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Prog. Theor. Phys. Vol. 70 No. 2 (1983) pp. 424-438

[ Full Text PDF : FREE ACCESS (637K) ]

Geometry of the Self-Consistent Collective-Coordinate Method for the Large-Amplitude Collective Motion

— Stability Condition of “Maximally-Decoupled” Collective Submanifold —

Fumihiko Sakata, Toshio Marumori,* Yukio Hashimoto* and Tsutomu Une*

Institute for Nuclear Study, University of Tokyo, Tanashi, Tokyo 188
*Institute of Physics, University of Tsukuba, Ibaraki 305

(Received May 2, 1983)

Abstract:

The geometry of the self-consistent collective-coordinate (SCC) method formulated within the frame-work of the time-dependent Hartree-Fock (TDHF) theory is investigated by associating the variational parameters with a symplectic manifold (a TDHF manifold). With the use of a canonical-variable parametrization, it is shown that the TDHF equation is equivalent to the canonical equations of motion in classical mechanics in the TDHF manifold. This enables us to investigate geometrical structure of the SCC method in the language of the classical mechanics. The SCC method turns out to give a prescription how to dynamically extract a “maximally-decoupled” collective submanifold (hypersurface) out of the TDHF manifold, in such a way that a certain kind of trajectories corresponding to the large-amplitude collective motion under consideration can be reproduced on the hypersurface as precisely as possible. The stability of the hypersurface at each point on it is investigated, in order to see whether the hypersurface obtained by the SCC method is really an approximate integral surface in the TDHF manifold or not.


URL : http://ptp.ipap.jp/link?PTP/70/424/
DOI : 10.1143/PTP.70.424

[ Full Text PDF : FREE ACCESS (637K) ] Citation:

References:

  1. T. Marumori, T. Maskawa, F. Sakata and A. Kuriyama, Prog. Theor. Phys. 64 (1980), 1294[PTP].
  2. T. Marumori, F. Sakata, T. Une, Y. Hashimoto and T. Maskawa, Prog. Theor. Phys. 66 (1981), 1651[PTP].
    T. Marumori, F. Sakata, T. Une and Y. Hashimoto, Prog. Theor. Phys. Suppl. Nos. 74 & 75 (1983), 221[PTP].
  3. T. Marumori, Prog. Theor. Phys. 57 (1977), 112[PTP].
    T. Marumori, A. Hayashi, T. Tomoda, A. Kuriyama and T. Maskawa, Prog. Theor. Phys. 63 (1980), 1576[PTP].
  4. T. Marumori, F. Sakata, T. Maskawa, T. Une and Y. Hashimoto, Proceedings of the 1982 Brasov International School (World Scientific Publishing Co. Pte. Ltd.).
  5. F. Sakata, Y. Hashimoto, T. Marumori and T. Une, Prog. Theor. Phys. 70 (1983), 163[PTP].
  6. J. da Providencia and J. N. Urbano, Proceedings of 1982 INS International Symposium on “Dynamics of Nuclear Collective Motion”. INS, 1982, July 6∼10, p. 361; Proceedings of 1982 Brasov International School (World Scientific Publishing Co. Pte. Ltd.).
    L. P. Brito and C. A. Sousa, J. of Phys. A: Math. Gen. 14 (1981), 2239[CrossRef].
  7. P. Kramer and M. Saraceno, Lecture Notes in Phys. No. 140 (Springer-Verlage, 1981).
  8. E. R. Marshalek and J. Weneser, Phys. Rev. C 2 (1970), 1682[APS].
    E. R. Marshalek, Nucl. Phys. A 161 (1971), 401[CrossRef].
    D. Janssen, F. Dönau, S. Frauendorf and R. V. Jolos, Nucl. Phys. A 172 (1971), 145[CrossRef].
  9. E. Cartan, Leçons sur les invariants intégraux, Hermann, Paris (1922), and Appendix in Ref.1).
  10. A. Kuriyama and M. Yamamura, Prog. Theor. Phys. 66 (1981), 2130[PTP].

