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Discrete symmetries in the cluster shell model

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Abstract

The role of discrete (or point-group) symmetries is discussed in the framework of the cluster shell model which describes the splitting of single-particle levels in the deformed field of cluster potentials. We discuss the classification of the eigenstates for the cases of a triangular and tetrahedral configuration of α-particles in terms of the irreducible representations of the double point groups D′3h and T′d, respectively, and show how the discrete symmetry of a given eigenstate can be determined. Finally, we derive the Coriolis coupling for each one of these geometrical configurations.

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References

  1. A. Bohr, B.R. Mottelson, inNuclear structure: nuclear deformations (W.A. Benjamin, Inc., 1975), Vol. II

  2. J. Dudek, A. Goźdź, N. Schunck, M. Miśkiewicz, Phys. Rev. Lett. 88, 252502 (2002)

    Article  ADS  Google Scholar 

  3. J. Dudek, D. Curien, N. Dubray, J. Dobaczewski, V. Pangon, P. Olbratowski, N. Schunck, Phys. Rev. Lett. 97, 072501 (2006)

    Article  ADS  Google Scholar 

  4. P. Van Isacker, A. Bouldjedri, S. Zerguine, Nucl. Phys. A 938, 45 (2015)

    Article  ADS  Google Scholar 

  5. J.A. Wheeler, Phys. Rev. 52, 1083 (1937)

    Article  ADS  Google Scholar 

  6. L.R. Hafstad, E. Teller, Phys. Rev. 54, 681 (1938)

    Article  ADS  Google Scholar 

  7. D.M. Brink, Int. Sch. Phys. inProc. Intl. School of Physics “Enrico Fermi”, 1965, Course XXXVI, p. 247

  8. D.M. Brink, H. Friedrich, A. Weiguny, C.W. Wong, Phys. Lett. B 33, 143 (1970)

    Article  ADS  Google Scholar 

  9. D. Robson, Phys. Rev. Lett. 42, 876 (1979)

    Article  ADS  Google Scholar 

  10. M. Freer et al., Phys. Rev. C 76, 034320 (2007)

    Article  ADS  Google Scholar 

  11. O.S.Kirsebom et al., Phys. Rev. C 81, 064313 (2010)

    Article  ADS  Google Scholar 

  12. D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Phys. Rev. Lett. 113, 012502 (2014)

    Article  ADS  Google Scholar 

  13. M. Itoh et al., Phys. Rev. C 84, 054308 (2011)

    Article  ADS  Google Scholar 

  14. M. Freer et al., Phys. Rev. C 86, 034320 (2012)

    Article  ADS  Google Scholar 

  15. W.R. Zimmerman et al., Phys. Rev. Lett. 110, 152502 (2013)

    Article  ADS  Google Scholar 

  16. M. Freer et al., Phys. Rev. C 83, 034314 (2011)

    Article  ADS  Google Scholar 

  17. M. Freer, H.O.U. Fynbo, Prog. Part. Nucl. Phys. 78, 1 (2014)

    Article  ADS  Google Scholar 

  18. P. Schuck, Y. Funaki, H. Horiuchi, G. Röpke, A. Tohsaki, T. Yamada, Phys. Scr. 91, 123001 (2016)

    Article  ADS  Google Scholar 

  19. M. Freer, H. Horiuchi, Y. Kanada-En’yo, D. Lee, U.-G. Meissner, Rev. Mod. Phys. 90, 035004 (2018)

    Article  ADS  Google Scholar 

  20. R. Bijker, F. Iachello, Phys. Rev. C 61, 067305 (2000)

    Article  ADS  Google Scholar 

  21. R. Bijker, F. Iachello, Ann. Phys. (N.Y.) 298, 334 (2002)

    Article  ADS  Google Scholar 

  22. R. Bijker, F. Iachello, Phys. Rev. Lett. 112, 152501 (2014)

    Article  ADS  Google Scholar 

  23. R. Bijker, F. Iachello, Nucl. Phys. A 957, 154 (2017)

    Article  ADS  Google Scholar 

  24. J. Dudek, D. Curien, I. Dedes, K. Mazurek, S. Tagami, Y.R. Shimizu, T. Bhattacharjee, Phys. Rev. C 97, 021302(R) (2018)

    Article  ADS  Google Scholar 

  25. R. Bijker, Phys. Scr. 91, 073005 (2016)

    Article  ADS  Google Scholar 

  26. V. Della Rocca, R. Bijker, F. Iachello, Nucl. Phys. A 966, 158 (2017)

    Article  ADS  Google Scholar 

  27. V. Della Rocca, F. Iachello, Nucl. Phys. A 973, 1 (2018)

    Article  ADS  Google Scholar 

  28. R. Bijker, F. Iachello, Phys. Rev. Lett. 122, 162501 (2019)

    Article  ADS  Google Scholar 

  29. R. Bijker, F. Iachello, Prog. Part. Nucl. Phys. 110, 103735 (2020)

    Article  Google Scholar 

  30. S.G. Nilsson, Kong. Dan. Vid. Sel. Mat. Fys. Med. 29, 1 (1955)

    Google Scholar 

  31. G.F. Koster, J.O. Dimmock, R.G. Wheeler, H. Statz,Properties of thirty-two pointgroups (MIT Press, 1963)

  32. G. Herzberg, inMolecular spectra and molecular structure. Electronic spectra and electronic structure of polyatomic molecules (Krieger Publishing Company, 1991), Vol. II

  33. J. Dudek, D. Curien, A. Góźdź, Y.R. Shimizu, S. Tagami, Acta Phys. Pol. B 44, 305 (2013)

    Article  ADS  Google Scholar 

  34. N. Schunck, J. Dudek, S. Frauendorf, Acta Phys. Pol. B 36, 1071 (2005)

    ADS  Google Scholar 

  35. S. Tagami, Y.R. Shimizu, J. Dudek, Phys. Rev. C 98, 024304 (2018)

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A.P. 70-543, 04510, México D.F., Mexico

    A. H. Santana Valdés & R. Bijker

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  1. A. H. Santana Valdés
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  2. R. Bijker
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Correspondence to R. Bijker.

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Santana Valdés, A.H., Bijker, R. Discrete symmetries in the cluster shell model. Eur. Phys. J. Spec. Top. 229, 2353–2366 (2020). https://doi.org/10.1140/epjst/e2020-000006-0

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