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Experimental observables of shape phase transition from vibrational to Gamma- unstablExperimental observables of shape phase transition from vibrational to Gamma- unstable in the odd and even nucleie in the odd and even nuclei

Document Type : Research Paper

Authors

1 Plasma and Nuclear Fusion Research School, Nuclear Science and Technology Research Institute, AEOI, P.O. Box: 14399-51113, Tehran - Iran

2 Department of Physics, Faculty of Basic Sciences, Ilam University, P.O.Box: 69315-516, Ilam - Iran

Abstract

In this paper, Quantum Phase Transition (QPT) for the Xenon (122-132Xe) isotopes chain in the frameworks of the IBM-1 and IBFM-1 is considered. In order to study the QPT in this chain, we have used the observables such as: binding energy, two neutron separation energy, Alpha decay energy, R4/2 and B(E2). The results show that transitional nuclei in the regions of  for even-even isotopes and  for even-odd isotopes are 130Xe and 127Xe respectively.

Highlights

  1. M. Ghapanvari, et al, High-spin level structure and Ground-state phase transition in the odd-mass 103-109 Rh isotopes in the framework of exactly solvable sdg- interacting boson-fermion model, Nuclear Phys. A, 971, 51 (2018).

 

  1. Feng Pan, 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).

 

  1. M.A. Jafarizadeh, M. Ghapanvari, N. Fouladi, Algebraic solutions for quantum phase transition in odd-mass-number nuclei, Phys. Rev. C., 92, 054306 (2015).

 

  1. S. Sachdev, Quantum Phase Transitions Cambridge, Cambridge University Press (2011).

 

  1. M. Vojta, Quantum phase transitions, Rep. Prog. Phys., 66, 2069 (2003).

 

  1. H. Löhneysen, et al, Non-Fermi-liquid behavior in strongly correlated electron systems, Phys. Rev. B Condens. Matter, 230, 550 (1997).

 

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

 

  1. J. Arias, C. Alonso, M. Lozano, Nuclear structure studies of the odd-mass Ba and La isotopes with the IBFA-2 model, Nuclear Phys. A., 466, 295 (1987).

 

  1. Xin Guan, et al, Ground state phase transition in the Nilsson mean-field plus standard pairing model, Phys. Rev. C, 94, 024309 (2016).

 

  1. Yu Zhang, et al, Excited-state quantum phase transitions in the interacting boson model: Spectral characteristics of 0+ states and effective order parameter, Phys. Rev. C, 93, 044302 (2016).

 

  1. R.F. Casten, Shape phase transitions and critical-point phenomena in atomic nuclei, Nat. Phys., 2, 811 (2006).

 

  1. T. Thomas, et al, Evidence for shape coexistence in 98Mo, Phys. Rev. C., 88, 064305 (2013).

 

  1. P. Van Isacker, J. Engel, K. Nomura, Neutron-proton pairing and double-β decay in the interacting boson model, Phys. Rev. C, 96, 064305 (2013).

 

  1. J. Kotila, et al, Shape phase transitions in the interacting boson model: Phenomenological versus microscopic descriptions, Phys. Rev. C, 85, 054309 (2012).

 

  1. P. Cejnar, J. Jolie, Quantum phase transitions in the interacting boson model, Prog. Part. Nucl. Phys., 62, 210-256 (2009).

 

  1. J.M. Arias, J. Dukelsky, J.E. García-Ramos, Quantum Phase Transitions in the Interacting Boson Model: Integrability, Level Repulsion, and Level Crossing, PRL, 91, 1765 (2003).

 

  1. P. Von Brentano, et al, Alternative Interpretation of Sharply Rising E0 Strengths in Transitional Regions, PRL, 93, 152502 (2004).

 

  1. D.H. Feng, R. Gilmore, S.R. Deans, Phase transitions and the geometric properties of the interacting boson model, Phys. Rev. C, 23, 1254 (1981).

