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16O within the Semimicroscopic Algebraic Cluster Model and the importance of the Pauli Exclusion Principle

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Abstract.

The Semimicroscopic Algebraic Cluster Model (SACM) is applied to 16O, assumed to consist of a system of four \(\alpha\)-clusters. For the 4-\(\alpha\) cluster system we take the model space already obtained in the past, which observes the Pauli Exclusion Principle (PEP) and is symmetric under permutation of the \(4\alpha\)-particles. A phenomenological Hamiltonian is used. The spectrum and transition values are determined. One of the main objectives is to test the importance of the Pauli Exclusion Principle (PEP), comparing the results with the Algebraic Cluster Model (ACM), which does not include the PEP, and claims that for the ground state the 16O shows evidence of a tetrahedral structure which can be explained easily by symmetry arguments. We show that the PEP is very important and cannot be neglected, otherwise it leads to a wrong interpretation of the band structure and to too many states at low energy, especially to an accumulation of parity doublets.

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References

  1. K.D. Launey, T. Dytrych, J.P. Draayer, Prog. Part. Nucl. Phys. 89, 101 (2016)

    Article  ADS  Google Scholar 

  2. T. Dytrych, Evidence for Symplectic Symmetry in ab initio no-core Shell Model Results, PhD Thesis, Lousiana State University (2008)

  3. P. Schuck, J. Phys.: Conf. Ser. 436, 012065 (2013)

    Google Scholar 

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

    Article  ADS  Google Scholar 

  5. Y. Funaki, Phys. Rev. C 97, 021304(R) (2018)

    Article  ADS  Google Scholar 

  6. A. Tohsaki, H. Horiuchi, P. Schuck, G. Röpke, Phys. Rev. Lett. 87, 192501 (2001)

    Article  ADS  Google Scholar 

  7. M. Freer, Rep. Prog. Phys. 70, 2149 (2007)

    Article  ADS  Google Scholar 

  8. M. Freer, H. Horiuchi, Y. Kanada-En’yo, D. Lee, U.-G. Meissner, Rev. Mod. Phys. 90, 03500 (2018)

    Article  Google Scholar 

  9. Y. Funaki, M. Girod, H. Horiuchi, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, J. Phys. G: Nucl. Part. Phys. 37, 064012 (2010)

    Article  ADS  Google Scholar 

  10. P. Schuck, AIP Conf. Proc. 2038, 020002 (2018)

    Article  Google Scholar 

  11. R. Bijker, F. Iachello, Phus. Rev. Lett. 112, 152501 (2014)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  14. D.J. Marín-Lámbarri, R. Bijker, M. Freer et al., Phys. Rev. Lett. 113, 012502 (2014)

    Article  ADS  Google Scholar 

  15. P.O. Hess, Eur. Phys. J. A 54, 32 (2018)

    Article  ADS  Google Scholar 

  16. J. Cseh, Phys. Lett. B 281, 173 (1992)

    Article  ADS  Google Scholar 

  17. J. Cseh, G. Lévai, Ann. Phys. (N.Y.) 230, 165 (1994)

    Article  ADS  Google Scholar 

  18. F. Hoyle, Astrophys. J. Suppl. 1, 121 (1954)

    Article  ADS  Google Scholar 

  19. V.C. Aguilera-Navarro, M. Moshinsky, P. Kramer, Ann. Phys. 54, 379 (1969)

    Article  ADS  Google Scholar 

  20. M. Moshinsky, Y. Smirnoc, The Harmonic Oscillator in Modern Physics (Harwood Academic Publishers, Australia, 1996)

  21. K. Katō, K. Fukatsu, H. Tanaka, Prog. Theor. Phys. 80, 663 (1988)

    Article  ADS  Google Scholar 

  22. K. Fukatsu, K. Katō, Prog. Theor. Phys. 87, 151 (1992)

    Article  ADS  Google Scholar 

  23. Y. Funaki, T. Yamada, H. Horiuchi, G. Röpke, P. Schuck, A. Tohsaki, Phys. Rev. Lett. 101, 082502 (2008)

    Article  ADS  Google Scholar 

  24. S. Saito, Prog. Theor. Phys. 40, 893 (1968)

    Article  ADS  Google Scholar 

  25. S. Saito, Prog. Theor. Phys. 41, 705 (1969)

    Article  ADS  Google Scholar 

  26. S. Saito, S. Okai, R. Tamagaki, M. Yasuno, Prog. Theor. Phys. 50, 1561 (1973)

    Article  ADS  Google Scholar 

  27. P.O. Hess, G. Lévai, J. Cseh, Phys. Rev. C 54, 2345 (1996)

    Article  ADS  Google Scholar 

  28. K. Wildermuth, Y.C. Tang, A Unified Theory of the Nucleus (Academic Press, New York, 1977)

  29. J.P. Elliott, Proc. R. Soc. London A 245, 128 (1958)

    Article  ADS  Google Scholar 

  30. J.P. Elliott, Proc. R. Soc. London A 245, 562 (1958)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  32. O. Castaños, J.P. Draayer, Y. Leschber, Z. Phys. A 329, 33 (1988)

    ADS  Google Scholar 

  33. G. Herzberg, Molecular Spectra and Molecular Structure (D. Van Nostrand Company INC, New York, 1963).

  34. J. Blomqvist, A. Molinari, Nucl. Phys. A 106, 545 (1968)

    Article  ADS  Google Scholar 

  35. O. Castaños, J.P. Draayer, Nucl. Phys. A 491, 349 (1989)

    Article  ADS  Google Scholar 

  36. O. Castaños, P.O. Hess, P. Rocheford, J.P. Draayer, Nucl. Phys. A 524, 469 (1991)

    Article  ADS  Google Scholar 

  37. O.S. van Roosmalen, PhD Thesis, University of Groningen, The Netherlands (1982)

  38. Y. Kanada-En’yo, Phys. Rev. C 96, 034306 (2017)

    Article  ADS  Google Scholar 

  39. http://www.nndc.bnl.gov/ensdf

  40. H. Yépez-Martínez, M.J. Ermamatov, P.R. Fraser, P.O. Hess, Phys. Rev. C 86, 034309 (2012)

    Article  ADS  Google Scholar 

  41. W. Greiner, J.M. Eisenberg, Nuclear Theory I: Nuclear Models (North-Holland, Amsterdam, 1987)

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Authors and Affiliations

  1. Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Ciudad Universitaria, Circuito Exterior S/N, A.P. 70-543, 04510, México D.F., Mexico

    P. O. Hess, J. R. M. Berriel-Aguayo & L. J. Chávez-Nuñez

  2. Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe Universität, Ruth-Moufang-Str.1, 60438, Frankfurt am Main, Germany

    P. O. Hess

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  1. P. O. Hess
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  2. J. R. M. Berriel-Aguayo
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  3. L. J. Chávez-Nuñez
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Correspondence to P. O. Hess.

Additional information

Communicated by F. Gulminelli

Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: All data generated during this study are contained in this published article.]

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Hess, P.O., Berriel-Aguayo, J.R.M. & Chávez-Nuñez, L.J. 16O within the Semimicroscopic Algebraic Cluster Model and the importance of the Pauli Exclusion Principle. Eur. Phys. J. A 55, 71 (2019). https://doi.org/10.1140/epja/i2019-12744-0

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