An International Double-Blind, Peer-Review Journal by NSTRI

Document Type : Research paper

Authors

Plasma and Nuclear Physics Research School, Nuclear Science and Technology Research Institute (NSTRI), P.O. Box: 14155-1339, Tehran, Iran

Abstract

In this paper‎, ‎we study the nature of the dynamics in second-order Quantum Phase Transition (QPT) between vibrational ( ) and -unstable ( ) nuclear shapes‎. ‎Using a transitional Hamiltonian according to an affine SU(1,1) algebra in combination with a coherent state formalism, Shape Phase Transitions (SPT) in odd-nuclei in the framework of the Interacting Boson Fermion Model (IBFM) are investigated‎. ‎Classical analysis reveals a change in the system along with the transition in a critical point‎. ‎The role of a fermion with angular momentum j at the critical point on quantum phase transitions in bosonic systems is investigated via a semi-classical approach‎. ‎The effect of the coupling of the odd particle to an even-even boson core is discussed along with the shape transition and‎, ‎in particular‎, ‎at the critical point‎. Our study confirms the importance of the odd nuclei as necessary signatures to characterize the occurrence of the phase transition and determine the critical point's precise position‎.

Keywords

  1. F. Iachello‎ ‎and A. Arima‎, ‎‎The Interacting Boson Model, Cambridge University Press‎, (1987).
  2. F. Iachello‎ and P. ‎Van Isacker‎, ‎The interacting boson-fermion model‎, Cambridge University Press, (1991).
  3. F. Iachello‎, ‎A. ‎Leviatan‎ and D. ‎Petrellis‎, Effect of a fermion on quantum phase transitions in bosonic systemsPhys. Lett. B‎ ‎705‎, ‎379 (2011)‎.
  4. D. Petrellis‎, ‎A. ‎Leviatan‎ and F. ‎Iachello‎, Quantum phase transitions in Bose–Fermi systems,‎‎‎ Ann. Phys. ‎326, ‎926 (2011).
  5. F. Iachello‎, ‎A. ‎Leviatan‎ and D. ‎Petrellis‎, Effect of a fermion on quantum phase transitions in bosonic systemsPhys. Lett. B‎ ‎705‎, ‎379 (2011)‎.
  6. C. E. Alonso‎, ‎J. M. ‎Arias‎, ‎L. ‎Fortunato‎ and A. ‎Vitturi‎, Phase transitions in the interacting boson fermion model: The γ-unstable case,Phys. Rev. C72‎, ‎061302 (2005)‎.
  7. R. Fossion‎, ‎C. E. ‎Alonso‎, ‎J. M. ‎Arias‎, L. ‎Fortunato‎ and ‎A. ‎Vitturi‎, Shape-phase transitions and two-particle transfer intensities, Phys. Rev. C 76‎, ‎014316‎ (2007).
  8. I. Inci‎, C. E. ‎Alonso‎, J. M. ‎Arias‎, ‎L. ‎Fortunato‎, A. ‎Vitturi‎, Coherent state approach to the interacting boson model: Test of its validity in the transitional region, Phys. Rev. C80‎, ‎034321 ‎(2009)‎.
  9. C. E. Alonso‎, ‎J. M. ‎Arias‎ and A. ‎Vitturi‎, Critical-point symmetries in Boson-Fermion systems: The case of shape transitions in odd nuclei in a multiorbit model, Phys. Rev. Lett. ‎98‎, ‎052501‎ ‎(2007).
  10. C. E. Alonso‎, ‎J. M. ‎Arias‎ and A. ‎Vitturi‎, Shape phase transition in odd nuclei in a multi-j model: The U B (6) U F (12) case, Phys. Rev. C75, ‎064316‎ ‎(2007).
  11. M. Boyukata‎, ‎C. E. ‎Alonso‎, ‎J. M. ‎Arias‎, ‎L. ‎Fortunato‎ and ‎A. ‎Vitturi‎,‎ Shape phase transition in odd-even nuclei: From spherical to deformed γ-unstable shapes, Phys. Rev. C82‎, ‎014317‎ ‎(2010).
  12. L. Fortunato‎, ‎C. E. ‎Alonso‎, ‎J. M. ‎Arias‎, ‎M. ‎Böyükata‎ and ‎A. ‎Vitturi‎, Odd nuclei and shape phase transitions: the role of the unpaired fermion,Int. J. Mod. Phys. E20‎, ‎207-212 ‎(2011)‎‎.
  13. M. Böyükata‎, ‎C. E. ‎Alonso‎, ‎J. M. ‎Arias‎, ‎L. ‎Fortunato‎ and ‎A. ‎Vitturi, ‎In EPJ Web of Conferences (Vol‎. ‎66‎, ‎p‎. ‎02014)‎, ‎ IBA-Europhysics Prize in Applied Nuclear Science and Nuclear Methods in Medicine 00003. EDP sciences‎ ‎(2014)‎.
  14. X. R.Yu‎, J. ‎Hu‎, ‎X. X. ‎Li‎, ‎S. Y. An‎ and Y. ‎Zhang‎, Effects of single particle on shape phase transitions and phase coexistence in odd-even nuclei, Chin. Phys. C ‎ ‎42‎, ‎034103 ‎(2018)‎.
  15. F. Pan and ‎J. P. .Draayer‎, New algebraic solutions for SO (6)↔ U (5) transitional nuclei in the interacting boson model, Nucl. Phys. A636‎, ‎156 ‎(1998)‎.
  16. F. Pan‎, ‎X. ‎Zhang and ‎J. P. Draayer‎, Algebraic solutions of an sl-boson system in the U (2l+ 1) O (2l+ 2) transitional region,J. Phys. A Math. Theor. ‎ ‎35‎, ‎7173‎ ‎(2002).
  17. M. J. Jafarizadeh‎, ‎A. J. ‎Majarshin‎, N. ‎Fouladi‎ and ‎M. ‎Ghapanvari‎, Investigation of quantum phase transitions in the spdf interacting boson model based on dual algebraic structures for the four-level pairing model, J. Phys. G: Nucl. Part. Phys. ‎43‎, ‎095108 ‎(2016).‎
  18. M. A. Jafarizadeh‎, ‎N. ‎Amiri‎, ‎M. ‎Ghapanvari and ‎N. ‎Fouladi‎, Algebraic solutions for q− sdl-and
    q− sdll′-boson systems in the transitional region,
    Nucl. Phys. A ‎977, ‎129 ‎(2018)‎.
  19. A. M. Jafarizadeh‎, ‎M. ‎Ghapanvari‎ and ‎N. Fouladi‎, Algebraic solutions for U B F (5)− O B F (6) quantum phase transition in odd-mass-number nuclei, Phys. Rev. C ‎92‎, ‎054306‎ ‎(2015).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

