Skip to main content
SpringerLink
Log in

O(12) limit and complete classification of symmetry schemes in proton-neutron interacting boson model

  • Research Articles
  • Published:
Pramana Aims and scope Submit manuscript

Abstract

It is shown that the proton-neutron interacting boson model (pnIBM) admits new symmetry limits withO(12) algebra which breakF spin but preserves theF z quantum numberM F. The generators ofO(12) are derived and the quantum numberU ofO(12) for a given boson numberN is determined by identifying the corresponding quasi-spin algebra. TheO(12) algebra generates two symmetry schemes and for both of them, complete classification of the basis states and typical spectra are given. With theO(12) algebra identified, complete classification of pnIBM symmetry limits with goodM F is established.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. F Iachello and A Arima,The interacting Boson model (Cambridge University Press, Cambridge, 1987)

    Google Scholar 

  2. I Talmi,Simple models of complex nuclei: The shell model and the interacting Boson model (Harwood, New York, 1993)

    Google Scholar 

  3. K L G Heyde,The nuclear shell model, 2nd edition (Springer, Berlin, 1994)

    Google Scholar 

  4. W Greiner and J A Maruhn,Nuclear models (Springer, Heidelberg, 1996)

    Google Scholar 

  5. P Van Isacker, K Heyde, J Jolie and A Sevrin,Ann. Phys. (N.Y.) 171, 253 (1986)

    Article  ADS  Google Scholar 

  6. A Frank and P Van Isacker,Algebraic methods in molecular and nuclear physics (Wiley, New York, 1994)

    MATH  Google Scholar 

  7. V K B Kota,Ann. Phys. (N.Y.) 265, 101 (1998)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  8. J E Garcia-Ramos and P Van Isacker,Ann. Phys. (N.Y.) 274, 45 (1999)

    Article  MATH  ADS  Google Scholar 

  9. V K B Kota,Ann. Phys. (N.Y.) 280, 1 (2000)

    Article  ADS  Google Scholar 

  10. Q Z Hahn, H Z Sun and G H Li,Phys. Rev. C35, 784 (1987)

    ADS  Google Scholar 

  11. P Halse, P Van Isacker and B R Barrett,Phys. Lett. B363, 145 (1995)

    ADS  Google Scholar 

  12. P Van Isacker and D D Warner,Phys. Rev. Lett. 78, 3266 (1997)

    Article  ADS  Google Scholar 

  13. V K B Kota,Pramana-J. Phys. 51, 727 (1998)

    ADS  Google Scholar 

  14. V K B Kota,J. Phys. G24, 1535 (1998)

    ADS  Google Scholar 

  15. D Kusnezov,Phys. Rev. Lett. 79, 537 (1997)

    Article  ADS  Google Scholar 

  16. A M Shirokov, N A Smirnova and Yu F Smirnov,Phys. Lett. B434, 237 (1998)

    ADS  Google Scholar 

  17. A M Shirokov, N A Smirnova, Yu F Smirnov, O Castonos and A Frank, inNuclear models 1998 edited by G Lo Bianco (University of Camerino Press, Camerino, Italy, 1999)

