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Description of critical point nuclei within an energy-dependent geometric model

  • A. I. Budaca
  • R. BudacaEmail author
Regular Article
  • 8 Downloads

Abstract.

An exactly solvable version of the Bohr Hamiltonian is proposed for a unified treatment of transitional nuclei. The model employs an energy-dependent potential in the \( \beta\) shape variable which is amended with a centrifugal contribution from the \( \gamma\) and angular degrees of freedom. The parametrization of the \( \gamma\) part of the potential enables the connection between the adiabatic separation of \( \beta\) and \( \gamma\) fluctuations suitable for critical point nuclei and the exactly separable solutions specific to deformed nuclei. The fully analytical model is applied to known critical point nuclei as well as a neighbouring isotope for each case. Beside very good agreement with experiment for energies and electromagnetic transitions, numerical results also reveal specific model characteristics for critical nuclei in comparison to more or less deformed nuclei.

References

  1. 1.
    F. Iachello, Phys. Rev. Lett. 85, 3580 (2000)ADSCrossRefGoogle Scholar
  2. 2.
    F. Iachello, Phys. Rev. Lett. 87, 052502 (2001)ADSCrossRefGoogle Scholar
  3. 3.
    A. Bohr, Mat. Fys. Medd. K. Dan. Vidensk. Selsk. 26, 14 (1952)Google Scholar
  4. 4.
    A. Bohr, B.R. Mottelson, Mat. Fys. Medd. Dan. Vidensk. Selsk. 27, 16 (1953)Google Scholar
  5. 5.
    P. Cejnar, J. Jolie, R.F. Casten, Rev. Mod. Phys. 82, 2155 (2010)ADSCrossRefGoogle Scholar
  6. 6.
    R. Krücken et al., Phys. Rev. Lett. 88, 232501 (2002)ADSCrossRefGoogle Scholar
  7. 7.
    R.F. Casten, N.V. Zamfir, Phys. Rev. C 66, 054310 (2001)ADSGoogle Scholar
  8. 8.
    D. Tonev et al., Phys. Rev. C 69, 034334 (2004)ADSCrossRefGoogle Scholar
  9. 9.
    M.A. Caprio et al., Phys. Rev. C 66, 054310 (2002)ADSCrossRefGoogle Scholar
  10. 10.
    Y. Zhang, Y.-X. Liu, F. Pan, Y. Sun, J.P. Draayer, Phys. Lett. B 732, 55 (2014)ADSCrossRefGoogle Scholar
  11. 11.
    Y. Zhang, F. Pan, Y.-A. Luo, J.P. Draayer, Phys. Lett. B 751, 423 (2015)ADSCrossRefGoogle Scholar
  12. 12.
    D.S. Brenner, AIP Conf. Proc. 638, 223 (2002)ADSCrossRefGoogle Scholar
  13. 13.
    P.G. Bizzeti, A.M. Bizzeti-Sona, Phys. Rev. C 66, 031301(R) (2002)ADSCrossRefGoogle Scholar
  14. 14.
    C. Hutter et al., Phys. Rev. C 67, 054315 (2003)ADSCrossRefGoogle Scholar
  15. 15.
    T. Togashi, Y. Tsunoda, T. Otsuka, N. Shimizu, Phys. Rev. Lett. 117, 172502 (2016)ADSCrossRefGoogle Scholar
  16. 16.
    A. Dewald et al., J. Phys. G: Nucl. Part. Phys. 31, s1427 (2005)CrossRefGoogle Scholar
  17. 17.
    D. Bonatsos, D. Lenis, D. Petrellis, P.A. Terziev, I. Yigitoglu, Phys. Lett. B 632, 238 (2008)ADSCrossRefGoogle Scholar
  18. 18.
    R. Budaca, P. Buganu, A.I. Budaca, Phys. Lett. B 776, 26 (2018)ADSCrossRefGoogle Scholar
  19. 19.
    M.A. Caprio, Phys. Rev. C 72, 054323 (2005)ADSCrossRefGoogle Scholar
  20. 20.
