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

Nuclear Physics

The stability of Hartree-Fock solutions and of collective motion

Nobuyuki Fukuda

Published Jun 1, 1963• 13 citations
Publisher
DOI
10.1016/0029-5582(63)90048-8

Related papers

Theories for large amplitude collective motion and constrained Hartree-Fock

K. Goeke

Nuclear Physics A•Jul 1, 1976•12 citations

Time-Dependent Hartree-Fock Description of Nuclear Collective Motion

Salam Adnan Faidi

•Jan 1, 1982•0 citations

An adiabatic time-dependent Hartree-Fock theory of collective motion in finite systems

Michel Baranger, M. Vénéroni

Annals of Physics•Sep 1, 1978•264 citations

Collective Oscillations of Atoms in the Hartree-Fock Approximation

Sol Wieder, Sidney Borowitz

Physical Review Letters•Oct 31, 1966•1 citation

HARTREE-FOCK THEORY AND COLLECTIVE MOTION

Felix M. H. Villars

University of Toronto Press eBooks•Dec 31, 1972•0 citations

Geometry of the Self-Consistent Collective-Coordinate Method for the Large-Amplitude Collective Motion: Stability Condition of ";Maximally-Decoupled" Collective Submanifold

Fumihiko Sakata, Toshio Marumori, Yukio Hashimoto +1 more

The geometry of the self-consistent collective-coordinate (SCC) method formulated within the frame-work of the time-dependent Hartree-Fock (TDHF) theory is investigated by associating the variational parameters with a symplectic manifold (a TDHF manifold). With the use of a canonical-variable parametrization, it is shown that the TDHF equation is equivalent to the canonical equations of motion in classical mechanics in the TDHF manifold. This enables us to investigate geometrical structure of the SCC method in the language of the classical mechanics. The SCC method turns out to give a prescription how to dynamically extract a “maximally-decoupled” collective submanifold (hypersurface) out of the TDHF manifold, in such a way that a certain kind of trajectories corresponding to the large-amplitude collective motion under consideration can be reproduced on the hypersurface as precisely as possible. The stability of the hypersurface at each point on it is investigated, in order to see whether the hypersurface obtained by the SCC method is really an approximate integral surface in the TDHF manifold or not.

Progress of Theoretical Physics•Aug 1, 1983•20 citations
The geometry of the self-consistent collective-coordinate (SCC) method formulated within the frame-work of the time-dependent Hartree-Fock (TDHF) theory is investigated by associating the variational parameters with a symplectic manifold (a TDHF manifold). With the use of a canonical-variable parametrization, it is shown that the TDHF equation is equivalent to the canonical equations of motion in classical mechanics in the TDHF manifold. This enables us to investigate geometrical structure of the SCC method in the language of the classical mechanics. The SCC method turns out to give a prescription how to dynamically extract a “maximally-decoupled” collective submanifold (hypersurface) out of the TDHF manifold, in such a way that a certain kind of trajectories corresponding to the large-amplitude collective motion under consideration can be reproduced on the hypersurface as precisely as possible. The stability of the hypersurface at each point on it is investigated, in order to see whether the hypersurface obtained by the SCC method is really an approximate integral surface in the TDHF manifold or not.