The Ginocchio Model and the Interacting Boson Approximation

  • Akito Arima
Part of the Ettore Majorana International Science Series book series (EMISS, volume 10)

Abstract

Various approaches to nuclear collective motions have been made since Bohr and Mottelson published their classic works.1) Among these, the Interacting Boson Approximation2) (IBA) and the boson expansion theory3) have been successful in explaining properties of vibrational, transitional and rotational nuclei. The interacting boson approximation assumes that the collective low-lying states of heavy nuclei are composed primarily of monopole and quadrupole pairs of fermions that are approximated as monopole and quadrupole bosons.4) The boson expansion method5) determines an expansion for the fermion operators by demanding that the commutation relations are preserved in the boson space. In general this leads to an infinite expansion for the fermion pair operators in powers of bosons. Furthermore all the fermion pairs, not just the collective pairs, are mapped onto bosons. This theory is implemented in practice by first making a BCS transformation from particles to quasiparticles.3) The boson expansions are then made in the quasiparticle basis. Ultimately only a collective quadrupole boson in this quasiparticle space is retained and an effective boson Hamiltonian for this collective quadrupole boson is derived.3)

Keywords

Fermion Operator Interact Boson Model Infinite Expansion Rotational Nucleus Multipole Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1).
    A. Bohr, Mat. Fys. Medd. Dan. Vid. Selsk. 26 (1952) no. 14Google Scholar
  2. A. Bohr and B. R. Mottelson, Mat. Fys. Medd. Dan, Vid. Selsk. 27 (1953) no. 16.Google Scholar
  3. 2).
    F. Iachello, ed., Interacting Bosons in Nuclear Physics (Plenum Press, NY. 1979) For example, O. Scholten, F. Iachello and A. Arima, Ann. of Phys. 115 (1978) 325Google Scholar
  4. 3).
    T. Kishimoto and T. Tamura, Nucl. Phys. A192 (1972) 246, A270 (1976) 317.T. Tamura, K. Weeks and T. Kishimoto, Phys. Rev. C20 (1979) 307.Google Scholar
  5. 4).
    T. Otsuka, A. Arima, F. Iachello and T. Talmi, Phys. Lett. 66B (1977) 205; 76B (1978) 139.Google Scholar
  6. 5).
    S. T. Belyaev and V. G. Zelevinsky, Nucl. Phys. 39 (1962) 582. E. R. Marshalek, Nucl. Phys. A161 (1971) 401; A224 (1974) 221, 245.Google Scholar
  7. 6).
    J. N. Ginocchio, Phys. Lett. 85B (1979) 9; Ann. of Phys. 126 (1980) 234.MathSciNetGoogle Scholar
  8. 7).
    T. Otsuka, A. Arima and F. Iachello, Nucl. Phys. A309 (1978) 1.Google Scholar

Copyright information

© Springer Science+Business Media New York 1981

Authors and Affiliations

  • Akito Arima
    • 1
  1. 1.Department of Physics, Faculty of ScienceUniversity of TokyoHongo, Bunkyo-ku, TokyoJapan

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