How to cite this article

M. Ghapanvari, A. Kargarian, Investigation of Structure and Nuclear Shape Phase Transition in Odd Nuclei in a multi-j model,

Journal of Nuclear Science and Applications, Vol. 3, No. 2, (2022), P 1-12, Url:                                            ,  DOI:

 

 

This work is licensed under the Creative Commons Attribution 4.0 International License.

To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0

 

 

 

 

 

  1.  M. A. Jafarizadeh‎, ‎N. ‎Fouladi‎, ‎M. ‎Ghapanvari‎ and ‎H. ‎Fathi, Phase transition studies of the odd-mass 1 2 3− 1 3 5 Xe isotopes based on SU (1, 1) algebra in IBFM, Int. J. Mod. Phys. E25‎, ‎1650048‎ ‎(2016).
  2. N. Amiri‎, ‎M. ‎Ghapanvari‎, ‎M. A. ‎Jafarizadeh ‎and S. ‎Vosoughi‎, Nuclear structure and phase transition of odd-odd Cu isotopes: A neutron-proton interacting boson-fermion-fermion model calculation,Nucl. Phys. A1002‎, ‎121961 ‎(2020)‎.
  3. J. Dukelsky‎, ‎S‎. ‎Pittel and ‎G‎. ‎Sierra, Colloquium: Exactly solvable Richardson-Gaudin models for many-body quantum systems,Rev. Mod. Phys 76, ‎643 ‎(2004).
  4. K. S. ‎Evgueni‎ ‎and T. Takebe‎, Algebraic Bethe ansatz for the XYZ Gaudin model,‎Phys. Lett. A 219, 217-225 (1996)‎.
  5. S. De. Baerdemacker‎‎, ‎ Richardson-Gaudin integrability in the contraction limit of the quasispin, Phys. Rev.  C 86, 044332 (2012)‎.
  6. I. Inci‎, ‎C. E. ‎Alonso‎, ‎J. M. ‎Arias‎, ‎L. ‎Fortunato ‎and ‎A. ‎Vitturi‎, Coherent state approach to the interacting boson model: Test of its validity in the transitional region, Phys. Rev. C80‎, ‎034321‎ ‎(2009).
  7. I. Inci‎, Test of the coherent state approach in the axially deformed region, Nucl. Phys . A924‎, ‎74 ‎(2014)‎.