Skip to main content
SpringerLink
Log in

Shell-model representations of the proton-neutron symplectic model

  • Regular Article - Theoretical Physics
  • Published:
The European Physical Journal A Aims and scope Submit manuscript

Abstract

The representation theory of the recently introduced proton-neutron symplectic model in the many-particle Hilbert space is considered. The relation of the Sp(12, R) irreducible representations (irreps) with the shell-model classification of the basis states is considered by extending of the state space to the direct product space of SU p (3) ⊗ SU n (3) irreps, generalizing in this way the Elliott’s SU(3) model for the case of two-component system. The Sp(12, R) model appears then as a natural multi-major-shell extension of the generalized proton-neutron SU(3) scheme, which takes into account the core collective excitations of monopole and quadrupole, as well as dipole type associated with the giant resonance vibrational degrees of freedom. Each Sp(12, R) irreducible representation is determined by a symplectic bandhead or an intrinsic U(6) space which can be fixed by the underlying proton-neutron shell-model structure, so the theory becomes completely compatible with the Pauli principle. It is shown that this intrinsic U(6) structure is of vital importance for the appearance of the low-lying collective bands without involving a mixing of different symplectic irreps. The full range of low-lying collective states can then be described by the microscopically based intrinsic U(6) structure, renormalized by coupling to the giant resonance vibrations.

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. A. Bohm, Y. Ne'eman, A.O. Barut (Editors), Dynamical Groups and Spectrum generating Algebras, Vols. 1 and 2 (World Scientific Publishing Co. Pte. Ltd., Singapore, 1988).

  2. R.F. Casten (Editor), Algebraic Approaches to Nuclear Structure: Interacting Boson and Fermion Models (Harwood Academic Publishers, New York, 1993).

  3. F. Iachello, Lie Algebras and Applications, in Lecture Notes in Physics, Vol. 708 (Springer-Verlag, Berlin Heidelberg, 2006).

  4. A. Frank, P.V. Isacker, J. Jolie, Symmetries in Atomic Nuclei: From Isospin to Supersymmetry, in Springer Tracks in Modern Physics, Vol. 230 (Springer-Verlag, New York, 2009).

  5. D.J. Rowe, J.L. Wood, Fundamentals of Nuclear Models: Foundational Models (World Scientific Publisher Press, Singapore, 2010).

  6. G. Rosensteel, D.J. Rowe, Ann. Phys. 96, 1 (1976).

    Article  MathSciNet  ADS  Google Scholar 

  7. G. Rosensteel, D.J. Rowe, Ann. Phys. 123, 36 (1978).

    Article  MathSciNet  ADS  Google Scholar 

  8. D.J. Rowe, G. Rosensteel, Ann. Phys. 126, 198 (1980).

    Article  MathSciNet  ADS  Google Scholar 

  9. O.L. Weaver, R.Y. Cussion, L.C. Biedenharn, Ann. Phys. (N.Y.) 102, 493 (1976).

    Article  ADS  Google Scholar 

  10. L. Weaver, L.C. Biedenharn, Nucl. Phys. A 185, 1 (1972).

    Article  ADS  Google Scholar 

  11. H. Ui, Prog. Theor. Phys. 44, 153 (1970).

    Article  MathSciNet  ADS  Google Scholar 

  12. L. Weaver, R.Y. Cusson, L.C. Biedenharn, Ann. Phys. (N.Y.) 77, 250 (1973).

    Article  MathSciNet  ADS  Google Scholar 

  13. D.J. Rowe, G. Rosensteel, Phys. Rev. Lett. 38, 10 (1977).

    Article  ADS  Google Scholar 

  14. V.V. Vanagas, Methods of the theory of group representations and separation of collective degrees of freedom in the nucleus, in Lecture notes at the Moscow Engineering Physics Institute (MIFI, Moscow, 1974) (in Russian).

