Ядерна фізика та енергетика Nuclear Physics and Atomic Energy   ISSN: 1818-331X (Print), 2074-0565 (Online)   Publisher: Institute for Nuclear Research of the National Academy of Sciences of Ukraine   Languages: Ukrainian, English   Periodicity: 4 times per year   Open access peer reviewed journal

Full text (en)

Fahmi Sh. Radhi¹, Huda H. Kassim², Mushtaq A. Al-Jubbori³, I. Hossain^4,*, Fadhil I. Sharrad^2,5, N. Aldahan⁵, Hewa Y. Abdullah<sup>6

1</sup> Department of Physics, College of Education for Pure Science, University of Basrah, Basrah, Iraq
² Department of Physics, College of Science, Karbala University, Karbala, Iraq
³ Department of Physics, College of Education for Pure Sciences, University of Mosul, Mosul, Iraq
⁴ Department of Physics, Rabigh College of Science & Arts, King Abdulaziz University, Rabigh, Saudi Arabia
⁵ College of Health and Medical Technology, University of Alkafeel, Najaf, Iraq
⁶ Physics Education Department, Faculty of Education, Tishk International University, Erbil, Iraq

^*Corresponding author. E-mail address: mihossain@kau.edu.sa

Abstract: In this paper, IBM-1 and IBM-2 with a SU(3) limit are used to describe the ¹⁵⁸Gd isotope. The calculations of energy levels in the ground state, beta-, and gamma-bands are made up, which account for 15 energy levels. However, we found that the energy states of the same spin of the beta- and vibrational bands become degenerate states. In breaking the SU(3) dynamical symmetry by introducing a value of pairing interaction, the degeneracy is lifted and the energy levels are brought up to the same order as the experimental ones.

Keywords: IBM-1, IBM-2, energy level, potential energy, ¹⁵⁸Gd.

1. F. Iachello, A. Arima. The Interacting Boson Model (Cambridge, Cambridge University Press, 1987). https://doi.org/10.1017/CBO9780511895517

2. G.L. Long, S.J. Zhu, H.Z. Sun. Description of ^116,118,120Cd in the interacting boson model. J. Phys. G: Nucl. Part. Phys. 21 (1995) 331. https://doi.org/10.1088/0954-3899/21/3/008

3. F. Iachello. Analytic Description of Critical Point Nuclei in a Spherical-Axially Deformed Shape Phase Transition. Phys. Rev. Lett. 87 (2001) 525052. https://doi.org/10.1103/PhysRevLett.87.052502

4. P. Cejnar, J. Jolie, R.F. Casten. Quantum phase transitions in the shapes of atomic nuclei. Rev. Mod. Phys. 82 (2010) 2155. https://doi.org/10.1103/RevModPhys.82.2155

5. R.F. Casten, E.A. McCutchan. Quantum phase transitions and structural evolution in nuclei. J. Phys. G: Nucl. Part. Phys. 34 (2007) R285. https://doi.org/10.1088/0954-3899/34/7/R01

6. H.R. Yazar et al. The Investigation of Electromagnetic Transition Probabilities of Gadolinium Isotopes with the IBFM-1 Model. Chin. J. Phys. 48(3) (2010) 344.

7. J.E. Garcia-Ramos et al. Two-neutron separation energies, binding energies and phase transitions in the interacting boson model. Nucl. Physics A 688 (2001) 735. https://doi.org/10.1016/S0375-9474(00)00592-3

8. J.E. Garcia-Ramos et al. Phase transitions and critical points in the rare-earth region. Phys. Rev. C 68 (2003) 024307. https://doi.org/10.1103/PhysRevC.68.024307

9. F. Iachello, N.V. Zamfir. Quantum Phase Transitions in Mesoscopic Systems. Phys. Rev. Lett. 92 (2004) 212501. https://doi.org/10.1103/PhysRevLett.92.212501

10. M.J.A. de Voigt, J. Dudek, Z. Szymanski. High-spin phenomena in atomic nuclei. Rev. Mod. Phys. 55 (1983) 949. https://doi.org/10.1103/RevModPhys.55.949

11. S.R. Lesher et al. New 0⁺ states in ¹⁵⁸Gd. Phys. Rev C 66 (2002) 051305. https://doi.org/10.1103/PhysRevC.66.051305

12. S.R. Lesher et al. Study of 0⁺ excitations in ¹⁵⁸Gd with the (n, n′γ) reaction. Phys. Rev. C 76 (2007) 034318. https://doi.org/10.1103/PhysRevC.76.034318

13. A.I. Levon et al. New data on 0⁺ states in ¹⁵⁸Gd. Phys. Rev. C 100 (2019) 034307. https://doi.org/10.1103/PhysRevC.100.034307

14. M.A. Al-Jubbori et al. Deformation properties of the even-even rare-earth Er-Os isotopes for N = 100. Int. J. Mod. Phys. E 27 (2018) 1850035. https://doi.org/10.1142/S0218301318500350

15. M.A. Al-Jubbori et al. Nuclear structure of the even-even rare-earth Er-Os nuclei for N = 102. Indian J. Phys. 94(3) (2020) 379. https://doi.org/10.1007/s12648-019-01461-3

