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

Pair Rotation in the Dynamical Nuclear Field Theory

Teruo Kishimoto, Tetsuo Kammuri

Published Dec 1, 1985• 2 citations
Publisher

Abstract

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).

DOI
10.1143/ptp.74.1245

Related papers

Concept of Ideal Collective Coordinate as the Foundation for a Phenomenological Theory of Nuclear Collective Motion: Basic Ideas and Relation to Other Phenomenological Methods

Abraham Klein, R. M. Dreizler, Robert E. Johnson

The concept of an ideal collective coordinate is introduced by means of the following example: Consider a one-dimensional vibration of a many-body system in the sense that a large subset of states $|n〉$ of the system exhibits an energy spectrum and relative transition probabilities following the laws of the (in general anharmonic) oscillator described by $\mathcal{H}$ (${p}_{\ensuremath{\alpha}}, \ensuremath{\alpha}$) $(\ensuremath{\alpha}|n)={\ensuremath{\omega}}_{n}(\ensuremath{\alpha}|n)$. We suppose the set of many-body states $|n〉$ to extend indefinitely, and we take the transform $|\ensuremath{\alpha}〉=\ensuremath{\Sigma}|n〉$ ($n|\ensuremath{\alpha}$) to define a many-body generating state of the band which is precisely localized in $\ensuremath{\alpha}$ space. The basic assumption of collectivity, that changing the state of at most a few particles cannot much alter the value of $\ensuremath{\alpha}$, is shown to be sufficient to derive a phenomenological theory from the many-body starting point. The phenomenological aspects of a recent theory of rotations due to Villars is seen to be contained in the above formulation as a special case. A brief review is given of the generator coordinate and similar projection methods in order to exhibit their relationship with the present method.

Physical Review•Jul 20, 1968•21 citations

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

T. Kishimoto, Tetsuo Kammuri, Hideo Sakamoto

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.

Progress of Theoretical Physics•May 1, 1991•1 citation

The Path Integral Approach for the Nuclear Collective Motion

D. Galetti, Salomon Sylvain Mizrahi, B. M. Pimentel

A procedure is developed for treating a nuclear collective motion via the path integral formalism by defining a collective propagator in the "phase space" of the collective subspace. This collective subspace is projected out of the full many-body Hilbert space by an approach of the Generator Coordinate Method. Under the approximation of quadratic "momentum" dependence we write the propagator in the coordinate representation from which we derive the collective Schrödinger equation in terms of a canonical pair and .

Physica Scripta•Feb 1, 1983•4 citations

Time-dependent coupled-cluster approximation to nuclear dynamics. I. Application to a solvable model

Pervez Amirali Hoodbhoy, John W. Negele

A general hierarchy of approximations to the many-body Schr\"odinger equation is presented which reduces to the time-dependent mean-field approximation in lowest order and provides systematic corrections in subsequent orders. The theory is applied to two interacting systems described by the Lipkin model Hamiltonian. Comparison of the results of the lowest two orders of approximation with the exact solution demonstrates the practicality of the method and its potential for generalizing nuclear dynamics beyond the mean field theory.NUCLEAR STRUCTURE Time-dependent approximation to nuclear dynamics. Corrections to time-dependent mean-field theory. Solution of Lipkin model for two interacting systems.

Physical Review C•Nov 1, 1978•65 citations

Comparative study of the requantization of the time-dependent mean field for the dynamics of nuclear pairing

Fang Ni, Takashi Nakatsukasa

To describe quantal collective phenomena, it is useful to requantize the time-dependent mean-field dynamics. We study the time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory for the two-level pairing Hamiltonian, and compare results of different quantization methods. The one constructing microscopic wave functions, using the TDHFB trajectories fulfilling the Einstein-Brillouin-Keller quantization condition, turns out to be the most accurate. The method is based on the stationary-phase approximation to the path integral. We also examine the performance of the collective model which assumes that the pairing gap parameter is the collective coordinate. The applicability of the collective model is limited for the nuclear pairing with a small number of single-particle levels, because the pairing gap parameter represents only a half of the pairing collective space.

arXiv:1712.02954•Physical Review C•Apr 12, 2018•3 citations
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).
The concept of an ideal collective coordinate is introduced by means of the following example: Consider a one-dimensional vibration of a many-body system in the sense that a large subset of states ∣n〉|n〉∣n〉 of the system exhibits an energy spectrum and relative transition probabilities following the laws of the (in general anharmonic) oscillator described by H\mathcal{H}H (${p}_{\ensuremath{\alpha}}, \ensuremath{\alpha}$) $(\ensuremath{\alpha}|n)={\ensuremath{\omega}}_{n}(\ensuremath{\alpha}|n)$. We suppose the set of many-body states ∣n〉|n〉∣n〉 to extend indefinitely, and we take the transform $|\ensuremath{\alpha}〉=\ensuremath{\Sigma}|n〉$ ($n|\ensuremath{\alpha}$) to define a many-body generating state of the band which is precisely localized in $\ensuremath{\alpha}$ space. The basic assumption of collectivity, that changing the state of at most a few particles cannot much alter the value of $\ensuremath{\alpha}$, is shown to be sufficient to derive a phenomenological theory from the many-body starting point. The phenomenological aspects of a recent theory of rotations due to Villars is seen to be contained in the above formulation as a special case. A brief review is given of the generator coordinate and similar projection methods in order to exhibit their relationship with the present method.
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.
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.
A procedure is developed for treating a nuclear collective motion via the path integral formalism by defining a collective propagator in the "phase space" of the collective subspace. This collective subspace is projected out of the full many-body Hilbert space by an approach of the Generator Coordinate Method. Under the approximation of quadratic "momentum" dependence we write the propagator in the coordinate representation from which we derive the collective Schrödinger equation in terms of a canonical pair and .
A general hierarchy of approximations to the many-body Schr\"odinger equation is presented which reduces to the time-dependent mean-field approximation in lowest order and provides systematic corrections in subsequent orders. The theory is applied to two interacting systems described by the Lipkin model Hamiltonian. Comparison of the results of the lowest two orders of approximation with the exact solution demonstrates the practicality of the method and its potential for generalizing nuclear dynamics beyond the mean field theory.NUCLEAR STRUCTURE Time-dependent approximation to nuclear dynamics. Corrections to time-dependent mean-field theory. Solution of Lipkin model for two interacting systems.
To describe quantal collective phenomena, it is useful to requantize the time-dependent mean-field dynamics. We study the time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory for the two-level pairing Hamiltonian, and compare results of different quantization methods. The one constructing microscopic wave functions, using the TDHFB trajectories fulfilling the Einstein-Brillouin-Keller quantization condition, turns out to be the most accurate. The method is based on the stationary-phase approximation to the path integral. We also examine the performance of the collective model which assumes that the pairing gap parameter is the collective coordinate. The applicability of the collective model is limited for the nuclear pairing with a small number of single-particle levels, because the pairing gap parameter represents only a half of the pairing collective space.