Journal of Nuclear Science, Engineering and Technology (JONSAT)
In cooperation with the Iranian Nuclear Society

Microscopic description of odd-odd transitional nuclei by using interacting-boson-fermion -model

Document Type : Research Paper

Authors

M. Ghapanvari 1
N. Amiri 2
M.A. Jafarizadeh 3
H. Hossein Khani 1

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

2 Department of Nuclear Physics, Faculty of Physics, University of Tabriz, P.O.Box: 51664, Tabriz –Iran

3 Department of Theoretical Physics and Astrophysics, University of Tabriz, P.O.Box: 51664, Tabriz –Iran

https://doi.org/10.24200/nst.2020.1137
Abstract
Studying the dynamical behavior of various nucleus systems has become an interesting subject of research over recent years in nuclear physics. The Energy spectrum and magnitude of momentum of electric and magnetic multi-poles may describe the behavior of a nuclei collection under a special symmetry group. In this paper, solvable algebraic models by using the affine SU(1,1) Lie Algebra and proton, and neutron degrees of freedom in the framework of an  interacting-boson-fermion-fermion model(IBFFM) is suggested to determine the exact energy and eigenstate of the  transitional odd-odd mass nuclei. The main goal is to study the dynamical behavior of the nucleus in the transition state and then to investigate the special conditions that make this transition process possible. The positive parity low-lying energy states of the 60−66Cu isotopes within the proposed methods are investigated. The obtained results compare well with the available experimental data and IBFFM-1, which augments the reliability of the wave function and Hamiltonian obtained within the suggested IBFFM-2 model. The values of control parameters confirm the mixing of both vibrating and rotating structures in the 60−66Cu isotopes.

Highlights

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

 

2. A. Arima, F. Iachello, The interacting boson model. Annual Review of Nuclear and Particle Science, 31(1), 75-105 (1981).

 

3. F. Iachello, P. Van. Isacker, The interacting boson-fermion model, Cambridge: Cambridge University Press (1991).

 

4. F. Iachello, O. Scholten, Interacting boson-fermion model of collective states in odd-A nuclei, Physical Review Letters, 43(10), 679 (1979).

 

5 F. Iachello, Dynamical supersymmetries in nuclei. Physical Review Letters, 44(12), 772 (1980).

 

6. J. Vervier, Boson-fermion symmetries and supersymmetries in nuclear physics. La Rivista del Nuovo Cimento, 10(9), 1-102 (1978).

 

7. S. Brant, V. Paar, D. Vretenar, SU(6) model for odd-odd nuclei (OTQM/IBOM) and boson-aligned phase diagram in O(6) limit, Zeitschrift für Physik A Atoms and Nuclei, 319(3), 355-356 (1984).

 

8. S. Brant, et al, IBFFM description of energy levels and electromagnetic properties of 134Cs, Physics Letters B, 195, 111-115 (1987).

 

9. S. Brant, V. Paar, IBFFM yrast states in odd-odd nuclei associated with O(6) and SU(3) limits, Zeitschrift für Physik A Atomic Nuclei, 329(2), 151-159 (1988).

 

10. P. Van Isacker, J. Jolie, Description of vibrational odd-odd nuclei with the interacting boson-fermion-fermion model, Nuclear Physics A, 503(2), 429-451 (1989).

 

11. T. Hübsch, V. Paar, Three dynamical boson-fermion symmetries for odd-odd nuclei. Zeitschrift für Physik A Atoms and Nuclei, 319(1), 111-112 (1984).

 

12. T. Hübsch, V. Paar, D. Vretenar, Spin(6) boson-fermion dynamical symmetry for odd-odd nuclei. Physics Letters B, 151(5-6), 320-324 (1985).

 

13 V. Kitipova, Description of even-even and odd-odd nuclei in the Interacting boson model. Zeitschrift für Physik A Hadrons and Nuclei, 323(2), 247-248 (1986).

 

14. D.D. Warner, R.F. Casten, A. Frank, Average resonance capture studies of 198Au: A test of symmetry schemes for odd-odd nuclei. Physics Letters B, 180(3), 207-212 (1986).

 

15. H. Toki, H.L.Yadav, Amand Faessler, Study of transitional odd-odd mass nuclei, Z. Physik A 292, 79-94 (1979).

 

16. T. Hübsch, V. Paar, Spin BFπυ(5) boson fermion dynamical symmetry and supersymmetry for odd-odd nuclei associated withUb(5) boson limit and exemplification for 62Cu, Zeitschrift für Physik A Atomic Nuclei, 327(3), 287-289 (1987).

 

17. M. Ghapanvari, et al, Isospin excitation and shape phase transition in odd-mass Cu isotopes, International Journal of Modern Physics E, 26(06), 1750036 (2017).

 

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

 

19. A.K. Singh, G. Gangopadhyay, Structure of odd-odd Cu isotopes in the framework of the interacting boson-fermion-fermion model. Physical Review C, 55(2), 726 (1997).

 

20. F. Pan, J.P. Draayer, New algebraic solutions for SO (6)↔U(5) transitional nuclei in the interacting boson model. Nuclear Physics A, 636(2), 156-168 (1998).

 

21. M.A. Jafarizadeh, M. Ghapanvari, N. Fouladi, Algebraic solutions for UBF(5)-OBF(6) quantum phase transition in odd-mass-number nuclei. Physical Review C, 92(5), 054306 (2015).

 

22. National Nuclear Data Center (Brookhaven National laboratory) Chart of nuclides, http://www.nndc.bnl.gov/chart/reColor.jspnewColor=dm.

