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SU(3) partial dynamical symmetry and nuclear shapes

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Abstract

We consider several variants of SU(3) partial dynamical symmetry in relation to quadrupole shapes in nuclei. Explicit construction of Hamiltonians with such property is presented in the framework of the interacting boson model (IBM), including higher order terms, and in its proton–neutron extension (IBM-2). The cases considered include a single prolate-deformed shape with solvable ground and γ or β bands, coexisting prolate-oblate shapes with solvable ground bands, and aligned axially-deformed proton–neutron shapes with solvable symmetric ground and γ bands and mixed-symmetry scissors and γ bands.

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References

  1. J.P. Elliott, Proc. Roy. Soc. A 245, 128 (1958)

    ADS  Google Scholar 

  2. J.P. Elliott, Proc. Roy. Soc. A 245, 562 (1958)

    ADS  Google Scholar 

  3. D.J. Rowe, Rep. Prog. Phys. 48, 1419 (1985)

    Article  ADS  Google Scholar 

  4. R.D. Ratna-Raju, K.T. Hecht, B.D. Chang, J.P. Draayer, Nucl. Phys. A 202, 433 (1973)

    Article  ADS  Google Scholar 

  5. J.N. Ginocchio, Ann. Phys. (NY) 126, 234 (1980)

    Article  ADS  Google Scholar 

  6. F. Iachello, A. Arima,The interacting boson model (Cambridge University Press, Cambridge, 1987)

  7. F. Iachello, P. Van Isacker,The interacting boson-fermion model (Cambridge University Press, Cambridge, 1991)

  8. F. Iachello,Lie algebras and applications (Springer-Verlag, Berlin, 2015)

  9. R. Gilmore, J. Math. Phys. 20, 891 (1979)

    Article  ADS  MathSciNet  Google Scholar 

  10. For a review see, W.M. Zhang, D.H. Feng, R. Gilmore, Rev. Mod. Phys. 62, 867 (1990)

    Article  ADS  Google Scholar 

  11. J.N. Ginocchio, M.W. Kirson, Phys. Rev. Lett. 44, 1744 (1980)

    Article  ADS  MathSciNet  Google Scholar 

  12. A.E.L. Dieperink, O. Scholten, F. Iachello, Phys. Rev. Lett. 44, 1747 (1980)

    Article  ADS  Google Scholar 

  13. For a review see, A. Leviatan, Prog. Part. Nucl. Phys. 66, 93 (2011)

    Article  ADS  Google Scholar 

  14. V.K.B. Kota,SU(3) symmetry in atomic nuclei (Springer Nature, Singapore, 2020)

  15. Y. Alhassid, A. Leviatan, J. Phys. A 25, L1265 (1992)

    Article  ADS  Google Scholar 

  16. J.E. García-Ramos, A. Leviatan, P. Van Isacker, Phys. Rev. Lett. 102, 112502 (2009)

    Article  ADS  Google Scholar 

  17. M.W. Kirson, A. Leviatan, Phys. Rev. Lett. 55, 2846 (1985)

    Article  ADS  Google Scholar 

  18. A. Leviatan, Ann. Phys. (NY) 179, 201 (1987)

    Article  ADS  Google Scholar 

  19. H. De Meyer, G. Vanden Berghe, J. Van der Jeugt, J. Math. Phys. 26, 3109 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  20. G. Vanden Berghe, H.E. De Meyer, P. Van Isacker, Phys. Rev. C 32, 1049 (1985)

    Article  ADS  Google Scholar 

  21. D. Bonatsos, Phys. Lett. B 200, 1 (1985)

    Article  ADS  Google Scholar 

  22. J. Vanthournout, Phys. Rev. C 41, 2380 (1990)

    Article  ADS  Google Scholar 

  23. G. Rosensteel, J.P. Draayer, K.J. Weeks, Nucl. Phys. A 419, 1 (1984)

    Article  ADS  Google Scholar 

  24. J.P. Draayer, G. Rosensteel, Nucl. Phys. A 439, 61 (1985)

    Article  ADS  Google Scholar 

  25. A. Leviatan, Phys. Rev. Lett. 77, 818 (1996)

    Article  ADS  Google Scholar 

  26. A. Leviatan, I. Sinai, Phys. Rev. C 60, 061301 (1999)

    Article  ADS  Google Scholar 

  27. P. Van Isacker, Phys. Rev. C 27, 2447 (1983)

    Article  ADS  Google Scholar 

  28. R.F. Casten, R.B. Cakirli, K. Blaum, A. Couture, Phys. Rev. Lett. 113, 112501 (2014)

    Article  ADS  Google Scholar 

  29. A. Couture, R.F. Casten, R.B. Cakirli, Phys. Rev. C 91, 014312 (2015)

    Article  ADS  Google Scholar 

  30. R.F. Casten, J. Jolie, R.B. Cakirli, A. Couture, Phys. Rev. C 94, 061303(R) (2016)

    Article  ADS  Google Scholar 

  31. A. Leviatan, J.E. Garc-a-Ramos, P. Van Isacker, Phys. Rev. C 87, 021302(R) (2013)

    Article  ADS  Google Scholar 

  32. A. Aprahamian, R.C. de Haan, S.R. Lesher, C. Casarella, A. Stratman, H.G. Börner, H. Lehmann, M. Jentschel, A.M. Bruce, Phys. Rev. C 98, 034303 (2018)

