. Rev. C 95, 044312 (2017)
A. Saxena, P.C. Srivastava, Phys. Rev. C 96, 024316 (2017)
P. Vogel, Nucl. Phys. A 662, 148 (2000)
NuDat 2.8, National Nuclear Data Center (Brookhaven National laboratory), http://www.nndc.bnl.gov/nudat2
T. Siiskonen, P.O. Lipas, J. Rikovska, Phys. Rev. C 60, 034312 (1999)
F. Pan, T. Wang, Y.-S. Huo, J.P. Draayer, J. Phys. G Nucl. Part. Phys. 35, 125105 (2008)
I. Angeli, K.P. Marinova, At. Data Nucl. Data Tables 99, 69 (2013)
W. Geithner et al., Phys. Rev. Lett. 101, 252502 (2008)
D.R. Tilley, H.R. Weller, C.M. Cheves, R.M. Chasteler, Nucl. Phys. A 595, 1 (1995)
X.W. Xia, Y. Lim, P.W. Zhao, H.Z. Liang, X.Y. Qu, Y. Chen, H. Liu, L.F. Zhang, S.Q. Zhang, Y. Kim, J. Meng, At. Data Nucl. Data Tables 121–122, 1 (2018)
C. Yuan, C. Qi, F. Xu, T. Suzuki, T. Otsuka, Phys. Rev. C 89, 044327 (2014)
M. Stanoiu, F. Azaiez, Z. Dombrádi et al., Phys. Rev. C 69, 034312 (2004)
B.-C. He, S.-Y. Zhang, Y. Zhang, Y.-A. Luo, F. Pan, J.P. Draayer, Eur. Phys. J. A 55, 143 (2019)
A. Bohr, B.R. Mottelson, Nuclear Structure Volume II: Nuclear Deformations (World Scientific, Singapore, 1998)
O. Casta\(\tilde{\rm n}\)os, J.P. Draayer, Y. Leschber, Z. Phys. A 329, 33 (1988)
P. Möller, A.J. Sierk, T. Ichikawa, H. Sagawa, At. Data Nucl. Data Tables 109, 1 (2016)
P. Raghavan, At. Data Nucl. Data Tables 42, 189 (1989)
D. Zhou, Y. Zheng, D. Yuan et al., J. Phys. G Nucl. Part. Phys. 34, 523 (2007)
T. Minamisono et al., Phys. Lett. B 457, 9 (1999)
A. Gladkov et al., Riken Accel. Prog. Rep. 51, 74 (2018)
F. Ajenberg-Selove, Nucl. Phys. A 392, 1 (1983)
R.V. Jolos, P. Von Brehtano, A. Gelberg, Prog. Part. Nucl. Phys. 28, 363 (1992)
A.A. Raduta, P. Buganu, Phys. Rev. C 83, 034313 (2011)
G. Thiamova, Eur. Phys. J. A 45, 81 (2010)
L. Fortunato, C.E. Alonso, J.M. Arias, J.E. García-Ramos, A. Vitturi, Phys. Rev. C 84, 014326 (2011)
J.P. Draayer, J. Math. Phys. 11, 3225 (1970)
J.-Q. Chen, X.-B. Wu, M.-J. Gao, Tables of the SU(MN)\(\supset \)SU(M)\(\otimes \)SU(N) Coefficients of Fractional Parentage (World Scientific, Singapore, 1991)
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The authors are grateful to the referee for helpful comments and suggestions. Support from the National Natural Science Foundation of China (11675071), the Liaoning Provincial Universities Overseas Training Program (2019GJWYB024), the U S National Science Foundation (OIA-1738287 and PHY-1913728), the Southeastern Universities Research Association, and the LSU-LNNU joint research program (9961) is acknowledged.
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Pan, F., He, Y., Li, A. et al. Mean-field plus quadrupole–quadrupole and pairing model in the ds-shell. Eur. Phys. J. Plus 136, 689 (2021). https://doi.org/10.1140/epjp/s13360-021-01668-6
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DOI: https://doi.org/10.1140/epjp/s13360-021-01668-6