Quantum phase transition of the neodymium isotope chain using the su(1,1) Affine Lie algebra in the framework of IBM-1

Document Type : Full length research Paper

Authors

Department of Physics, Faculty of Science, Ilam University, Ilam, Iran

Abstract

In this research, we have considered quantum phase transition for even-even neodymium isotopes ( ) using the Hamiltonian of Interacting Boson Model (IBM-1) in the framework of affine SU(1,1) Lie algebra. The energy spectrum of this chain has obtained by calculating the Hamiltonian control parameters with Least Squares method. In the following, energy surfaces using coherent state formalism has calculated. Changes observed in the energy surfaces and the values of showed that the  isotope is the transitional nuclei between U(5) and SO(6) limits. The results of this model are in good agreement with New Empirical Formula (NEF).

Keywords

Main Subjects

References

[1] I. Talmi, Simple models of complex nuclei, Harvard Academic Publishers, (1993). https://doi.org/10.1063/1.2808408
[2] A. Bohr, B.A. Motelson, nuclear structure, World Scientific Publishing Co. Pte. Ltd, (1998). https://doi.org/10.1142/3530 
[3] F. Iachello, A. Arima, The Interacting Boson Model, Cambridge University Press, (1987). https://doi.org/10.1017/CBO9780511895517
[4] P. Van Isacker, Jin-Quan Chen, Classical limit of the interacting boson Hamiltonian, Physical Review C 24 (1981) 684. https://doi.org/10.1103/PhysRevC.24.684
[5] A. Arima, F. Iachello, Collective Nuclear States as Representations of a SU(6) Group, Physicl Review Letter 35 (1975) 1061. https://doi.org/10.1103/PhysRevLett.35.1069
[6] H. Sabri, M. Seidi, Energy spectra and E2 transition rates of 124-130 Ba,  International Journal of Modern Physics E,  25 (2016) 1650086. https://doi.org/10.1142/S0218301316500865 
[7] M. Macek, P. Stránský, A. Leviatan, P.  Cejnar, Excited-state quantum phase transitions in systems with two degrees of freedom. III. Interacting boson systems, Physical Review C 99 (2019) 064323. https://doi.org/10.1103/PhysRevC.99.064323
[8] K. Nomura, Y. Zhang, Two-neutron transfer reactions and shape phase transitions in the microscopically formulated interacting boson model, Physical Review C, 99 (2019) 024324. https://doi.org/10.1103/PhysRevC.99.024324
[9] Yu Zhang, Yan Zuo, Feng Pan, J.P. Draayer, Excited-state quantum phase transitions in the interacting boson model: Spectral characteristics of 0+ states and effective order parameter, Physical Review C 93 (2016) 044302. https://doi.org/10.1103/PhysRevC.93.044302
[10] Y. Zhang, F. Iachello, Two-nucleon transfer reactions as a test of quantum phase transitions in nuclei,  Physical Review C 95 (2017) 034306. https://doi.org/10.1103/PhysRevC.95.034306
[11] K. Nomura et al, Shape coexistence in the microscopically guided interacting boson model, Journal of Physics G: Nuclear and Particle Physics, 43 (2016) 024008. https://doi.org/10.1088/0954-3899/43/2/024008
[12] L. Fortunato, C.E. Alonso, J.M. Arias, J.E. Garcıa-Ramos, A. Vitturi, Phase diagram for a cubic-Q interacting boson model Hamiltonian: Signs of triaxiality, Physical Review C 84 (2011) 014326.
https://doi.org/10.1103/PhysRevC.84.014326
[13] Yu Zhang, Feng Pan, Yu-Xin Liu, Yan-An Luo, J. P. Draayer, Analytically solvable prolate-oblate shape phase transitional description within the SU(3) limit of the interacting boson model, Physical Review C, 85 (2012) 064312. https://doi.org/10.1103/PhysRevC.85.064312
[14] H. Fathi, M. Ghadami, H. Sabri, N. Fouladi, M. A. Jafarizadeh, Investigation of shape phase transition in the U(5) ↔ SO(6) transitional region by catastrophe theory and critical exponents of some quantities, International Journal of Modern Physics E, 23 (2014) 1450045. https://doi.org/10.1142/S0218301314500451
[15] A.M. Khalaf, A.M. Ismail, A.A. Zaki, Nuclear shape transition between the limiting symmetries U(5) and SU(3) of interacting boson model applied to double even Hafnium isotopic chain, Nuclear Physics A 996 (2020) 121704. https://doi.org/10.1016/j.nuclphysa.2020.121704
[16] F. Pan, J. Draayer, New algebraic solutions for SO(6) ↔ U(5) transitional nuclei in the interacting boson model , Nuclear Physics A, 636 (1998) 156. https://doi.org/10.1016/S0375-9474(98)00207-3
[17] F. Pan, X. Zhang, J.P. Draayer, Algebraic solutions of an sl-boson system in the U(2l + 1) O(2l + 2) transitional region, Journal of Physics A: Mathematical and General,  35 (2002) 7173. https://doi.org/10.1088/0305-4470/35/33/313
[18] M.A. Al-Jubbori, F.S. Radhi, A. AIbrahim, S.A. Abdullah Albakri, H.H. Kassim, F. I.Sharrad, Determine the 134–140Nd isotopes identity using IBM and NEF, Nuclear Physics A 971 (2018) 35. https://doi.org/10.1016/j.nuclphysa.2018.01.011
[19] T.R. Rodriguez, J. Luis Egido, A beyond mean field analysis of the shape transition in the Neodymium isotopes, Physical Letter B, 663 (2008) 49. https://doi.org/10.1016/j.physletb.2008.03.061
[20] A.A. Sonzogni, Nuclear Data Sheets for A = 134, Nuclear Data Sheets 103 (2004) 1. https://doi.org/10.1016/j.nds.2004.11.001
[21] E.A. Mccutchan, Nuclear Data Sheets for A=136, Nuclear Data Sheets 152 (2018) 331. https://doi.org/10.1016/j.nds.2018.10.002
[22] A.A. Sonzogni, Nuclear Data Sheets for A=138, Nuclear Data Sheets, 98 (2003) 515. https://doi.org/10.1006/ndsh.2003.0004.
[23] N. Nica, Nuclear Data Sheets for A=140, Nuclear Data Sheets 108 (2007) 1287. https://doi.org/10.1016/j.nds.2007.06.001
[24] L.K. Peker, Nuclear Data Sheets for A = 142, Nuclear Data Sheets, 63 (1991) 647. DOI: 10.1016/S0090-3752(05)80011-0
[25] J.K. Tuli, Nuclear Data Sheets for A=144, Nuclear Data Sheets, 56 (1989) 607. https://doi.org/10.1016/S0090-3752(89)80050-X.
[26] R.F. Casten, Shape phase transitions and critical-point phenomena in atomic nuclei, Nature Physics 2 (2006) 811. DOI: 10.1038/nphys451

Files

History

  • Receive Date: 22 April 2020
  • Revise Date: 07 November 2020
  • Accept Date: 09 May 2021

Share

How to cite

Statistics