    D. Bonatsos, D. Lenis, E.A. Mccutchan, D. Petrellis, I. Yigitoglu, Phys. Lett. B 649, 394 (2007)ADSCrossRefGoogle Scholar
  21. 21.
    D. Bonatsos, E.A. Mccutchan, N. Minkov, R.F. Casten, P. Yotov, D. Lenis, D. Petrellis, I. Yigitoglu, Phys. Rev. C 76, 064312 (2007)ADSCrossRefGoogle Scholar
  22. 22.
    L. Wilets, M. Jean, Phys. Rev. 102, 788 (1956)ADSCrossRefGoogle Scholar
  23. 23.
    L. Fortunato, Phys. Rev. C 70, 011302 (2004)ADSCrossRefGoogle Scholar
  24. 24.
    A. Bohr, B.R. Mottelson, Nuclear Structure, Vol. 2 (Benjamin, Reading, Massachusetts, 1975)Google Scholar
  25. 25.
    W.M. Frank, D.J. Land, R.M. Spector, Rev. Mod. Phys. 43, 36 (1971)ADSCrossRefGoogle Scholar
  26. 26.
    S.A. Coon, B.R. Holstein, Am. J. Phys. 70, 513 (2002)ADSCrossRefGoogle Scholar
  27. 27.
    V. Efimov, Yadern. Fiz. 12, 1080 (1970)Google Scholar
  28. 28.
    D.V. Fedorov, A.S. Jensen, Phys. Rev. Lett. 71, 4103 (1993)ADSCrossRefGoogle Scholar
  29. 29.
    P. Naidon, S. Endo, Rep. Prog. Phys. 80, 056001 (2017)ADSCrossRefGoogle Scholar
  30. 30.
    J. Formanek, R.J. Lombard, J. Mares, Czech. J. Phys. 54, 289 (2004)ADSCrossRefGoogle Scholar
  31. 31.
    R. Yekken, R.J. Lombard, J. Phys. A 43, 125301 (2010)ADSMathSciNetCrossRefGoogle Scholar
  32. 32.
    R. Yekken, M. Lassaut, R.J. Lombard, Few-Body Syst. 54, 2113 (2012)ADSCrossRefGoogle Scholar
  33. 33.
    A.I. Budaca, R. Budaca, Phys. Scr. 92, 084001 (2017)ADSCrossRefGoogle Scholar
  34. 34.
    G.P. Lepage, Phys. Rev. A 16, 863 (1977)ADSCrossRefGoogle Scholar
  35. 35.
    H. Sazdjian, J. Math. Phys. 29, 1620 (1988)ADSMathSciNetCrossRefGoogle Scholar
  36. 36.
    D. Bonatsos, P. Georgoudis, D. Lenis, N. Minkov, C. Quesne, Phys. Lett. B 683, 264 (2010)ADSCrossRefGoogle Scholar
  37. 37.
    P.E. Georgoudis, Phys. Lett. B 731, 122 (2014)ADSMathSciNetCrossRefGoogle Scholar
  38. 38.
    D. Bonatsos, N. Minkov, D. Petrellis, J. Phys. G 42, 095104 (2015)ADSCrossRefGoogle Scholar
  39. 39.
    D. Bonatsos, P.E. Georgoudis, D. Lenis, N. Minkov, C. Quesne, Phys. Rev. C 83, 044321 (2011)ADSCrossRefGoogle Scholar
  40. 40.
    D. Bonatsos, P.E. Georgoudis, N. Minkov, D. Petrellis, C. Quesne, Phys. Rev. C 88, 034316 (2013)ADSCrossRefGoogle Scholar
  41. 41.
    M. Chabab, A. Lahbas, M. Oulne, Phys. Rev. C 91, 064307 (2015)ADSCrossRefGoogle Scholar
  42. 42.
    M. Chabab, A. El Batoul, A. Lahbas, M. Oulne, J. Phys. G 43, 125107 (2016)ADSCrossRefGoogle Scholar
  43. 43.
    M. Alimohammadi, H. Hassanabadi, S. Zare, Nucl. Phys. A 960, 78 (2017)ADSCrossRefGoogle Scholar
  44. 44.
    H. Hassanabadi, M. Alimohammadi, S. Zare, Mod. Phys. Lett. A 32, 1750085 (2017)ADSCrossRefGoogle Scholar
  45. 45.
    P. Buganu, M. Chabab, A. El Batoul, A. Lahbas, M. Oulne, Nucl. Phys. A 970, 272 (2018)ADSCrossRefGoogle Scholar
  46. 46.
    O. Von Roos, Phys. Rev. B 27, 7547 (1983)ADSCrossRefGoogle Scholar
  47. 47.
    R. Yekken, M. Lassaut, R. Lombard, Ann. Phys. (NY) 338, 195 (2013)ADSCrossRefGoogle Scholar
  48. 48.
    R. Budaca, Ann. Acad. Rom. Sci. Ser. Math. Appl. 9, 205 (2017)MathSciNetGoogle Scholar
