Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Progress of Theoretical Physics

Exact Relation between Dynamical Nuclear Field Theory and Boson Expansion Theory in a Tamm-Dancoff-Boson System

T. Kishimoto, Tetsuo Kammuri, Hideo Sakamoto

Published May 1, 1991• 1 citation
Publisher

Abstract

In the treatment of the vibrational mode of even-even nuclei, Dynamical Nuclear Field Theory (DNFT) in the Tamm-Dancoff (TD) representation exhibited the defect to include unlinked cluster terms. We aim to remove this deficiency. In lowest order of the repetitive actions of the particle-boson couplings, we generate |0)B⊗|nTD fermion pairs> states out of |0>F⊗|nbosons) states. We impose the lowest order self-consistency. The modified DNFT gives the normal-ordered linked-cluster expansion, in complete equivalence with the boson expansion theory (BET), of Kishimoto, Tamura and Sakamoto.

DOI
10.1143/ptp.85.1057

Related papers

Perturbation Expa]nsion in Dynamical Nuclear Field Theory and Its Relation with Boson Expansion Theory

Teruo Kishimoto, Tetsuo Kammuri

With the Dynamical Nuclear Field Theory (DNFT) in the Tamm-Dancoff representation we examine higher order corrections in the vibrational mode of a spherical nuclear system. Due to the effects of bubble diagrams, the perturbation expansion in terms of the unrenormalized coupling strength and boson energy fails at full self-consistency. On the other hand, it becomes applicable in the form of linked-cluster expansion when we use these constants renormalized by the effect of bubble diagrams, in the schematic model. However, in comparison with the boson expansion theory, serious defects are found in higher order DNFT.

Progress of Theoretical Physics•Sep 1, 1990•1 citation

On a Boson Expansion Method with Two-Body Correlations

T. Kishimoto, Tetsuo Kammuri, Hideo Sakamoto

Dynamical Nuclear Field Theory which was modified in the previous paper so as to bring complete equivalence with Boson Expansion Theory (BET) is now extended to derive a BET under the influence of two-body correlations. For this purpose, the driving Hamiltonian of the vibrating Hartree field approximation is supplemented by the residual two-body interaction. Effective forms of Tamm-Dancoff fermion-pair and scattering operators are expanded perturbatively. Effects of three kinds of bubble diagrams can be incorporated by the renormalization procedure, but the contributions from unlinked diagrams remain uncancelled. Comparisons with Nuclear Field Theory are discussed.

Progress of Theoretical Physics•Jul 1, 1992•0 citations

Exact and approximate aspects of the boson expansion theories

Taro Tamura, Kenneth J. Weeks, V. G. Pedrocchi

It is shown that a boson expansion theory of the Kishimoto-Tamura type not only maps the operators exactly but also the space, and, consequently, the matrix elements of the fermion system onto those of the bosons. Significance of approximations made in calculations is also discussed.NUCLEAR STRUCTURE Boson expansion theories, Pauli principles, pair representation, Tamm-Dancoff representation, exact mapping, collective approximation, ideal boson states.

Physical Review C•Mar 1, 1981•12 citations

Pair Rotation in the Dynamical Nuclear Field Theory

Teruo Kishimoto, Tetsuo Kammuri

A many•body technique called the dynamical nuclear field theory is developed by taking the example of pair rotation.The time-dependent one-body Hamiltonian contains the collective coordinates; the magnitude and phase aIigleof the energy gap.Effective forms of the original Hamiltonian and other operators are derived for a direct-product space of the collective states and a restricted set of the particle states defined by the driving Hamiltonian in the intrinsic frame.Pair rotations of even-and odd-A systems are treated in the lowest order approximation.The particle-rotor picture and the cranking model are shown to be equivalent.*) Brief report on DNFT in the Tamm-Dancoff approximation can be found in Ref. 13).

Progress of Theoretical Physics•Dec 1, 1985•2 citations

Bosonization of fermion operators as linked-cluster expansions

T. Kishimoto, Taro Tamura

In order for a boson-expansion theory to be useful for practical purposes, it must satisfy at least two requirements: It must be in the form of a linked-cluster expansion, and the pure (ideal) boson states must be usable as basis states. Previously, we constructed such a boson theory and used it successfully for many realistic calculations. This construction, however, lacked mathematical rigor. In the present paper, we develop an entirely new approach, which results in the same boson expansions obtained earlier, but now in a mathematically rigorous fashion. The achievement of the new formalism goes beyond this. Its framework is much more general and flexible than was that of the earlier formalism, and it allows us to extend the calculations beyond what had been done in the past.NUCLEAR STRUCTURE Boson expansion theories, commutator method, Marumori-Yamamura-Tokunaga method, fermion system, norm matrix, linked-cluster expansion, ideal-boson state, physical boson state, even-even nucleus, odd-$A$ nucleus, nuclear collectivity.

