Skip to main content

SU(3) in Interacting Boson–Fermion Models

  • Chapter
  • First Online:
SU(3) Symmetry in Atomic Nuclei
  • 316 Accesses

Abstract

In this chapter presented are results from the SU(3) limits of the interacting boson-fermion models for odd-A nuclei, odd-odd nuclei and two quasi-particle excitations in even-even nuclei. In all these sdIBM-1 core is employed. It is demonstrated that the SU(3) limits are in correspondence with the well known Nilsson model in the asymptotic limit with the boson number (of the core nucleus involved) \(N \rightarrow \infty \). Examples from data for various SU(3) limits are also presented. In addition, some results for M1 distributions with sdgIBM core and IBM-2 core are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 159.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 159.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. F. Iachello, D. Vretenar, Physics of high-spin states in nuclei. Phys. Rev. C 43, R945–R948 (1991)

    Google Scholar 

  2. P. Chowdhury et al., Large \(B(M1)\) staggering at high spins in \(^{86}\)Zr: broken boson pairs in the four-quasiparticle regime. Phys. Rev. Lett. 67, 2950–2953 (1991)

    Article  ADS  Google Scholar 

  3. D. Vretenar, G. Bonsignori, M. Savoia, One and two broken pairs in the interacting boson model: High-spin states In \(^{190,192,194}\)Hg. Phys. Rev. C 47, 2019–2023 (1993)

    Article  ADS  Google Scholar 

  4. F. Iachello, O. Scholten, Interacting boson-fermion model of collective states in odd-A nuclei. Phys. Rev. Lett. 43, 679–682 (1979)

    Article  ADS  Google Scholar 

  5. A. Arima, A. Gelberg, O. Scholten, Coriolis coupling in the interacting boson fermion model. Phys. Lett. B 185, 259–264 (1987)

    Article  ADS  Google Scholar 

  6. A. Frank, J.M. Arias, P. VanIsacker, Search for scissors states in odd-mass nuclei. Nucl. Phys. A531, 125–142 (1991)

    Article  ADS  Google Scholar 

  7. R. Bijker, V.K.B. Kota, Interacting boson fermion model of collective states : the \(SU(3) \otimes U(2)\) limit. Ann. Phys. (N.Y.) 187, 148–197 (1988)

    Google Scholar 

  8. J.D. Vergados, \(SU(3) \supset R(3)\) Wigner coefficients in the \(2s-1d\) shell. Nucl. Phys. A 111, 681–754 (1968)

    Article  ADS  Google Scholar 

  9. A.R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton University Press, Princeton, 1974)

    MATH  Google Scholar 

  10. A. Bohr, B.R. Mottelson, Nuclear Structure Vol II: Nuclear Deformations (W.A. Benjamin, Inc., Reading, 1975)

    Google Scholar 

  11. R. Bijker, V.K.B. Kota, Dynamical symmetries in deformed odd - even nuclei. Phys. Rev. C 37, 2149–2155 (1988)

    Article  ADS  Google Scholar 

  12. Y. Akiyama, J.P. Draayer, A user’s guide to fortran programs for Wigner and Racah coefficients of \(SU_3\). Comput. Phys. Commun. 5, 405–415 (1973)

    Article  ADS  Google Scholar 

  13. V.K.B. Kota, Applications of the \(SU(3)\) dynamical symmetry of interacting boson model. Rev. Mex. Fis. 42, Suplemento 1, 131–143 (1996)

    Google Scholar 

  14. D.D. Warner, P. Van Isacker, Rotational intensity rules in the pseudo SU(3) scheme. Phys. Lett. B 247, 1–4 (1990)

    Article  ADS  Google Scholar 

  15. C.M. Lederer, V.S. Shirley, Table of Isotopes, 7th edn. (Wiley, New York, 1978)

    Google Scholar 

  16. M.K. Pal, Theory of Nuclear Structure (Affiliated East-West Press, New Delhi, 1982)

    Google Scholar 

  17. Y.A. Ellis-Akovali, Nuclear data sheets for A=187. Nucl. Data Sheets 36, 559–653 (1982)

    Article  ADS  Google Scholar 

  18. H.Q. Jin et al., Electromagnetic properties of the \([303]5/2, 7/2\) pseudo-spin doublet in \(^{175}\)Re. Phy. Lett. B 277, 387–392 (1992)

    Article  ADS  Google Scholar 

  19. R.F. Casten, P. Kleinheinz, P.J. Daly, B. Elbek, A study of energy levels and coriolis coupling in odd-mass Wolfram nuclei by means of \((d, p)\) and \((d, t)\) reactions. Mat. Fys. Medd. Dan. Vid. Selsk. 38(13), 1–66 (1972)

    Google Scholar 

  20. F. Iachello, P. Van Isacker, The Interacting Boson-Fermion Model (Cambridge University Press, Cambridge, 1991)

    Book  Google Scholar 

  21. S. Brant, V. Paar, D.K. Sunko, D. Vretenar, Band structure and determination of \(K\) quantum numbers for odd-odd systems in the interacting boson-fermion-fermion model. Phys. Rev. C 37, 830–837 (1988)

    Google Scholar 

  22. D. Vretenar, S. Brant, V. Paar, D.K. Sunko, K representation for odd-odd nuclei in the interacting boson-fermion-fermion model. II. Band mixing in the normal and conflicting case and electromagnetic properties. Phys. Rev. C 41, 757–770 (1990)

    Google Scholar 

  23. C.J. Gallagher, S.A. Moszkowski, Coupling of angular momenta in odd-odd Nuclei. Phys. Rev. 111, 1282–1290 (1958)

    Article  ADS  Google Scholar 

  24. V.K.B. Kota, U. Datta Pramanik, Strong coupled and doubly decoupled bands in the \(SU^{BF}(3) \otimes U^F(2j+1)\) limit of interacting boson - fermion - fermion model. Z. Phys. A - At. Nucl. 358, 25–31 (1997)