  15. V. Vanagas, Fiz. Elem. Chastits At. Yadra. 7, 309 (1976) (Sov. J. Part. Nucl. 7.

    Google Scholar 

  16. H.G. Ganev, Eur. Phys. J. A 50, 183 (2014).

    Article  ADS  Google Scholar 

  17. J.P. Elliott, Proc. R. Soc. London Ser. A 245, 128 (1958).

    Article  ADS  Google Scholar 

  18. J.P. Elliott, Proc. R. Soc. London Ser. A 245, 562 (1958).

    Article  ADS  Google Scholar 

  19. G.F. Filippov, V.I. Ovcharenko, Yu.F. Smirnov, Microscopic Theory of Collective Excitations in Nuclei (Naukova Dumka, Kiev, 1981) (in Russian). .

  20. M. Moshinsky, C. Quesne, J. Math. Phys. 11, 1631 (1970).

    Article  MathSciNet  ADS  Google Scholar 

  21. V.V. Vanagas, Algebraic foundations of microscopic nuclear theory (Nauka, Moscow, 1988) (in Russian).

  22. D.J. Rowe, M.J. Carvalho, J. Repka, Rev. Mod. Phys. 84, 711 (2012).

    Article  ADS  Google Scholar 

  23. A. Georgieva, P. Raychev, R. Roussev, J. Phys. G 8, 1377 (1982).

    Article  ADS  Google Scholar 

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

  25. H. Ganev, V.P. Garistov, A.I. Georgieva, Phys. Rev. C 69, 014305 (2004).

    Article  ADS  Google Scholar 

  26. V. Vanagas, E. Nadjakov, P. Raychev, Preprint Trieste TC/75/40 (1975).

  27. V. Vanagas, E. Nadjakov, P. Raychev, Bulg. J. Phys. 2, 558 (1975).

    MathSciNet  Google Scholar 

  28. N. Lo Iudice, F. Palumbo, Phys. Rev. Lett. 41, 1532 (1978).

    Article  ADS  Google Scholar 

  29. N. Lo Iudice, F. Palumbo, Nucl. Phys. A 326, 193 (1979).

    Article  ADS  Google Scholar 

  30. O. Castanos, J.P. Draayer, Y. Leschber, Ann. Phys. 180, 290 (1987).

    Article  ADS  Google Scholar 

  31. G. Rosensteel, D.J. Rowe, Phys. Rev. Lett. 46, 1119 (1981).

    Article  ADS  Google Scholar 

  32. M.J. Carvalho, D.J. Rowe, S. Karram, C. Bahri, Nucl. Phys. A 703, 167 (1987).

    Article  ADS  Google Scholar 

  33. O. Castanos, P.O. Hess, J.P. Draayer, P. Rochford, Nucl. Phys. A 524, 469 (1991).

    Article  ADS  Google Scholar 

  34. D. Troltenier, J.P. Draayer, P.O. Hess, O. Castanos, Nucl. Phys. A 576, 351 (1994).

    Article  ADS  Google Scholar 

  35. S.G. Nilsson, Dan. Mat. Fys. Medd. 29, 1 (1955).

    MathSciNet  Google Scholar 

  36. R.D. Ratnnu Raju, J.P. Draayer, K.T. Hecht, Nucl. Phys. A 202, 433 (1973).

    Article  ADS  Google Scholar 

  37. J.P. Draayer, K.J. Weeks, Ann. Phys. 156, 41 (1984).

    Article  ADS  Google Scholar 

  38. J.P. Draayer, K.J. Weeks, K.T. Hecht, Nucl. Phys. A 381, 1 (1982).

    Article  ADS  Google Scholar 

  39. J. Carvalho et al., Nucl. Phys. A 452, 240 (1986).

    Article  ADS  Google Scholar 

  40. D.J. Rowe, Rep. Prog. Phys. 48, 1419 (1985).

    Article  ADS  Google Scholar 

  41. V.V. Vanagas, Algebraic methods in nuclear theory (Mintis, Vilnius, 1971) (in Russian).

Download references

Author information

Author notes

  1. H. G. Ganev

    Present address: Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria

Authors and Affiliations

  1. Joint Institute for Nuclear Research, Dubna, Russia

    H. G. Ganev

Authors
  1. H. G. Ganev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to H. G. Ganev.

Additional information

Communicated by D. Blaschke

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ganev, H.G. Shell-model representations of the proton-neutron symplectic model. Eur. Phys. J. A 51, 84 (2015). https://doi.org/10.1140/epja/i2015-15084-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epja/i2015-15084-1

Keywords

Search

Navigation