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 71 No. 4 (1984) pp. 752-774 :
    Generalization of Equation of Collective Submanifold
    Masatoshi Yamamura and Atsushi Kuriyama
  2. Progress of Theoretical Physics Vol. 73 No. 2 (1985) pp. 386-396 :
    Applicability of the Concept of “Optimal” Collective Submanifold Determined by the Self-Consistent Collective-Coordinate Method
    Yukio Hashimoto, Fumihiko Sakata and Toshio Marumori
  3. Progress of Theoretical Physics Vol. 74 No. 1 (1985) pp. 51-65 :
    Intrinsic Excitation Modes Compatible with Large-Amplitude Collective Motion in the TDHF Theory
    Fumihiko Sakata, Toshio Marumori, Kazuhiro Muramatsu and Yukio Hashimoto
  4. Progress of Theoretical Physics Vol. 76 No. 2 (1986) pp. 387-399 :
    Concept of Dynamical Collective Submanifold for Large-Amplitude Collective Motion in the TDHF Theory
    Fumihiko Sakata, Toshio Marumori, Yukio Hashimoto, Kazuhiro Muramatsu and Masanori Ogura
  5. Progress of Theoretical Physics Vol. 76 No. 2 (1986) pp. 400-413 :
    Quantum Theory of Dynamical Collective Subspace for Large-Amplitude Collective Motion
    Fumihiko Sakata, Toshio Marumori and Masanori Ogura
  6. Progress of Theoretical Physics Vol. 77 No. 2 (1987) pp. 347-361 :
    Collective, Dissipative and Stochastic Motions in the TDHF Theory
    Kazuhiro Muramatsu, Fumihiko Sakata, Yoshifumi Yamamoto and Toshio Marumori
  7. Progress of Theoretical Physics Vol. 77 No. 5 (1987) pp. 1192-1208 :
    Non-Unitary Realization of the Selfconsistent Collective-Coordinate Method
    Yoshifumi R. Shimizu and Kenjiro Takada
  8. Progress of Theoretical Physics Vol. 78 No. 6 (1987) pp. 1351-1363 :
    Extraction of a Collective Submanifold for the Hénon-Heiles System
    Kunio Takabayashi
  9. Progress of Theoretical Physics Vol. 78 No. 6 (1987) pp. 1364-1391 :
    Optimum Collective Submanifold in Resonant Cases by the Self-Consistent Collective-Coordinate Method for Large-Amplitude Collective Motion
    Yukio Hashimoto, Toshio Marumori and Fumihiko Sakata
  10. Progress of Theoretical Physics Vol. 80 No. 4 (1988) pp. 678-693 :
    Extraction of Dynamical Collective Subspace for Large-Amplitude Collective Motion
    Kazuhiro Muramatsu, Fumihiko Sakata and Toshio Marumori
  11. Progress of Theoretical Physics Vol. 82 No. 6 (1989) pp. 1084-1105 :
    Dissipation Mechanism of the Large-Amplitude Collective Motion
    Masayuki Matsuo, Fumihiko Sakata and Toshio Marumori
  12. Progress of Theoretical Physics Vol. 85 No. 4 (1991) pp. 805-828 :
    Single-Particle Motion in Large-Amplitude Quadrupole Shape Transition
    Kazuya Yamada
  13. Progress of Theoretical Physics Vol. 85 No. 6 (1991) pp. 1235-1270 :
    Microscopic Description of Nuclear Collective Rotation by Means of the Self-Consistent Collective Coordinate Method
    Jun Terasaki, Toshio Marumori and Fumihiko Sakata
  14. Progress of Theoretical Physics Vol. 91 No. 6 (1994) pp. 1135-1147 :
    Quantum Nonlinear Resonance
    Hidehiko Tsukuma, Fumihiko Sakata, Toshio Marumori, Kazuo Iwasawa, Hiroshi Itabashi, Yukio Hashimoto and Takeshi Tanaka
  15. Progress of Theoretical Physics Vol. 110 No. 3 (2003) pp. 499-516 :
    Correlation Analysis of Quantum Fluctuations and Repulsion Effects of Classical Dynamics in SU(3) model
    Shigeyasu Fujiwara and Fumihiko Sakata
  16. Progress of Theoretical Physics Supplement No.93 (1987) pp. 1-175 :
    Time-Dependent Hartree-Fock Method and Its Extension
    Masatoshi Yamamura and Atsushi Kuriyama
  17. Progress of Theoretical Physics Supplement No.141 (2001) pp. 1-111 :
    Nonlinear Dynamics of Nuclear Collective Motion
    Fumihiko Sakata, Toshio Marumori, Yukio Hashimoto and Shi-Wei Yan
  18. Progress of Theoretical Physics Supplement No.141 (2001) pp. 179-241 :
    Non-Unitary Boson Mapping and Its Application to Nuclear Collective Motions
    Kenjiro Takada

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