Study of 100-106Ru isotopic chain in the three levels interacting boson model

Document Type : Full length research Paper

Authors

1 Department of Physics, University of Tabriz, Tabriz 51664, Iran.

2 Faculty of physics, University of Tabriz, Tabriz,Iran

Abstract

In this paper, we have considered the energy levels and energy surfaces of nuclei located between the spherical and the gamma soft shapes. We have used a three levels spd-interacting boson model which are defined in the affine SU(1,1) algebra to describe both positive and negative parity states. The energy surfaces of 100-106Ru isotopes are determined via catastrophe theory and coherent states formalism in the U(5)-SO(9) transitional region of interacting boson model. The agreement between the theoretical prediction of model and the most recent experimental counterparts is acceptable. Also, the variation of the energy surface’s shapes suggest a second order shape phase transition in this isotopic chain. The values of the control parameters and also the shape of energy surfaces suggest 100Ru as the best candidate for the critical point of this transitional region.

Keywords

References

[1] D. Rowe, Phase transitions and quasidynamical symmetry in nuclear collective models: I. The U (5) to O (6) phase transition in the IBM, Nuclear Physics A 745 (2004) 47-78.
[2] P. Turner, D. Rowe, Phase transitions and quasidynamical symmetry in nuclear collective models. II. The spherical vibrator to gamma-soft rotor transition in an SO (5)-invariant Bohr model, Nuclear Physics A 756 (2005) 333-355.
[3] G. Rosensteel, D. Rowe, Phase transitions and quasi-dynamical symmetry in nuclear collective models, III: The U (5) to SU (3) phase transition in the IBM, Nuclear Physics A 759 (2005) 92-128.
[4] F. Iachello, Interacting bosons in nuclear physics, Springer Science & Business Media, (2012).
[5] A. Bohr, B.R. Mottelson, Nuclear structure, vol. II, Benjamin, New York, (1975).
[6] R. Gilmore, S. Deans, Phase transitions and the geometric properties of the interacting boson model, Physical Review C 23 (1981) 1254-1266.
[7] R. Gilmore, Comparison of the logical structure of the liquid drop model and the interacting boson model, Progress in Particle and Nuclear Physics 9 (1983) 495-509.
[8] A. Leviatan, Broken O (5) and O (3) symmetries in a general non-spherical boson basis, Zeitschrift für Physik A Atoms and Nuclei 321 (1985) 467-472.
[9] M. Spieker, S. Pascu, A. Zilges, F. Iachello, Origin of Low-Lying Enhanced E 1 Strength in Rare-Earth Nuclei, Physical Review Letters 114 (2015) 192504-192507.
[10] J. Arias, E2 transitions and quadrupole moments in the E (5) symmetry, Physical Review C 63 (2001) 034308-034315.
[11] F. Iachello, Dynamic symmetries at the critical point, Physical Review Letters 85 (2000) 3580-3584.
[12] F. Iachello, Analytic description of critical point nuclei in a spherical-axially deformed shape phase transition, Physical Review Letters 87 (2001) 052502-052508.
[13] D. Rowe, M. Carvalho, J. Repka, Dual pairing of symmetry and dynamical groups in physics, Reviews of Modern Physics 84 (2012) 711.
[14] F. Iachello, A. Arima, The interacting boson model, Cambridge University Press (1987).
[15] M. Jafarizadeh, A.J. Majarshin, N. Fouladi, M. Ghapanvari, Investigation of quantum phase transitions in the spdf interacting boson model based on dual algebraic structures for the four-level pairing model, Journal of Physics G: Nuclear and Particle Physics 43 (2016) 095108-095115.
[16] F. Pan, Y. Zhang, H.C. Xu, L.R. Dai, J.P. Draayer, (2015). Alternative solvable description of the E (5) critical point symmetry in the interacting boson model. Physical Review C 91(2015) 034305-034311.
[17] A. Leviatan, Intrinsic and collective structure in the interacting boson model, Annals of Physics 179 (1987) 201-271.
[18] F. Pan, J. Draayer, New algebraic solutions for SO (6)↔ U (5) transitional nuclei in the interacting boson model, Nuclear Physics A 636 (1998) 156-168.
[19] G. Maino, A. Ventura, L. Zuffi, F. Iachello,. Properties of giant resonances in the interacting boson model. Physical Review C 30(6), (1984) 2101-2111.
[20] C. Alonso, M. Andrés, J. Arias, E. Lanza, A. Vitturi, Coupling of dipole mode to γ-unstable quadrupole oscillations, Nuclear Physics A 679 (2001) 359-372.
[21] F. Scholtz, F. Hahne, Giant dipole resonances in the interacting boson model, Physics Letters B 123 (1983) 147-150.
[22] F. Pan, X. Zhang, J. Draayer, Algebraic solutions of an sl-boson system in the U (2l+ 1) longleftrightarrow O (2l+ 2) transitional region, Journal of Physics A: Mathematical and General 35 (2002) 7173-7178.
[23] K. Nomura, D. Vretenar, T. Nikšić, B.-N. Lu, Microscopic description of octupole shape-phase transitions in light actinide and rare-earth nuclei, Physical Review C 89 (2014) 024312-024322.
[24] H. Fathi, M. Ghadami, H. Sabri, N. Fouladi, M. 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) 1450045-1450060.
[25] M. Jafarizadeh, A.J. Majarshin, N. Fouladi, Simultaneous description of low-lying positive and negative parity states in s p d, s d f and s p d f interacting boson model, International Journal of Modern Physics E 25 (2014) 1650089-1650099.
[26] A. Jalili Majarshin, M. Jafarizadeh, N. Fouladi, Algebraic solutions for two-level pairing model in IBM-2 and IVBM, European Physical Journal Plus 131 (2016) 337-356.
[27] B. Singh, Nuclear Data Sheets for A=100, Nuclear Data Sheets 109 (2008) 297-311.
[28] D. De Frenne, Nuclear Data Sheetsfor A=102, Nuclear Data Sheets 110 (2009) 1745-1855.
 [29] J. Blachot, Nuclear Data Sheetsfor A=104, Nuclear Data Sheets 108 (2007) 2035-2187.  
[30] D. De Frenne, A. Negret, Nuclear Data Sheetsfor A=106, Nuclear Data Sheets 109(2008) 943-1108. 
 
Journal of Research on Many-body Systems
Volume 7, Issue 15
December 2017
Pages 33-44

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History

  • Receive Date: 05 January 2017
  • Revise Date: 27 April 2017
  • Accept Date: 29 May 2017

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