Non-Unitary Boson Mapping and Its Application to Nuclear Collective Motions
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概要
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First, the general theory of boson mapping for even-number many-fermion systems is surveyed. In order to overcome the confusion concerning the so-called unphysical or spurious states in the boson mapping, the correct concept of the unphysical states is precisely given in a clear-cut way. Next, a method to apply the boson mappirug to a truncated many-fermion Hilbert space consisting of collective phonons is proposed, by putting special emphasis on the Dyson-type non-unitary boson mapping. On the basis of this method, it becomes possible for the first time to apply the Dyson-type boson mapping to analyses of collective motions in realistic nuclei. This method is also extertded to be applicable to odd-number-fermion systems. As known well, the Dyson-type boson mapping is a non-unitary transformation and it gives a non-Hermitian boson Hamiltonian. It is not easy (but not impossible) to solve the eigenstates of the non-Hermitian Hamiltonian. A Hermitian treatment of this non-Hermitian eigenvalue problem is discussed and it is shown that this treatment is a very good approximation. Using this Hermitian treatment, we can obtain the normal-ordered Holstein-Primakoff-type boson expansion in the multi-collective-phonon subspace. Thereby the convergence of the boson expansion can be tested. Some examples of application of the Dyson-type non-unitary boson mapping to simplified models and realistic nuclei are also shown, and we can see that it is quite useful for analysis of the collective motions in realistic nuclei. In contrast to the above-mentioned ordinary type of boson mapping, which may be called a "static" boson mapping, the Dyson-type non-unitary selfconsistent-collective-coordinate method is discussed. The latter is, so to speak, a "dynamical" boson mapping, which is a dynamical extension of the ordinary boson mapping to be capable to include the coupling effects from the non-collective degrees of freedom selfconsistently. Thus all of the Dyson-type non-unitary boson mapping from A to Z is summarized in this paper.
- 理論物理学刊行会の論文
- 2001-04-27
著者
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TAKADA Kenjiro
Department of Physics, Kyushu University
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Takada Kenjiro
Department Of Physics Kuushu University
関連論文
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- Role of Particle-Hole Interaction in the Four-Particle-Four-Hole States in ^O
- Two-Octupole-Phonon States in ^Gd
- Non-Unitary Realization of the Selfconsistent Collective-Coordinate Method : Nuclear Physics
- A Microscopic Theory of the So-Called "Two-Phonon" States in Even-Even Nuclei. II : Formulation
- Dyson Boson Mapping and Shell-Model Calculations for Even-Even Nuclei(Nuclear Physics)
- Chapter 2 Outline of the Mode-Mode Coupling Theory
- A New Method for Microscopic Description of the So-Called "Many-Phonon" States in Spherical Even-Even Nuclei. I
- Structure of the Anomalous 0^ Excited States in Spherical Even-Even Nuclei with N or Z≈ 40
- In What Sense Does the Phonon Picture Persist in Spherical Even-Even Nuclei?
- Axially Asymmetric Deformation and Its Stability in sd-Shell Nuclei
- Quasiparticle-Shell-Model Calculations of So-Called Two-Phonon States in Cd and Sn Isotopes
- Nuclear Deformation and Nuclear Force. II
- Chapter 5 Dynamical Interplay between Pairing and Quadrupole Correlations in Odd-Mass Nuclei
- Chapter 4 Dynamical Interplay between Pairing and Quadrupole Correlations : Anharmonicity in the So-Called Two-Phonon Triplet States in Medium-Heavy Nuclei
- Chapter 3 A New Microscopic Method for Describing the Elementary Modes of Excitation in the Intrinsic Subspace : Dressed n-Quasiparticle Modes and Multi-Phonon Excitation
- Dynamical Anharmonicity Effects in Low-Lying Negative-Parity States of Odd-Mass Sn Isotopes
- On the Four-Body Correlations in Light Nuclei : Reduction of the Effective Interaction due to the Pauli Principle
- Non-Unitary Boson Mapping and Its Application to Nuclear Collective Motions
- Alpha-Like Spatial Four-Body Correlations in Light Nuclei : Vertically-Truncated-Subspace Shell Model for the Core Plus Four-Particle System
- Test of Validity of the Hermitian Treatment of the Dyson Boson Mapping
- Convergence of Boson Expansion Theory : Nuclear Physics
- A Comment on the New Formulation of a Many-Level Shell Model
- A New Formulation of a Many-Level Shell Model : A Method of Constructing Orthonormal Basis States Analytically
- A Non-Linear Extension of the Quasiparticle Random-Phase Approximation for Description of Nuclear Collective Motions : Application of Sawada's Attached Field Method
- Convergence of Boson Expansion Theory : Nuclear Physics
- Present Status of the Microscopic Study of Low-Lying Collective States in Spherical and Transitional Nuclei (Microscopic Study of Low-Lying Collective States in Spherical and Transitional Nuclei--Dynamical Interplay between Pairing and Quadrupole Modes)