Skip to main content
SpringerLink
Log in

Nuclear Shape Phase Transitions Using IBM Applied to Erbium and Ruthenium Nuclei

  • PHYSICS OF ELEMENTARY PARTICLES AND ATOMIC NUCLEI. THEORY
  • Published:
Physics of Particles and Nuclei Letters Aims and scope Submit manuscript

Abstract

The Hamiltonian of the sd version of the interacting boson model (sd IBM) is written in the consistent-Q-form and used to establish the nuclear shape phase transitional structures. The potential energy surfaces (PES’s) corresponding to the consistent-Q Hamiltonian are obtained by using the intrinsic coherent state formalism which introduces the shape variables \(\beta \) and \(\gamma \). The quadrupole–quadrupole interaction is constructed in terms of a new external factor as a linear function of the total number of bosons. The effect of this factor on the position of critical points is studied. We showed that the critical points take different positions for different choice of this external factor, the larger the factor value the smaller the critical point value. For applications to our model, the Erbium (Er) and Ruthenium (Ru) isotopic chains are taken as an examples in illustrating the U(5)–Su(3) and U(5)–O(6) shape phase transitions respectively. Some selected energy levels and reduced E2 transition probabilities B(E2) for each nucleus are calculated to adjust the model parameters by using a simulated computer search fitting program to fit the experimental data with the IBM calculations by minimizing the root mean square deviation between the experimental energies and reduced electric quadrupole transition probabilities and the calculated ones.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.

Similar content being viewed by others

REFERENCES

  1. F. Iachello and A. Arima, The Interacting Boson Model (Cambridge Univ. Press, Cambridge UK, 1987).

    Book  Google Scholar 

  2. D. Bonatsos, Interacting Boson Models of Nuclear Structure (Clarendon, Oxford, 1988).

    MATH  Google Scholar 

  3. I. Talmi, Simple Models of Complex Nuclei The Shell Model and Interacting Boson Models (Harwood Academic, 1993).

    Google Scholar 

  4. A. Arima and F. Iachello, Ann. Phys. (N.Y.) 99, 253 (1976);

    Article  ADS  Google Scholar 

  5. Ann. Phys. (N.Y.) 111, 201 (1978);

  6. Ann. Phys. (N.Y.) 123, 468 (1979).

  7. R. F. Casten, Nuclear Structure from a Simple Perspectives (Oxford Univ. Press, Oxford, 1990).

    Google Scholar 

  8. D Warner, Nature (London, U.K.) 420, 614 (2002).

    Article  ADS  Google Scholar 

  9. J. Jolie et al., Phys. Lett. 89, 182502 (2002).

    Article  Google Scholar 

  10. P. Cejnar, Phys. Rev. Lett. 90, 112501 (2003).

    Article  ADS  Google Scholar 

  11. J. M. Arias, J. Dukelsky, and J. E. Gracia Ramos, Phys. Rev. Lett. 91, 162502 (2003).

    Article  ADS  Google Scholar 

  12. F. Iachello, Int. J. Mod. Phys. B 20, 2687 (2006).

    Article  ADS  Google Scholar 

  13. R. F. Casten, Prog. Part. Nucl. Phys. 62, 183 (2009).

    Article  ADS  Google Scholar 

  14. J. Barea, J. M. Arias, and J. E. Garcia Ramos, Phys. Rev. C 82, 024316 (2010).

    Article  ADS  Google Scholar 

  15. A. M. Khalaf et al., Phys. Part. Nucl. Lett. 13, 163 (2016).

    Article  Google Scholar 

  16. A. M. Khalaf et al., Nucl. Phys. A 991, 121610 (2019).

    Article  Google Scholar 

  17. A. M. Khalaf et al., Nucl. Phys. A 997, 121719 (2020).

    Article  Google Scholar 

  18. A. M. Khalaf, A. M. Ismail, and A. A. Zaki, Nucl. Phys. A 996, 121704 (2020).

    Article  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  20. J. N. Ginocchio, Nucl. Phys. A 376, 438 (1982).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  22. Y. Alhassid and N. Whelan, Phys. Rev. Lett. 67, 816 (1991).