 

23. M.M. King, Nuclear data sheets update for A= 60. Nuclear Data Sheets, 69(1), 1 (1993).

 

24. A.L. Nichols, B. Singh, J.K. Tuli, Nuclear data sheets for A= 62. Nuclear Data Sheets, 113(4), 973-1114 (2012).

 

25. B. Singh, Nuclear data sheets for A= 64. Nuclear Data Sheets, 108(2), 197-364 (2007).

 

26. E. Browne, J.K. Tuli, Nuclear data sheets for A= 66. Nuclear Data Sheets, 111(4), 1093-1209 (2010).

Keywords

Affine SU(1
1) algebra
Interacting-boson-fermion- model
Odd-odd mass nuclei
1. A. Arima, F. Iachello. The Interacting Boson Model (Cambridge University Press, Cambridge, 1987).
 
2. A. Arima, F. Iachello, The interacting boson model. Annual Review of Nuclear and Particle Science, 31(1), 75-105 (1981).
 
3. F. Iachello, P. Van. Isacker, The interacting boson-fermion model, Cambridge: Cambridge University Press (1991).
 
4. F. Iachello, O. Scholten, Interacting boson-fermion model of collective states in odd-A nuclei, Physical Review Letters, 43(10), 679 (1979).
 
5 F. Iachello, Dynamical supersymmetries in nuclei. Physical Review Letters, 44(12), 772 (1980).
 
6. J. Vervier, Boson-fermion symmetries and supersymmetries in nuclear physics. La Rivista del Nuovo Cimento, 10(9), 1-102 (1978).
 
7. S. Brant, V. Paar, D. Vretenar, SU(6) model for odd-odd nuclei (OTQM/IBOM) and boson-aligned phase diagram in O(6) limit, Zeitschrift für Physik A Atoms and Nuclei, 319(3), 355-356 (1984).
 
8. S. Brant, et al, IBFFM description of energy levels and electromagnetic properties of 134Cs, Physics Letters B, 195, 111-115 (1987).
 
9. S. Brant, V. Paar, IBFFM yrast states in odd-odd nuclei associated with O(6) and SU(3) limits, Zeitschrift für Physik A Atomic Nuclei, 329(2), 151-159 (1988).
 
10. P. Van Isacker, J. Jolie, Description of vibrational odd-odd nuclei with the interacting boson-fermion-fermion model, Nuclear Physics A, 503(2), 429-451 (1989).
 
11. T. Hübsch, V. Paar, Three dynamical boson-fermion symmetries for odd-odd nuclei. Zeitschrift für Physik A Atoms and Nuclei, 319(1), 111-112 (1984).
 
12. T. Hübsch, V. Paar, D. Vretenar, Spin(6) boson-fermion dynamical symmetry for odd-odd nuclei. Physics Letters B, 151(5-6), 320-324 (1985).
 
13 V. Kitipova, Description of even-even and odd-odd nuclei in the Interacting boson model. Zeitschrift für Physik A Hadrons and Nuclei, 323(2), 247-248 (1986).
 
14. D.D. Warner, R.F. Casten, A. Frank, Average resonance capture studies of 198Au: A test of symmetry schemes for odd-odd nuclei. Physics Letters B, 180(3), 207-212 (1986).
 
15. H. Toki, H.L.Yadav, Amand Faessler, Study of transitional odd-odd mass nuclei, Z. Physik A 292, 79-94 (1979).
 
16. T. Hübsch, V. Paar, Spin BFπυ(5) boson fermion dynamical symmetry and supersymmetry for odd-odd nuclei associated withUb(5) boson limit and exemplification for 62Cu, Zeitschrift für Physik A Atomic Nuclei, 327(3), 287-289 (1987).
 
17. M. Ghapanvari, et al, Isospin excitation and shape phase transition in odd-mass Cu isotopes, International Journal of Modern Physics E, 26(06), 1750036 (2017).
 
18. M.A. Jafarizadeh, et.al. Study of phase transition of even and odd nuclei based on q-deforme SU (1, 1) algebraic model. Nuclear Physics A, 972, 86-106 (2018).
 
19. A.K. Singh, G. Gangopadhyay, Structure of odd-odd Cu isotopes in the framework of the interacting boson-fermion-fermion model. Physical Review C, 55(2), 726 (1997).
 
20. F. Pan, J.P. Draayer, New algebraic solutions for SO (6)↔U(5) transitional nuclei in the interacting boson model. Nuclear Physics A, 636(2), 156-168 (1998).
 
21. M.A. Jafarizadeh, M. Ghapanvari, N. Fouladi, Algebraic solutions for UBF(5)-OBF(6) quantum phase transition in odd-mass-number nuclei. Physical Review C, 92(5), 054306 (2015).
 
22. National Nuclear Data Center (Brookhaven National laboratory) Chart of nuclides, http://www.nndc.bnl.gov/chart/reColor.jspnewColor=dm.
 
23. M.M. King, Nuclear data sheets update for A= 60. Nuclear Data Sheets, 69(1), 1 (1993).
 
24. A.L. Nichols, B. Singh, J.K. Tuli, Nuclear data sheets for A= 62. Nuclear Data Sheets, 113(4), 973-1114 (2012).
 
25. B. Singh, Nuclear data sheets for A= 64. Nuclear Data Sheets, 108(2), 197-364 (2007).
 
26. E. Browne, J.K. Tuli, Nuclear data sheets for A= 66. Nuclear Data Sheets, 111(4), 1093-1209 (2010).

Home