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Progress of Theoretical Physics

Interplay of Pairing and Intrinsic Modes of Excitation in Nuclei. I: Transcription of Nucleon System into Ideal Boson-Quasi-Particle Space

T. Suzuki, K. Matsuyanagi

Published Oct 1, 1976• 46 citations
Publisher

Abstract

A new method treating the interplay of pairing and intrinsic modes of excitation is proposed. In this method, the pairing mode associated with the J = 0-coupled nucleon pairs is represented by pairing bosons and the intrinsic mode characterized by the seniority quantum number is explicitly treated by ideal quasi-particle operators. We obtain a closed expression of the single-nucleon operator in terms of pairing bosons and ideal quasi-particles. As a simple illustration, the superconducting system is treated by introducing the coherent state of pairing bosons and the relation to the Bogoliubov transformation is discussed. The relation between this method and the canonical transformation method with auxiliary variables is also clarified.

DOI
10.1143/ptp.56.1156

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Progress of Theoretical Physics Vol. 55 No. 5 (1976) pp. 1680–1683Representation of Nucleon Operators in the Product Space Composed of Pairing Bosons and “Quasi-Particles” Tōru Suzuki Progress of Theoretical Physics Vol. 56 No. 4 (1976) pp. 1140–1155Structure of the Anomalous 0+' Excited States in Spherical Even-Even Nuclei with N or Z ≈40 Saburo Iwasaki, Toshio Marumori, Fumihiko Sakata and Kenjiro Takada Progress of Theoretical Physics Vol. 56 No. 6 (1976) pp. 1786–1801A Semi-Microscopic Derivation of Coupling between Rotational and Intrinsic Motions. I Atsushi Kuriyama Progress of Theoretical Physics Vol. 60 No. 5 (1978) pp. 1366–1382Interplay of Pairing and Intrinsic Modes of Excitation in Nuclei. II Tōru Suzuki Progress of Theoretical Physics Vol. 61 No. 2 (1979) pp. 680–681Spurious Mode Due to Number Non-Conservation and the RPA Ground States Yoshinao Miyanishi and Goro Watanuki Progress of Theoretical Physics Vol. 61 No. 4 (1979) pp. 1082–1092Property of Many-Phonon Norm Matrix Tōru Suzuki, Masahiko Fuyuki and Kenichi Matsuyanagi Progress of Theoretical Physics Vol. 61 No. 6 (1979) pp. 1682–1696Dynamical Interplay of Pairing and Quadrupole Modes in Transitional Nuclei. I Tōru Suzuki, Masahiko Fuyuki and Kenichi Matsuyanagi Progress of Theoretical Physics Vol. 62 No. 3 (1979) pp. 690–705Dynamical Interplay of Pairing and Quadrupole Modes in Transitional Nuclei. II Tōru Suzuki, Masahiko Fuyuki and Kenichi Matsuyanagi Progress of Theoretical Physics Vol. 65 No. 5 (1981) pp. 1667–1683Dynamical Interplay of Pairing and Quadrupole Modes in Transitional Nuclei. III Tōru Suzuki, Masahiko Fuyuki and Kenichi Matsuyanagi Progress of Theoretical Physics Vol. 67 No. 5 (1982) pp. 1441–1455Attenuation Factors for B(E2) in the Microscopic Description of Multiphonon States Kenichi Matsuyanagi Progress of Theoretical Physics Supplement No.71 (1981) pp. 1–47Chapter 1. Present Status of the Microscopic Study of Low-Lying Collective States in Spherical and Transitional Nuclei Toshio Marumori, Kenjiro Takada and Fumihiko Sakata Progress of Theoretical Physics Supplement No.71 (1981) pp. 48–70Chapter 2. Outline of the Mode-Mode Coupling Theory Fumihiko Sakata, Toshio Marumori and Kenjiro Takada Progress of Theoretical Physics Supplement No.71 (1981) pp. 123–179Chapter 4. Dynamical Interplay between Pairing and Quadrupole Correlations Shigeru Tazaki, Kenjiro Takada, Kazunari Kaneko and Fumihiko Sakata Progress of Theoretical Physics Supplement No.71 (1981) pp. 180–220Chapter 5. Dynamical Interplay between Pairing and Quadrupole Correlations in Odd-Mass Nuclei Kazunari Kaneko, Kenjiro Takada, Fumihiko Sakata and Shigeru Tazaki

