Physics of Atomic Nuclei

, 74:1139 | Cite as

Self-consistent RPA based on a many-body vacuum

  • M. JemaïEmail author
  • P. Schuck
Nuclei Theory


Self-Consistent RPA is extended in a way so that it is compatible with a variational ansatz for the ground-state wave function as a fermionic many-body vacuum. Employing the usual equation-of-motion technique, we arrive at extended RPA equations of the Self-Consistent RPA structure. In principle the Pauli principle is, therefore, fully respected. However, the correlation functions entering the RPA matrix can only be obtained from a systematic expansion in powers of some combinations of RPA amplitudes. We demonstrate for a model case that this expansion may converge rapidly.


Atomic Nucleus Pauli Principle Couple Cluster Theory Hypernetted Chain Lipkin Model 
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  1. 1.
    P. Schuck and S. Ethofer, Nucl. Phys. A 212, 269 (1973); J. Dukelsky,G. Röepke and P. Schuck, Nucl. Phys. A 628, 17 (1998); D. S. Delion, P. Schuck, and J. Dukelsky, Phys. Rev. C 72, 064305 (2005).ADSCrossRefGoogle Scholar
  2. 2.
    J. P. Blaizot and G. Ripka, Quantum Theory of Finite Systems (MIT Press, 1986).Google Scholar
  3. 3.
    P. Fulde, Electron Correlations in Molecules and Solids, Springer Series in Solid-State Sciences, Vol. 100 (Springer, Berlin, 1995).CrossRefGoogle Scholar
  4. 4.
    F. Gebhard, The Mott Metal-Insulator Transition, Springer Tracts in Modern Physics, Vol. 137 (Springer, Berlin, 1997).Google Scholar
  5. 5.
    R. F. Bishop, Theor. Chem. Acta 80, 95 (1991).CrossRefGoogle Scholar
  6. 6.
    S. Takahara, M. Tohyama, and P. Schuck, Phys. Rev. C 70, 057307 (2004); M. Tohyama and P. Schuck, arXiv:1003.0246 [nucl-th].ADSCrossRefGoogle Scholar
  7. 7.
    P. Ring and P. Schuck, The Nuclear Many-Body Problem (Springer, New York, 1980).Google Scholar
  8. 8.
    J. Dukelsky and P. Schuck, Nucl. Phys. A 512, 466 (1990).ADSCrossRefGoogle Scholar
  9. 9.
    J.G. Hirsch, A. Mariano, J. Dukelsky, and P. Schuck, Ann. Phys. (N.Y.) 296, 187 (2002).ADSCrossRefGoogle Scholar
  10. 10.
    P. Schuck, unpublished notes (1987).Google Scholar
  11. 11.
    H. J. Lipkin, N. Meshkov, and A. J. Glick,Nucl. Phys. 62, 188 (1965).MathSciNetCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  1. 1.Département de Physique, Faculté des Sciences de TunisUniversité de Tunis El-ManarTunisTunisie
  2. 2.Institut de Physique Nucléaire d’OrsayUniversité Paris-Sud, CNRS-IN2P3 15Orsay CedexFrance
  3. 3.Laboratoire de Physique et Modélisation des Milieux Condensés (LPMMC) (UMR 5493)Maison Jean PerrinGrenoble Cedex 9France

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