16. M.A. Al-Jubbori et al. Nuclear Structure of Rare-Earth ¹⁷²Er, ¹⁷⁴Yb, ¹⁷⁶Hf, ¹⁷⁸W, ¹⁸⁰Os Nuclei. Ukr. J. Phys. 67(2) (2022) 127. https://doi.org/10.15407/ujpe67.2.127

17. N.V. Zamfir, Jing-ye Zhang, R.F. Casten. Interpreting recent measurements of 0⁺ states in ¹⁵⁸Gd. Phys. Rev. C 66 (2002) 057303. https://doi.org/10.1103/PhysRevC.66.057303

18. A.I. Levon et al. High-resolution study of excited states in ¹⁵⁸Gd with the (p, t) reaction. Phys. Rev. C 102 (2020) 014308. https://doi.org/10.1103/PhysRevC.102.014308

19. R.F. Casten, D.D. Warner. The interacting boson approximation. Rev. Mod. Phys. 60 (1988) 389. https://doi.org/10.1103/RevModPhys.60.389

20. A. Arima, F. Iachello. Interacting boson model of collective nuclear states II. The rotational limit. Ann. Phys. 111 (1978) 201. https://doi.org/10.1016/0003-4916(78)90228-2

21. A. Arima, F. Iachello. Interacting boson model of collective states I. The vibrational limit. Ann. Phys. 99 (1976) 253. https://doi.org/10.1016/0003-4916(76)90097-X

22. F. Iachello. Dynamical Supersymmetries in Nuclei. Phys. Rev. Lett. 44 (1980) 772. https://doi.org/10.1103/PhysRevLett.44.772

23. A. Arima et al. Collective nuclear states as symmetric couplings of proton and neutron excitations. Phys. Lett. B 66(3) (1977) 205. https://doi.org/10.1016/0370-2693(77)90860-7

24. T. Otsuka et al. Shell model description of interacting bosons. Phys. Lett. B 76 (1978) 139. https://doi.org/10.1016/0370-2693(78)90260-5

25. G. Puddu, O. Scholten, T. Otsuka. Collective Quadrupole States of Xe, Ba and Ce in the Interacting Boson Model. Nucl. Phys. A 348 (1980) 109. https://doi.org/10.1016/0375-9474(80)90548-5

26. T. Otsuka, N. Yoshida. User's manual of the program NPBOS. Report JAERI-M 85-094 (Japan Atomic Energy Research Institute, 1985) 57 p. https://inis.iaea.org/collection/NCLCollectionStore/_Public/17/033/17033326.pdf

27. http://www.nndc.bnl.gov/ensdf/DatasetFetchServlet

28. R.G. Helmer. Nuclear Data Sheets for A = 158. Nuclear Data Sheets 101 (2004) 325. https://doi.org/10.1016/j.nds.2004.02.001

29. N. Nica. Nuclear Data Sheets for A=158. Nucl. Data Sheets 141 (2017) 1. https://doi.org/10.1016/j.nds.2017.03.001

30. H.H. Kassim. Description of the Ba - Dy (N = 92) nuclei in the interacting boson model. Int. J. Mod. Phys. E 26(4) (2017) 1750019. https://doi.org/10.1142/S0218301317500197

31. O. Scholten, A.E.L. Dieperink. In: Interacting Boson-Fermi Systems in Nuclei. Proc. of a seminar, Erice, Italy, June 1980. F. Iachello (Ed.) (New York, Plenum, 1981).

32. J. Lange, K. Kumar, J.H. Hamilton. E0-E2-M1 multipole admixtures of transitions in even-even nuclei. Rev. Mod. Phys. 54 (1982) 119. https://doi.org/10.1103/RevModPhys.54.119

33. L.I. Govor, A.M. Demidov, I.V. Mikhailov. Multipole mixtures in gamma transitions in ¹⁵⁸Gd from the (n, n′γ) reaction. Phys. of Atom. Nuclei 64 (2001) 1254. https://doi.org/10.1134/1.1389552

34. L.M. Robledo, R. Rodríguez-Guzmán, P. Sarriguren. Role of triaxiality in the ground-state shape of neutron-rich Yb, Hf, W, Os and Pt isotopes. J. Phys. G: Nucl. Part. Phys. 36 (2009) 115104. https://doi.org/10.1088/0954-3899/36/11/115104

35. K. Nomura et al. Derivation of IBM Hamiltonian for deformed nuclei. J. Phys.: Conf. Ser. 267 (2011) 012050. https://doi.org/10.1088/1742-6596/267/1/012050

36. I. Bentley, S. Frauendorf. Microscopic calculation of interacting boson model parameters by potential-energy surface mapping. Phys. Rev. C 83 (2011) 064322. https://doi.org/10.1103/PhysRevC.83.064322

37. K. Nomura et al. Microscopic formulation of the interacting boson model for rotational nuclei. Phys. Rev. C 83 (2011) 041302(R). https://doi.org/10.1103/PhysRevC.83.041302