    Google Scholar 

  25. A.J. Kreiner et al., Pseudospin flip in doubly decoupled structures and identical bands. Phy. Rev. C 50, R530–R533 (1994)

    Article  ADS  Google Scholar 

  26. F.S. Stephens, Coriolis effects and rotation alignment in nuclei. Rev. Mod. Phys. 47, 43–65 (1975)

    Article  ADS  Google Scholar 

  27. M.A. Cardona et al., Pseudospin doublet aligned structure in doubly odd \(^{186}\)Ir. Phys. Rev. C 55, 144–147 (1997)

    Article  ADS  Google Scholar 

  28. P.E. Garrett, D.G. Burke, Study of \(^{190}\)Ir via single-proton and single-neutron transfer reactions. Nucl. Phys. A 581, 267–293 (1995)

    Article  ADS  Google Scholar 

  29. V.K.B. Kota, U. Datta Pramanik, \(SU(3)\) coupling schemes for odd-odd nuclei in the interacting boson - fermion - fermion model with both odd proton and odd neutron in natural parity orbits. Euro. Phys. J. A3, 243–253 (1998)

    Google Scholar 

  30. P.E. Garrett, D.G. Burke, Mixed target ground-state effects in single-nucleon transfer to odd-odd nuclei. J. Phys. G: Nucl. Part. Phys. 19, 1021–1028 (1993)

    Article  ADS  Google Scholar 

  31. P.C. Sood, D.M. Headly, R.K. Sheline, Intrinsic structures and associated rotational bands in deformed even-even nuclei with \(60 \le \) Z \(\le 76\) and \(90 \le \) N \(\le 114\). At. Data Nucl. Data Tables 47, 89–173 (1991)

    Article  ADS  Google Scholar 

  32. P.C. Sood, D.M. Headly, R.K. Sheline, Intrinsic structures and associated rotational bands in deformed even-even nuclei of the actinide region. At. Data Nucl. Data Tables 51, 273–320 (1992)

    Article  ADS  Google Scholar 

  33. V.G. Soloviev, Theory of Atomic Nuclei: Quasiparticles and Phonons (Institute of Physics Publishing, Bristol, Philadelphia, 1992)

    Google Scholar 

  34. D. Vretenar, V. Paar, G. Bonsignori, M. Savoia, Two- and four-quasiparticle states in the interacting boson model: strong-coupling and decoupled band patterns in the \(SU(3)\) limit. Phys. Rev. C 42, 993–1003 (1990)

    Google Scholar 

  35. D. Vretenar, V. Paar, M. Savoia, G. Bonsignori, Two-quasiparticle states in the interacting boson model. II. Electromagnetic properties in the \(SU(3)\) limit. Phys. Rev. C 44, 223–232 (1991)

    Google Scholar 

  36. Y.D. Devi, V.K.B. Kota, Correspondence between SU(3) \(\otimes \) U(2) limit of IBF\(^2\)M and two quasi - particle Nilsson configurations. Phys. Lett. B 334, 253–258 (1994)

    Google Scholar 

  37. I. Bauske et al., First observation of scissors mode states in an odd-mass nucleus. Phys. Rev. Lett. 71, 975–978 (1993)

    Google Scholar 

  38. Y.D. Devi, V.K.B. Kota, M1 Distributions for \(^{163}\)Dy and \(^{157}\)Gd in SU\(^{BF}_{sdg}\)(3) and SU\(^{BF}_{sd}\)(3) \(\times \) 1g limits of pn-sdgIBFM. Nucl. Phys. A 600, 20–36 (1996)

    Google Scholar 

  39. Y.D. Devi, V.K.B. Kota, M1 distributions in p-n sdgIBFM for odd-A Nuclei. Phys. Lett. B 287, 9–13 (1992)

    Article  ADS  Google Scholar 

  40. V.G. Soloviev, A.V. Sushkov, N.Y. Shirikova, Low-lying magnetic dipole strength in \(^{163}\)Dy, Phys. Rev. C 53,1022-1024(1996). (1996)

    Google Scholar 

  41. E. Tabar, A theoretical study on the ground and low-energy magnetic dipole characteristics of \(^{239}\)Pu nucleus. Nucl. Phys. A 987, 202–221 (2019)

    Article  ADS  Google Scholar 

  42. P. Van Isacker, A. Frank, H.Z. Sun, The \(U(6/12)\) supersymmetric limit of the interacting boson-fermion model. Ann. Phys. (N.Y.) 157, 183–231 (1984)

    Google Scholar 

  43. V.K.B. Kota, \(U^B(15) \otimes U^F(30)\) Boson-Fermion symmetry scheme in the interacting Boson-Fermion model including g bosons and the Nilsson model for \(^{185}\)W. Phys. Rev. C 33, 2218–2221 (1986)

    Google Scholar 

  44. Y.D. Devi, V.K.B. Kota, Scissors states with and without g - bosons in the interacting boson - Fermion model for even - odd nuclei in N = 82-126 shell. Nucl. Phys. A 541, 173–192 (1992)

    Article  ADS  Google Scholar 

  45. V.P. Garistov, A.I. Georgieva, Introduction of fermion degrees of freedom in IVBM for the description of spectra of odd Nuclei. Bulg. J. Phys. 44, 478–488 (2017)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. K. B. Kota .

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Kota, V.K.B. (2020). SU(3) in Interacting Boson–Fermion Models. In: SU(3) Symmetry in Atomic Nuclei. Springer, Singapore. https://doi.org/10.1007/978-981-15-3603-8_8

Download citation

Publish with us

Policies and ethics