    Google Scholar 

  18. P Cejnar and J Jolie,Phys. Rev. E58, 387 (1998);E61, 6237 (2000)

    ADS  Google Scholar 

  19. F Iachello,Phys. Rev. Lett. 85, 3580 (2000);87, 052502 (2001).

    Article  ADS  Google Scholar 

  20. Yu F Smirnov, N A Smirnova and P Van Isacker,Phys. Rev. C61, 041302 (2000)

    ADS  Google Scholar 

  21. P Van Isacker,Phys. Rev. Lett. 83, 4269 (1999)

    Article  ADS  Google Scholar 

  22. K H Kim, A Gelberg, T Mizusaki, T Otsuka and P von Brentano,Nucl. Phys. A604, 163 (1996)

    ADS  Google Scholar 

  23. D Bohle et al,Phys. Lett. B137, 27 (1984)

    ADS  Google Scholar 

  24. A Richter,Prog. Part. Nucl. Phys. 34, 261 (1995)

    Article  ADS  Google Scholar 

  25. U Kneissl, H H Pitz and A Zilges,Prog. Part. Nucl. Phys. 37, 349 (1996)

    Article  Google Scholar 

  26. P von Brentanoet al, Phys. Rev. Lett. 76, 2029 (1996)

    Article  Google Scholar 

  27. H Maseret al, Phys. Rev. C54, R2129 (1996)

    ADS  Google Scholar 

  28. N Pietrallaet al, Phys Rev. C58, 796 (1998);Phys. Rev. Lett. 83, 1303 (1999);84, 3375 (2000)

    ADS  Google Scholar 

  29. A Novoselski and I Talmi,Phys. Lett. B160, 13 (1985)

    ADS  Google Scholar 

  30. O Engel, A Richter and H J Wortche,Nucl. Phys. A565, 596 (1993)

    ADS  Google Scholar 

  31. A Wolf, O Scholten and R F Casten,Phys. Lett. B312, 372 (1993)

    ADS  Google Scholar 

  32. V K B Kota, inStructure of atomic nuclei edited by L Satpathy (Narosa Publishing, New Delhi, India, 1999) p. 203

    Google Scholar 

  33. V S Lac, J P Elliott and J A Evans,Phys. Lett. B394, 231 (1997)

    ADS  Google Scholar 

  34. In general it is easily seen that, 73–01

  35. V K B Kota and Y D Devi,Nuclear shell model and the interacting boson model: Lecture notes for practitioners (IUCDAEF-CC, Kolkata, India, 1996)

    Google Scholar 

  36. B G Wybourne,Symmetry principles in atomic spectroscopy (John Wiley and Sons, New York, 1970)

    Google Scholar 

  37. D E Littlewood,The theory of group characters and matrix representations of groups (Oxford University Press, Oxford, London, 1950)

    MATH  Google Scholar 

  38. V K B Kota,Pramana-J. Phys. 48, 1035 (1997)

    Article  ADS  Google Scholar 

  39. P C Sood, D M Headly and R K Sheline,At. Data Nucl. Data Tables 47, 89 (1991);51, 273 (1992)

    Article  ADS  Google Scholar 

  40. V K B Kota,J. Math. Phys. 38, 6639 (1997)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  41. In the Uπ(6) ⊕Uv (6) limit, the special case of coupling at the Up(6) level itself, i.e. coupling the Uπ(6) and Uv(6) to give Uπ+v(6), is equivalent toU (6) b0 SUF(2). This special case is often used in literature to describe the U(6) b0 SUF(2) symmetry schemes [1,3].

  42. Y Alhassid, A Novoselsky and N Whelan,Phys. Rev. Lett. 65, 2971 (1990)

    Article  ADS  Google Scholar 

  43. N Whelan, Y Alhassid and A Leviatan,Phys. Rev. Lett. 71, 2208 (1993)

    Article  ADS  Google Scholar 

  44. N Whelan and Y Alhassid,Nucl. Phys. A556, 42 (1993)

    ADS  Google Scholar 

  45. J Jolie, R F Casten, P von Brentano and V Werner,Phys. Rev. Lett. 87, 162501 (2001)

    Article  ADS  Google Scholar 

  46. E Canetta and G Maino,Phys. Lett. B483, 55 (2000)

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Physical Research Laboratory, 380 009, Ahmedabad, India

    V. K. B. Kota

Authors
  1. V. K. B. Kota
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kota, V.K.B. O(12) limit and complete classification of symmetry schemes in proton-neutron interacting boson model. Pramana - J Phys 60, 59–74 (2003). https://doi.org/10.1007/BF02705069

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02705069

Keywords

PACS Nos

Search

Navigation