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Prog. Theor. Phys. Vol. 32 No. 5 (1964) pp. 726-737

On the “Anharmonic Effects” on the Collective Oscillation in Spherical Even Nuclei. II

Toshio Marumori, Masatoshi Yamamura, Akira Tokunaga and Kenjiro Takada^*

Department of Physics, Kyoto University, Kyoto
^*Research Institute for Atomic Energy, Osaka City University, Osaka

(Received July 3, 1964)

Abstract:

On the basis of a kind of perturbation theory starting with the solutions of the “harmonic approximation” (the random phase approximation) as the zeroth-order approximation, a method to evaluate the correction to the first 2⁺ state and the splitting of the triplet (0⁺, 2⁺, 4⁺) in the spherical even nuclei is presented. An essential difficulty that the states obtained under the “harmonic approximation” do not form an orthogonal set in rigorous sense is overcome by transcribing the original quasi-particle system into the “ideal boson space” according to the theory proposed in a previous paper. In this “ideal boson space”, the states obtained under the “harmonic approximation” form a complete orthogonal set, so that we can safely use them as the zeroth-order approxiation. By adopting the Hamiltonian with “pairing plus quadrupole force”, our results are compared with those obtained by Do Dang and Klein with their “spectral decomposition method”. It is shown that our results are very similar to theirs in so far as the “phonon-quasi-particle coupling” is neglected. The advantage of our method in evaluating the effects of “phonon-quari-particle coupling” is emphasized.

URL : http://ptp.ipap.jp/link?PTP/32/726/
DOI : 10.1143/PTP.32.726

[ Full Text PDF : FREE ACCESS (589K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

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References:

1. T. Marumori, M. Yamamura and A. Tokunaga, Prog. Theor. Phys. 31 (1964), 1009[PTP].
2. G. Do Dang and A. Klein, Phys. Rev. 133 (1964), B257[APS].

Citing Article(s) :

1. Progress of Theoretical Physics Vol. 37 No. 2 (1967) pp. 315-335 :

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

   Akira Tokunaga

2. 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

3. 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

4. Progress of Theoretical Physics Vol. 63 No. 1 (1980) pp. 160-175 :

   Study of the Anharmonic Effects on Low-Lying States of Odd-Mass Nuclei in 1g_9/2⁺ Shell Region

   Masahiro Nakano

5. Progress of Theoretical Physics Vol. 115 No. 4 (2006) pp. 739-757 :

   A New Boson Realization of the Two-Level Pairing Model in a Many-Fermion System and Its Classical Counterpart

   Constança Providência, João da Providência, Yasuhiko Tsue and Masatoshi Yamamura

6. Progress of Theoretical Physics Supplement No.58 (1975) pp. 1-8 :

   Introduction

   Atsushi Kuriyama, Toshio Marumori and Kenichi Matsuyanagi

7. 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

8. 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

9. Progress of Theoretical Physics Supplement No.74 & 75 (1983) pp. 89-114 :

   Boson-Fermion Expansions

   E. R. Marshalek

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