    Article  ADS  Google Scholar 

  33. For a review see, K. Heyde, J.L. Wood, Rev. Mod. Phys. 83, 1467 (2011)

    Article  ADS  Google Scholar 

  34. A. Leviatan, Phys. Rev. Lett. 98, 242502 (2007)

    Article  ADS  Google Scholar 

  35. A. Leviatan, D. Shapira, Phys. Rev. C 93, 051302(R) (2016)

    Article  ADS  Google Scholar 

  36. A. Leviatan, N. Gavrielov, Phys. Scr. 92, 114005 (2017)

    Article  ADS  Google Scholar 

  37. For a review see, F. Iachello, I. Talmi, Rev. Mod. Phys. 59, 339 (1987)

    Article  ADS  Google Scholar 

  38. For a review see, K. Heyde, P. von Neumann Cosel, A. Richter, Rev. Mod. Phys. 82, 2365 (2010)

    Article  ADS  Google Scholar 

  39. A. Arima, T. Otsuka, F. Iachello, I. Talmi, Phys. Lett. B 66, 205 (1977)

    Article  ADS  Google Scholar 

  40. T. Otsuka, A. Arima, F. Iachello, I. Talmi, Phys. Lett. B 76, 139 (1978)

    Article  ADS  Google Scholar 

  41. A. Leviatan, M.W. Kirson, Ann. Phys. (NY) 201, 13 (1990)

    Article  ADS  Google Scholar 

  42. J.N. Ginocchio, A. Leviatan, Ann. Phys. (NY) 216, 152 (1992)

    Article  ADS  Google Scholar 

  43. A. Leviatan, J.N. Ginocchio, M.W. Kirson, Phys. Rev. Lett. 65, 2853 (1990)

    Article  ADS  Google Scholar 

  44. A. Leviatan, J.N. Ginocchio, Phys. Rev. C 61, 024305 (2000)

    Article  ADS  Google Scholar 

  45. H.C. Wu, A.E. Dieperink, S. Pittel, Phys. Rev. C 34, 703 (1986)

    Article  ADS  Google Scholar 

  46. P. Van Isacker, K. Heyde. J. Jolie, A. Sevrin, Ann. Phys. (NY) 171, 253 (1986)

    Article  ADS  Google Scholar 

  47. A. Leviatan, P. Van Isacker, Phys. Rev. Lett. 89, 222501 (2002)

    Article  ADS  Google Scholar 

  48. C. Kremer, J. Beller, A. Leviatan, N. Pietralla, G. Rainovski, R. Trippel, P. Van Isacker, Phys. Rev. C 89, 041302(R) (2014)

    Article  ADS  Google Scholar 

  49. A. Leviatan, N. Gavrielov, J.E. Garc-a-Ramos, P. Van Isacker, Phys. Rev. C 98, 031302(R) (2018)

    Article  ADS  Google Scholar 

  50. I. Talmi, Phys. Lett. B 405, 1 (1997)

    Article  ADS  Google Scholar 

  51. P. Van Isacker, J. Jolie, T. Thomas, A. Leviatan, Phys. Rev. C 92, 011301(R) (2015)

    Article  ADS  Google Scholar 

  52. J. Escher, A. Leviatan, Phys. Rev. Lett. 84, 1866 (2000)

    Article  ADS  Google Scholar 

  53. J. Escher, A. Leviatan, Phys. Rev. C 65, 054309 (2002)

    Article  ADS  Google Scholar 

  54. D.J. Rowe, G. Rosensteel, Phys. Rev. Lett. 87, 172501 (2001)

    Article  ADS  Google Scholar 

  55. G. Rosensteel, D.J. Rowe, Phys. Rev. C 67, 014303 (2003)

    Article  ADS  Google Scholar 

  56. P. Van Isacker, S. Heinze, Phys. Rev. Lett. 100, 052501 (2008)

    Article  ADS  Google Scholar 

  57. I. Talmi, Nucl. Phys. A 846, 31 (2010)

    Article  ADS  Google Scholar 

  58. P. Van Isacker, S. Heinze, Ann. Phys. 349, 73 (2014)

    Article  ADS  Google Scholar 

  59. N. Whelan, Y. Alhassid, A. Leviatan, Phys. Rev. Lett. 71, 2208 (1993)

    Article  ADS  Google Scholar 

  60. A. Leviatan, N.D. Whelan, Phys. Rev. Lett. 77, 5202 (1996)

    Article  ADS  Google Scholar 

  61. M. Macek, A. Leviatan, Ann. Phys. (NY) 351, 302 (2014)

    Article  ADS  Google Scholar 

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  1. Racah Institute of Physics, The Hebrew University, Jerusalem, 91904, Israel

    A. Leviatan

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Leviatan, A. SU(3) partial dynamical symmetry and nuclear shapes. Eur. Phys. J. Spec. Top. 229, 2405–2427 (2020). https://doi.org/10.1140/epjst/e2020-000204-8

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