Physical Review C•Jan 1, 1983•34 citations

A New Tamm-Dancoff Method Based on the SO (2N+1) Regular Representation of Fermion Many-Body Systems

Hideo Fukutome

A new Tamm-Dancoff method is developed on the basis of the SO(2N + 1) regular representation formalism of Fermion many-body systems. The Schrodinger equation in the SO(2N + 1) generator coordinate representation is decomposed into symmetry subspaces by means of a Peierls-Yoccoz, projection procedure. The decomposed Schrödinger equation is transformed to a quasi-particle frame by a transformation of the generator coordinate and expanded by the symmetry projected Tamm-Dancoff bases. The Tamm-Danco[f equation and wave function thus obtained satisfy all symmetry requirements at every order of the expansion. The first order Tamm-Dancoff wave function is neither an independent particle nor quasi-particle approximation but represents Bose condensed Fermion pairs (and an unpaired particle) performing a coherent motion. The higher order terms represent fluctuations of Fermion pairs (and the unpaired particle) from the Bose condensate.

Progress of Theoretical Physics•Dec 1, 1978•18 citations
In the treatment of the vibrational mode of even-even nuclei, Dynamical Nuclear Field Theory (DNFT) in the Tamm-Dancoff (TD) representation exhibited the defect to include unlinked cluster terms. We aim to remove this deficiency. In lowest order of the repetitive actions of the particle-boson couplings, we generate |0)B⊗|nTD fermion pairs> states out of |0>F⊗|nbosons) states. We impose the lowest order self-consistency. The modified DNFT gives the normal-ordered linked-cluster expansion, in complete equivalence with the boson expansion theory (BET), of Kishimoto, Tamura and Sakamoto.
With the Dynamical Nuclear Field Theory (DNFT) in the Tamm-Dancoff representation we examine higher order corrections in the vibrational mode of a spherical nuclear system. Due to the effects of bubble diagrams, the perturbation expansion in terms of the unrenormalized coupling strength and boson energy fails at full self-consistency. On the other hand, it becomes applicable in the form of linked-cluster expansion when we use these constants renormalized by the effect of bubble diagrams, in the schematic model. However, in comparison with the boson expansion theory, serious defects are found in higher order DNFT.
Dynamical Nuclear Field Theory which was modified in the previous paper so as to bring complete equivalence with Boson Expansion Theory (BET) is now extended to derive a BET under the influence of two-body correlations. For this purpose, the driving Hamiltonian of the vibrating Hartree field approximation is supplemented by the residual two-body interaction. Effective forms of Tamm-Dancoff fermion-pair and scattering operators are expanded perturbatively. Effects of three kinds of bubble diagrams can be incorporated by the renormalization procedure, but the contributions from unlinked diagrams remain uncancelled. Comparisons with Nuclear Field Theory are discussed.
A many•body technique called the dynamical nuclear field theory is developed by taking the example of pair rotation.The time-dependent one-body Hamiltonian contains the collective coordinates; the magnitude and phase aIigleof the energy gap.Effective forms of the original Hamiltonian and other operators are derived for a direct-product space of the collective states and a restricted set of the particle states defined by the driving Hamiltonian in the intrinsic frame.Pair rotations of even-and odd-A systems are treated in the lowest order approximation.The particle-rotor picture and the cranking model are shown to be equivalent.*) Brief report on DNFT in the Tamm-Dancoff approximation can be found in Ref. 13).
In order for a boson-expansion theory to be useful for practical purposes, it must satisfy at least two requirements: It must be in the form of a linked-cluster expansion, and the pure (ideal) boson states must be usable as basis states. Previously, we constructed such a boson theory and used it successfully for many realistic calculations. This construction, however, lacked mathematical rigor. In the present paper, we develop an entirely new approach, which results in the same boson expansions obtained earlier, but now in a mathematically rigorous fashion. The achievement of the new formalism goes beyond this. Its framework is much more general and flexible than was that of the earlier formalism, and it allows us to extend the calculations beyond what had been done in the past.NUCLEAR STRUCTURE Boson expansion theories, commutator method, Marumori-Yamamura-Tokunaga method, fermion system, norm matrix, linked-cluster expansion, ideal-boson state, physical boson state, even-even nucleus, odd-AAA nucleus, nuclear collectivity.
A new Tamm-Dancoff method is developed on the basis of the SO(2N + 1) regular representation formalism of Fermion many-body systems. The Schrodinger equation in the SO(2N + 1) generator coordinate representation is decomposed into symmetry subspaces by means of a Peierls-Yoccoz, projection procedure. The decomposed Schrödinger equation is transformed to a quasi-particle frame by a transformation of the generator coordinate and expanded by the symmetry projected Tamm-Dancoff bases. The Tamm-Danco[f equation and wave function thus obtained satisfy all symmetry requirements at every order of the expansion. The first order Tamm-Dancoff wave function is neither an independent particle nor quasi-particle approximation but represents Bose condensed Fermion pairs (and an unpaired particle) performing a coherent motion. The higher order terms represent fluctuations of Fermion pairs (and the unpaired particle) from the Bose condensate.