 

  1. A.E.L. Dieperink, O. Scholten, F. Iachello, Classical Limit of the Interacting-Boson Model, PRL, 44, 1747 (1980).

 

  1. O. Scholten, N. Blasi, Description of the Europium isotopes in the interacting boson-fermion model, Nuclear Phys. A, 380, 509 (1982).

 

  1. C. Alonso, et al, UBF(5) to SUBF(3) shape phase transition in odd nuclei for j=1/2, 3/2, and 5/2 orbits: The role of the odd particle at the critical point, Phys. Rev. C, 79, 014306 (2009).

 

  1. M. Boyukata, et al, Shape phase transition in odd-even nuclei: From spherical to deformed γ-unstable shapes, Phys. Rev. C, 82, 014317 (2010).

 

  1. K. Nomura, T. Niksic, D. Vretenar, Shape-phase transitions in odd-mass γ-soft nuclei with mass A≈130, Phys. Rev. C, 96, 014304 (2017).

 

  1. F. Pan, J. Draayer, New algebraic solutions for

SO(6) ↔ U(5) transitional nuclei in the interacting boson model, Nuclear Phys. A, 636, 156 (1998).

 

  1. R. Fossion, et al, Nuclear binding energies: Global collective structure and local shell-model correlations, Nuclear Phys. A, 697, 703–747 (2002).

 

  1. J.E. Garc´ıa-Ramos, et al, Two-neutron separation energies, binding energies and phase transitions in the interacting boson model, Nuclear Phys. A, 688, 735–754 (2001).

 

  1. N. Zamfir, S. Anghel, G. Cata-Danil, Phase/Shape Transitions and the Two Neutron Separation Energies, AIP Conference Proceedings, 1072, 118 (2008).

 

  1. S.S.M. Wong, Introductory Nuclear Physics, (John Wiley & Sons, 2004).

 

  1. Yu Zhang, et al, Ground-state phase transition in odd-A and odd-odd nuclei near N=90, Phys. Rev. C, 88, 064305 (2013).

 

  1. I. Talmi, Simple models of complex nuclei, Harvard Academic Publishers, (1993).

 

  1. P. Cejnar, J. Jolie, R.F. Casten, Quantum phase transitions in the shapes of atomic nuclei, RMP, 82, 2155 (2010).

 

  1. T. Tamura, Nuclear Data Sheets for A = 122, Nucl. Data Sheets, 108, 455-632 (2007).

 

  1. S. Ohya, Nuclear Data Sheets for A = 123, Nucl. Data Sheets, 102, 547-718 (2004).

 

  1. J. Katakura, Z.D. Wu, Nuclear Data Sheets for A = 124, Nucl. Data Sheets, 109,1655-1877 (2008).

 

  1. J. Katakura, Nuclear Data Sheets for A = 125, Nucl. Data Sheets, 112, 495-705 (2011).

 

  1. J. Katakura, K. Kitao, Nuclear Data Sheets for A = 126, Nucl. Data Sheets, 97, 765-926 (2002).

 

  1. A. Hashizume, Nuclear Data Sheets for A = 127, Nucl. Data Sheets, 112, 1647-1831 (2011).

 

  1. Z. Elekes, J. Timar, Nuclear Data Sheets for A = 128, Nucl. Data Sheets, 129, 191-436 (2015).

 

  1. J. Timar, Z, Elekes, B. Singh, Nuclear Data Sheets for A = 129, Nucl. Data Sheets, 121, 143-394 (2014).

 

  1. B. Jsingh, Nuclear Data Sheets for A = 130, Nucl. Data Sheets, 93, 33-242 (2001).

 

  1. Yu. Khazov, I. Mitropolsky, A. Rodionov, Nuclear Data Sheets for A = 131, Nucl. Data Sheets, 107, 2715-2936 (2006).

 

  1. Yu. Khazov, et al, Nuclear Data Sheets for A = 132, Nucl. Data Sheets, 104, 497-790 (2005).

 

  1. M.A. Jafarizadeh, et al, Phase transition studies of the odd-mass 123–135Xe isotopes based on SU(1, 1) algebra in IBFM, Int. J. Mod. Phys. E, 25, 1650048 (2016).