  49. 49.
    L.J. Wood, E.F. Zganjar, C. De Coster, K. Heyde, Nucl. Phys. A 651, 323 (1999)ADSCrossRefGoogle Scholar
  50. 50.
    K. Heyde, J.L. Wood, Rev. Mod. Phys. 83, 1467 (2011)ADSCrossRefGoogle Scholar
  51. 51.
    J.O. Rasmussen, Nucl. Phys. 19, 85 (1960)CrossRefGoogle Scholar
  52. 52.
    A.S. Reiner, Nucl. Phys. 27, 115 (1961)CrossRefGoogle Scholar
  53. 53.
    A.S. Davydov, V.S. Rostovsky, Nucl. Phys. 60, 529 (1964)CrossRefGoogle Scholar
  54. 54.
    J. Bonnet, A. Krugmann, J. Beller, N. Pietralla, R.V. Jolos, Phys. Rev. C 79, 034307 (2009)ADSCrossRefGoogle Scholar
  55. 55.
    D. Bonatsos, D. Lenis, N. Minkov, P.P. Raychev, P.A. Terziev, Phys. Rev. C 69, 014302 (2004)ADSCrossRefGoogle Scholar
  56. 56.
    M.A. Caprio, Phys. Rev. C 83, 064309 (2011)ADSCrossRefGoogle Scholar
  57. 57.
    R. Budaca, Phys. Lett. B 751, 39 (2015)ADSCrossRefGoogle Scholar
  58. 58.
    R. Budaca, Eur. Phys. J. A 52, 314 (2016)ADSCrossRefGoogle Scholar
  59. 59.
    P. Von Brentano, V. Werner, R.F. Casten, C. Scholl, E.A. Mccutchan, R. Krücken, J. Jolie, Phys. Rev. Lett. 93, 152502 (2004)ADSCrossRefGoogle Scholar
  60. 60.
    N. Blasi, L. Guerro, A. Saltarelli, O. Wieland, L. Fortunato, Phys. Rev. C 88, 014318 (2013)ADSCrossRefGoogle Scholar
  61. 61.
    D. Bonatsos, A. Klein, At. Data Nucl. Data Tables 30, 27 (1984)ADSCrossRefGoogle Scholar
  62. 62.
    A.A. Raduta, R. Budaca, Phys. Rev. C 84, 044323 (2011)ADSCrossRefGoogle Scholar
  63. 63.
    R. Budaca, A.A. Raduta, J. Phys. G 40, 025109 (2013)ADSCrossRefGoogle Scholar
  64. 64.
    D. De Frenne, Nucl. Data Sheets 110, 1745 (2009)ADSCrossRefGoogle Scholar
  65. 65.
    D. De Frenne, A. Negret, Nucl. Data Sheets 109, 943 (2008)ADSCrossRefGoogle Scholar
  66. 66.
    Yu. Khazov, A. Rodionov, G. Shulyak, Nucl. Data Sheets 136, 163 (2016)ADSCrossRefGoogle Scholar
  67. 67.
    N. Nica, Nucl. Data Sheets 117, 1 (2014)ADSCrossRefGoogle Scholar
  68. 68.
    S.K. Basu, A.A. Sonzogni, Nucl. Data Sheets 114, 435 (2013)ADSCrossRefGoogle Scholar
  69. 69.
    M.J. Martin, Nucl. Data Sheets 114, 1497 (2013)ADSCrossRefGoogle Scholar
  70. 70.
    C.W. Reich, Nucl. Data Sheets 110, 2257 (2009)ADSCrossRefGoogle Scholar
  71. 71.
    C.W. Reich, Nucl. Data Sheets 113, 2537 (2012)ADSCrossRefGoogle Scholar
  72. 72.
    N. Nica, Nucl. Data Sheets 141, 1 (2017)ADSCrossRefGoogle Scholar
  73. 73.
    G.A. Lalazissis, S. Raman, P. Ring, At. Data Nucl. Data Tables 71, 1 (1999)ADSCrossRefGoogle Scholar
  74. 74.
    T. Kibèdi, R.H. Spear, At. Data Nucl. Data Tables 89, 77 (2005)ADSCrossRefGoogle Scholar
  75. 75.
    N. Blasi, L. Atanasova, D. Balabanski, S. Das Gupta, K. Gladinski, L. Guerro, S. Nardelli, A. Saltarelli, Phys. Rev. C 90, 044317 (2014)ADSCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Horia Hulubei National Institute of Physics and Nuclear EngineeringBucharest-MagureleRomania
  2. 2.Academy of Romanian Scientists54 Splaiul IndependenţeiBucharestRomania

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