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Prog. Theor. Phys. Vol. 37 No. 2 (1967) pp. 315-335

[ Full Text PDF : FREE ACCESS (1246K) ]

On Applicability of the Random Phase Approximation to the Collective Excitation in Spherical Even Nuclei. I

— Correction to the First 2+ States in Single Closed Shell Nuclei —

Akira Tokunaga

Research Institute for Fundamental Physics, Kyoto University, Kyoto

(Received October 14, 1966)

Abstract:

In order to check the applicability of the random phase approximation (the RPA), the correction to the RPA for the first 2+ state in spherical even nuclei is evaluated using a kind of perturbation theory (starting with the solutions of the RPA as zeroth-order approximation). According to our method, in so far as the first-order correction is concerned, some ambiguities depending on various methods (presented by several authors) to transcribe the system into the boson space are avoidable. Physical implication of the correction is considered. Numerical results for Ni-isotopes (Ni60 and Ni62) and for the single j = 15/2 shell model show that the correction to the RPA is unexpectedly large in the region of “phonon” energy which we are interested in. We are thus forced to conclude that the conventional approach in terms of the RPA should be modified since in nuclear problems the total number of states in the shell under consideration, Ω, is not so large to guarantee the RPA and, as a result, the magnitude of correction in that region becomes highly sensitive to the force-strength χ.


URL : http://ptp.ipap.jp/link?PTP/37/315/
DOI : 10.1143/PTP.37.315

[ Full Text PDF : FREE ACCESS (1246K) ] Citation:

References:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 37 No. 2 (1967) pp. 336-352 :
    On Applicability of the Random Phase Approximation to the Collective Excitation in Spherical Even Nuclei. II
    Masatoshi Yamamura, Akira Tokunaga and Toshio Marumori
  2. Progress of Theoretical Physics Vol. 38 No. 2 (1967) pp. 332-352 :
    On the Effect of the Pauli Principle on the Collective Oscillations in Spherical Even Nuclei
    Yoshinao Miyanishi and Masatoshi Yamamura
  3. Progress of Theoretical Physics Vol. 38 No. 6 (1967) pp. 1285-1296 :
    Effective Interaction and Effective Charge for Valence Nucleons in Collective Vibration and Core Polarization
    Hiroharu Bandō
  4. Progress of Theoretical Physics Vol. 39 No. 6 (1968) pp. 1468-1486 :
    Selfconsistent Treatment of Collective Vibrations in Terms of Boson Expansions
    Bent Sørensen
  5. Progress of Theoretical Physics Vol. 40 No. 1 (1968) pp. 60-83 :
    Four-Body Correlation in Light Nuclei
    Jörg Eichler, Toshio Marumori and Kenjiro Takada
  6. Progress of Theoretical Physics Vol. 40 No. 3 (1968) pp. 499-522 :
    A Theory of Anharmonic Vibrations in Spherical Even-Even Nuclei
    Teruo Kishimoto and Kiyomi Ikeda
  7. Progress of Theoretical Physics Vol. 49 No. 1 (1973) pp. 181-205 :
    A Microscopic Theory of the So-Called “Two-Phonon” States in Even-Even Nuclei. I
    Nobuo Kanesaki, Toshio Marumori, Fumihiko Sakata and Kenjiro Takada
  8. Progress of Theoretical Physics Vol. 56 No. 1 (1976) pp. 124-134 :
    An a priori Quantized Time-Dependent Hartree-Bogoliubov Theory
    Masatoshi Yamamura and Seiya Nishiyama
  9. Progress of Theoretical Physics Vol. 57 No. 1 (1977) pp. 96-111 :
    Derivation of Random Phase Approximation on the Basis of the Generalized Schwinger Representation of the Fermion-Pairs
    Yutaka Mizobuchi, Seiya Nishiyama and Masatoshi Yamamura
  10. Progress of Theoretical Physics Vol. 57 No. 5 (1977) pp. 1554-1571 :
    A New Fermion Many-Body Theory Based on the SO(2N+1) Lie Algebra of the Fermion Operators
    Hideo Fukutome, Masatoshi Yamamura and Seiya Nishiyama
  11. Progress of Theoretical Physics Supplement No.58 (1975) pp. 1-8 :
    Introduction
    Atsushi Kuriyama, Toshio Marumori and Kenichi Matsuyanagi
  12. Progress of Theoretical Physics Supplement No.71 (1981) pp. 1-47 :
    Chapter 1. Present Status of the Microscopic Study of Low-Lying Collective States in Spherical and Transitional Nuclei
    Toshio Marumori, Kenjiro Takada and Fumihiko Sakata
  13. Progress of Theoretical Physics Supplement No.71 (1981) pp. 71-122 :
    Chapter 3. A New Microscopic Method for Describing the Elementary Modes of Excitation in the Intrinsic Subspace
    Kenjiro Takada, Kazunari Kaneko, Fumihiko Sakata and Shigeru Tazaki

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