 

  1. M.A. Jafarizadeha, et al, Study of phase transition of even and odd nuclei based on q-deforme SU(1, 1) algebraic model, Nuclear Phys. A, 972, 86–106 (2018).

Keywords

References
  1. M. Ghapanvari, et al, High-spin level structure and Ground-state phase transition in the odd-mass 103-109 Rh isotopes in the framework of exactly solvable sdg- interacting boson-fermion model, Nuclear Phys. A, 971, 51 (2018).

 

  1. Feng Pan, 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).

 

  1. M.A. Jafarizadeh, M. Ghapanvari, N. Fouladi, Algebraic solutions for quantum phase transition in odd-mass-number nuclei, Phys. Rev. C., 92, 054306 (2015).

 

  1. S. Sachdev, Quantum Phase Transitions Cambridge, Cambridge University Press (2011).

 

  1. M. Vojta, Quantum phase transitions, Rep. Prog. Phys., 66, 2069 (2003).

 

  1. H. Löhneysen, et al, Non-Fermi-liquid behavior in strongly correlated electron systems, Phys. Rev. B Condens. Matter, 230, 550 (1997).

 

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

 

  1. J. Arias, C. Alonso, M. Lozano, Nuclear structure studies of the odd-mass Ba and La isotopes with the IBFA-2 model, Nuclear Phys. A., 466, 295 (1987).

 

  1. Xin Guan, et al, Ground state phase transition in the Nilsson mean-field plus standard pairing model, Phys. Rev. C, 94, 024309 (2016).

 

  1. Yu Zhang, et al, Excited-state quantum phase transitions in the interacting boson model: Spectral characteristics of 0+ states and effective order parameter, Phys. Rev. C, 93, 044302 (2016).

 

  1. R.F. Casten, Shape phase transitions and critical-point phenomena in atomic nuclei, Nat. Phys., 2, 811 (2006).

 

  1. T. Thomas, et al, Evidence for shape coexistence in 98Mo, Phys. Rev. C., 88, 064305 (2013).

 

  1. P. Van Isacker, J. Engel, K. Nomura, Neutron-proton pairing and double-β decay in the interacting boson model, Phys. Rev. C, 96, 064305 (2013).

 

  1. J. Kotila, et al, Shape phase transitions in the interacting boson model: Phenomenological versus microscopic descriptions, Phys. Rev. C, 85, 054309 (2012).

 

  1. P. Cejnar, J. Jolie, Quantum phase transitions in the interacting boson model, Prog. Part. Nucl. Phys., 62, 210-256 (2009).

 

  1. J.M. Arias, J. Dukelsky, J.E. García-Ramos, Quantum Phase Transitions in the Interacting Boson Model: Integrability, Level Repulsion, and Level Crossing, PRL, 91, 1765 (2003).

 

  1. P. Von Brentano, et al, Alternative Interpretation of Sharply Rising E0 Strengths in Transitional Regions, PRL, 93, 152502 (2004).

 

  1. D.H. Feng, R. Gilmore, S.R. Deans, Phase transitions and the geometric properties of the interacting boson model, Phys. Rev. C, 23, 1254 (1981).

 

  1. A.E.L. Dieperink, O. Scholten, F. Iachello, Classical Limit of the Interacting-Boson Model, PRL, 44, 1747 (1980).

 

  1. O. Scholten, N. Blasi, Description of the Europium isotopes in the interacting boson-fermion model, Nuclear Phys. A, 380, 509 (1982).

 

  1. C. Alonso, et al, UBF(5) to SUBF(3) shape phase transition in odd nuclei for j=1/2, 3/2, and 5/2 orbits: The role of the odd particle at the critical point, Phys. Rev. C, 79, 014306 (2009).

