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Prog. Theor. Phys. Vol. 64 No. 6 (1980) pp. 2091-2106

[ Full Text PDF : FREE ACCESS (1257K) ]

Convergent Theory for Effective Interaction in Nuclei

Kenji Suzuki and Shyh Yuan Lee*

Department of Physics, Kyushu Institute of Technology, Kitakyushu 804
*Department of Physics, State University of New York at Stony Brook, New York 11794

(Received July 9, 1980)

Abstract:

A general equation is derived for constructing the effective interaction on the basis of the similarity transformation theory. It is proved that the equation is equivalent to Bloch's equation for the degenerate perturbation theory and, therefore, the present approach is also equivalent to the energy independent Rayleigh-Schrödinger theory. Some iteration methods are proposed to solve the equation, and the convergence conditions for the iteration procedures are discussed. Two iteration methods–self-energy insertion and vertex renormalization–are obtained to reach the true eigenvalues of the full Hamiltonian even when there are some intruder states. It is proved that the self-energy insertion procedure produces the eigenvalues of eigenstates which have large overlap with the model space. One the other hand, the vertex renormalization procedure gives the eigenvalues nearest to the unperturbed starting energy.


URL : http://ptp.ipap.jp/link?PTP/64/2091/
DOI : 10.1143/PTP.64.2091

[ Full Text PDF : FREE ACCESS (1257K) ] Citation:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 65 No. 3 (1981) pp. 919-937 :
    Four Particle-Two Hole Correlations and the Effective Interaction
    Hiroharu Bandō, Toshio Motoba and Kenji Suzuki
  2. Progress of Theoretical Physics Vol. 68 No. 1 (1982) pp. 246-260 :
    Construction of Hermitian Effective Interaction in Nuclei
    Kenji Suzuki
  3. Progress of Theoretical Physics Vol. 68 No. 5 (1982) pp. 1627-1643 :
    Unitary-Model-Operator Approach to Nuclear Effective Interaction. I
    Kenji Suzuki
  4. Progress of Theoretical Physics Vol. 68 No. 6 (1982) pp. 1999-2013 :
    Unitary-Model-Operator Approach to Nuclear Effective Interaction. II
    Kenji Suzuki
  5. Progress of Theoretical Physics Vol. 70 No. 2 (1983) pp. 439-451 :
    Degenerate Perturbation Theory in Quantum Mechanics
    Kenji Suzuki and Ryoji Okamoto
  6. Progress of Theoretical Physics Vol. 71 No. 6 (1984) pp. 1221-1238 :
    General Structure of Effective Interaction in Degenerate Perturbation Theory
    Kenji Suzuki and Ryoji Okamoto
  7. Progress of Theoretical Physics Vol. 75 No. 6 (1986) pp. 1388-1404 :
    Unitary-Model-Operator Approach to Nuclear Many-Body Problem. I
    Kenji Suzuki and Ryoji Okamoto
  8. Progress of Theoretical Physics Vol. 92 No. 6 (1994) pp. 1045-1080 :
    Effective Interaction Theory and Unitary-Model-Operator Approach to Nuclear Saturation Problem
    Kenji Suzuki and Ryoji Okamoto
  9. Progress of Theoretical Physics Vol. 104 No. 1 (2000) pp. 123-141 :
    Three-Body Cluster Effects on Λ Single-Particle Energies in Λ17O and Λ41Ca
    Shinichiro Fujii, Ryoji Okamoto and Kenji Suzuki
  10. Progress of Theoretical Physics Supplement No.146 (2002) pp. 159-168 :
    Low Momentum Nucleon-Nucleon Interaction and Halo Nuclei
    T. T. S. Kuo and S. K. Bogner
  11. Progress of Theoretical Physics Supplement No.192 (2012) pp. 1-238 :
    Recent Developments in Nuclear Cluster Physics
    Hisashi Horiuchi, Kiyomi Ikeda and Kiyoshi Katō

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