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Progress of Theoretical Physics•Jul 1, 1991•4 citations
A new method treating the interplay of pairing and intrinsic modes of excitation is proposed. In this method, the pairing mode associated with the J = 0-coupled nucleon pairs is represented by pairing bosons and the intrinsic mode characterized by the seniority quantum number is explicitly treated by ideal quasi-particle operators. We obtain a closed expression of the single-nucleon operator in terms of pairing bosons and ideal quasi-particles. As a simple illustration, the superconducting system is treated by introducing the coherent state of pairing bosons and the relation to the Bogoliubov transformation is discussed. The relation between this method and the canonical transformation method with auxiliary variables is also clarified.
For strongly pair-correlated systems, a new transformation is derived similar in form to the usual Bogoliubov-Valatin transformation, but with the transformation coefficients replaced by operators. The original fermion operators are now replaced by two sets of independent operators, the pair operators and the quasi-fermions . The transformation conserves the particle number. Among other applications, it is particularly suited for the construction of a microscopic theory of the type of the interacting boson model. The new transformation given here also serves to provide a connection between the usual ph picture of a phonon and the pp picture-of bosons in IBM. However, the boson picture that evolves from the present formulation differs from the ideal boson picture in IBM..
Progress of Theoretical Physics Vol. 55 No. 5 (1976) pp. 1680–1683Representation of Nucleon Operators in the Product Space Composed of Pairing Bosons and “Quasi-Particles” Tōru Suzuki Progress of Theoretical Physics Vol. 56 No. 4 (1976) pp. 1140–1155Structure of the Anomalous 0+' Excited States in Spherical Even-Even Nuclei with N or Z ≈40 Saburo Iwasaki, Toshio Marumori, Fumihiko Sakata and Kenjiro Takada Progress of Theoretical Physics Vol. 56 No. 6 (1976) pp. 1786–1801A Semi-Microscopic Derivation of Coupling between Rotational and Intrinsic Motions. I Atsushi Kuriyama Progress of Theoretical Physics Vol. 60 No. 5 (1978) pp. 1366–1382Interplay of Pairing and Intrinsic Modes of Excitation in Nuclei. II Tōru Suzuki Progress of Theoretical Physics Vol. 61 No. 2 (1979) pp. 680–681Spurious Mode Due to Number Non-Conservation and the RPA Ground States Yoshinao Miyanishi and Goro Watanuki Progress of Theoretical Physics Vol. 61 No. 4 (1979) pp. 1082–1092Property of Many-Phonon Norm Matrix Tōru Suzuki, Masahiko Fuyuki and Kenichi Matsuyanagi Progress of Theoretical Physics Vol. 61 No. 6 (1979) pp. 1682–1696Dynamical Interplay of Pairing and Quadrupole Modes in Transitional Nuclei. I Tōru Suzuki, Masahiko Fuyuki and Kenichi Matsuyanagi Progress of Theoretical Physics Vol. 62 No. 3 (1979) pp. 690–705Dynamical Interplay of Pairing and Quadrupole Modes in Transitional Nuclei. II Tōru Suzuki, Masahiko Fuyuki and Kenichi Matsuyanagi Progress of Theoretical Physics Vol. 65 No. 5 (1981) pp. 1667–1683Dynamical Interplay of Pairing and Quadrupole Modes in Transitional Nuclei. III Tōru Suzuki, Masahiko Fuyuki and Kenichi Matsuyanagi Progress of Theoretical Physics Vol. 67 No. 5 (1982) pp. 1441–1455Attenuation Factors for B(E2) in the Microscopic Description of Multiphonon States Kenichi Matsuyanagi Progress of Theoretical Physics Supplement No.71 (1981) pp. 1–47Chapter 1. Present Status of the Microscopic Study of Low-Lying Collective States in Spherical and Transitional Nuclei Toshio Marumori, Kenjiro Takada and Fumihiko Sakata Progress of Theoretical Physics Supplement No.71 (1981) pp. 48–70Chapter 2. Outline of the Mode-Mode Coupling Theory Fumihiko Sakata, Toshio Marumori and Kenjiro Takada Progress of Theoretical Physics Supplement No.71 (1981) pp. 123–179Chapter 4. Dynamical Interplay between Pairing and Quadrupole Correlations Shigeru Tazaki, Kenjiro Takada, Kazunari Kaneko and Fumihiko Sakata Progress of Theoretical Physics Supplement No.71 (1981) pp. 180–220Chapter 5. Dynamical Interplay between Pairing and Quadrupole Correlations in Odd-Mass Nuclei Kazunari Kaneko, Kenjiro Takada, Fumihiko Sakata and Shigeru Tazaki
The present paper attempts to give independent descriptions of the collective degrees of freedom of nuclei such as the monopole and quadrupole ones in order to avoid the seniority mixing problem. This is done by the operatorized Bogoliubov transformation (OBT) which separates the degree of freedom from the rest described by the seniority particle operator which is not coupling to the pairs, and in terms of which the independent pair is composed. The OBT is derived in such a way that it can be generalized easily to include a new kind of “seniority particle operator” neither coupling to the nor to the pairs. In terms of this new particle operator the independent pair or the independent odd particle in odd nuclei is constructed.
We propose a new method that transcribes the fermion system to the boson-fermion system by introducing a unitary operator defined in the whole boson-fermion space. We obtain the boson-fermion expansion of the fermion pair operators such that only the collective pair modes are transformed into boson operators while the non-collective modes are unchanged in the lowest order approximation. The odd- A system is treated in the same formalism as the even-even nuclear system. We briefly discuss the relation between our method and the conventional boson expansion theory.