 

  1. M. Boyukata, et al, Shape phase transition in odd-even nuclei: From spherical to deformed γ-unstable shapes, Phys. Rev. C, 82, 014317 (2010).

 

  1. K. Nomura, T. Niksic, D. Vretenar, Shape-phase transitions in odd-mass γ-soft nuclei with mass A≈130, Phys. Rev. C, 96, 014304 (2017).

 

  1. F. Pan, J. Draayer, New algebraic solutions for

SO(6) ↔ U(5) transitional nuclei in the interacting boson model, Nuclear Phys. A, 636, 156 (1998).

 

  1. R. Fossion, et al, Nuclear binding energies: Global collective structure and local shell-model correlations, Nuclear Phys. A, 697, 703–747 (2002).

 

  1. J.E. Garc´ıa-Ramos, et al, Two-neutron separation energies, binding energies and phase transitions in the interacting boson model, Nuclear Phys. A, 688, 735–754 (2001).

 

  1. N. Zamfir, S. Anghel, G. Cata-Danil, Phase/Shape Transitions and the Two Neutron Separation Energies, AIP Conference Proceedings, 1072, 118 (2008).

 

  1. S.S.M. Wong, Introductory Nuclear Physics, (John Wiley & Sons, 2004).

 

  1. Yu Zhang, et al, Ground-state phase transition in odd-A and odd-odd nuclei near N=90, Phys. Rev. C, 88, 064305 (2013).

 

  1. I. Talmi, Simple models of complex nuclei, Harvard Academic Publishers, (1993).

 

  1. P. Cejnar, J. Jolie, R.F. Casten, Quantum phase transitions in the shapes of atomic nuclei, RMP, 82, 2155 (2010).

 

  1. T. Tamura, Nuclear Data Sheets for A = 122, Nucl. Data Sheets, 108, 455-632 (2007).

 

  1. S. Ohya, Nuclear Data Sheets for A = 123, Nucl. Data Sheets, 102, 547-718 (2004).

 

  1. J. Katakura, Z.D. Wu, Nuclear Data Sheets for A = 124, Nucl. Data Sheets, 109,1655-1877 (2008).

 

  1. J. Katakura, Nuclear Data Sheets for A = 125, Nucl. Data Sheets, 112, 495-705 (2011).

 

  1. J. Katakura, K. Kitao, Nuclear Data Sheets for A = 126, Nucl. Data Sheets, 97, 765-926 (2002).

 

  1. A. Hashizume, Nuclear Data Sheets for A = 127, Nucl. Data Sheets, 112, 1647-1831 (2011).

 

  1. Z. Elekes, J. Timar, Nuclear Data Sheets for A = 128, Nucl. Data Sheets, 129, 191-436 (2015).

 

  1. J. Timar, Z, Elekes, B. Singh, Nuclear Data Sheets for A = 129, Nucl. Data Sheets, 121, 143-394 (2014).

 

  1. B. Jsingh, Nuclear Data Sheets for A = 130, Nucl. Data Sheets, 93, 33-242 (2001).

 

  1. Yu. Khazov, I. Mitropolsky, A. Rodionov, Nuclear Data Sheets for A = 131, Nucl. Data Sheets, 107, 2715-2936 (2006).

 

  1. Yu. Khazov, et al, Nuclear Data Sheets for A = 132, Nucl. Data Sheets, 104, 497-790 (2005).

 

  1. M.A. Jafarizadeh, et al, Phase transition studies of the odd-mass 123–135Xe isotopes based on SU(1, 1) algebra in IBFM, Int. J. Mod. Phys. E, 25, 1650048 (2016).

 

  1. M.A. Jafarizadeha, et al, Study of phase transition of even and odd nuclei based on q-deforme SU(1, 1) algebraic model, Nuclear Phys. A, 972, 86–106 (2018).
Journal of Nuclear Science, Engineering and Technology (JONSAT)
Volume 43, Issue 4 - Serial Number 102
December 2022
Pages 17-27
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