    Article  ADS  Google Scholar 

  23. Y. Alassid and N. Whelan, Phys. Rev. C 43, 2637 (1991).

    Article  ADS  Google Scholar 

  24. A. Bohr and B. R. Mottelson, Nuclear Structure (Benjamin, New York, 1975), Vol. 2.

    MATH  Google Scholar 

  25. G. Gneuss, U. Mosel, and W. Greiner, Phys. Lett. B 30, 397 (1969);

    Article  ADS  Google Scholar 

  26. Phys. Lett. B 31, 269 (1970).

  27. G. Gneuss and W. Greiner, Nucl. Phys. A 171, 449 (1971).

    Article  ADS  Google Scholar 

  28. A. M. Khalaf and A. M. Ismail, Prog. Phys. 2, 51 (2013); Prog. Phys. 2, 98 (2013).

    Google Scholar 

  29. M. Kotb, Phys. Part. Nucl. Lett. 13, 451 (2016).

    Article  Google Scholar 

  30. F. Iachello, Phys. Rev. Lett. 85, 3580 (2000).

    Article  ADS  Google Scholar 

  31. F. Iachello, Phys. Rev. Lett. 87, 052502 (2001).

    Article  ADS  Google Scholar 

  32. R. F. Casten and D. D. Warner, Rev. Mod. Phys. 60, 389 (1988);

    Article  ADS  Google Scholar 

  33. E. Rossensteel, Phys. Rev. C 41, 730 (1990).

    Article  ADS  Google Scholar 

  34. K. Hayde et al., Phys. Rev. C 29, 1420 (1984).

    Article  ADS  Google Scholar 

  35. A. M. Khalaf, M. Kotb, and H. A. Ghanim, Indian J. Phys. 94, 2033 (2020).

    Article  ADS  Google Scholar 

  36. D. D. Warner and R. F. Casten, Phys. Rev. C 28, 1798 (1983).

    Article  ADS  Google Scholar 

  37. N. Whelan and Y. Alhassid, Nucl. Phys. A 556, 42 (1993).

    Article  ADS  Google Scholar 

  38. N. V. Zamfir et al., Phys. Rev. C 66, 021304 (2002).

    Article  ADS  Google Scholar 

  39. N. V. Zamfir, E. A. McCutohen, and R. F. Casten, Phys. At. Nucl. 67, 1829 (2004).

    Article  Google Scholar 

  40. A. M. Khalaf and M. M. Taha, J. Theor. Appl. Phys. 9, 127 (2015).

    Article  ADS  Google Scholar 

  41. I. Iachello, N. V. Zamfir, and R. F. Casten, Phys. Rev. Lett. 81, 1191 (1998).

    Article  ADS  Google Scholar 

  42. E. William, R. J. Casperson, and V. Werner, Phys. Rev. C 81, 054306 (2010).

    Article  ADS  Google Scholar 

  43. A. A. Abdalaty, M. Kotb, M. D. Okasha, and A. M. Khalaf, Phys. At. Nucl. 83, 849 (2020).

    Article  Google Scholar 

  44. M. D. Okasha, Int. J. Adv. Res. Phys. Sci. 2, 59 (2015).

    Google Scholar 

  45. O. Scholten, Computer Code PHINT, KVI (Groningen, 1980).

    Google Scholar 

  46. W. H. Press, B. P. Flonnery, S. A. Teukalsly, and W. T. Vetterling, Numerical Relipes (Labridge Univ. Press, Cambridge, 1986), p. 294.

    Google Scholar 

  47. National Nuclear Data Center NNDC, Brookhaven National Laboratory. http://www.nndc.bnl.gov/chart/.

  48. M. A. Al-Jubbari et al., Indian J. Phys. 94, 379 (2020).

    Article  ADS  Google Scholar 

  49. A. Bohr and B. Mottelson, Den. Mat. Fys. Medd. 30 (1) (1955).

  50. M. A. J. Mariscotti, G. Scharf-Goldheber, and B. Buck, Phys. Rev. 178, 1864 (1969).

    Article  ADS  Google Scholar 

  51. M. Sakai, in Proceedings of the International Symposium on Nuclear Structure: Coexistence of Single Particle and Collective Type Excitation, Balatonfured, Hungary, 1975 (Budapest, 1976), Vol. 1.

  52. I. N. Mikhailov, P. Quentin, and D. Samsoem, Nucl. Phys. A 627, 259 (1997).

    Article  ADS  Google Scholar 

  53. M. Boyukata, P. van Isacker, and I. Uluer, J. Phys. G 37, 105102 (2010).

    Article  ADS  Google Scholar 

  54. A. Frank, C. E. Alonso and J. M. Arias, Phys. Rev. C 65, 014301 (2001).

    Article  ADS  Google Scholar 

  55. A. M. Khalaf et al., Phys. At. Nucl. 83, 866 (2020).

    Article  Google Scholar 

  56. A. M. Khalaf, M. Sirag, and M. Kotb, Commun. Theor. Phys. 64, 90 (2015).

    Article  ADS  Google Scholar 

  57. A. M. Khalaf, M. Kotb, and T. M. Awwad, Int. J. Mod. Phys. E 26, 1750011 (2017).

    Article  ADS  Google Scholar 

  58. D. Troltenier et al., Nucl. Phys. A 601, 56 (1996).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Physics Department, Faculty of Science, Al-Azhar University, 11651, Cairo, Egypt

    M. Ramadan, A. M. Khalaf & M. Kotb

  2. Physics Department, Faculty of Science (Girls College), Al-Azhar University, 11651, Cairo, Egypt

    M. D. Okasha

Authors
  1. M. Ramadan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. M. Khalaf
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Kotb
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. D. Okasha
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Kotb.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ramadan, M., Khalaf, A.M., Kotb, M. et al. Nuclear Shape Phase Transitions Using IBM Applied to Erbium and Ruthenium Nuclei. Phys. Part. Nuclei Lett. 18, 527–539 (2021). https://doi.org/10.1134/S1547477121050095

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1547477121050095

Keywords:

Search

Navigation