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Progress of Theoretical Physics

Unique Specification of Collective Submanifold

M. Yamamura, A. Kuriyama, Shinji Iida

Published Jan 1, 1984• 8 citations
Publisher

Abstract

It is shown that the ordinary framework of (adiabatic) time-dependent Hartree-Fock method can uniquely specify the collective submanifold and its canonical coordinate system, with the aid of the RPA and the canonicity condition. Some criticism is given to the pesimistic viewpoint concerning the unique specification of collective submanifold within the adiabatic time-dependent Hartree-Fock method. A decisive foundation of the approach developed by Marumori, Maskawa, Sakata and one of the present author (A. K.) is given.

DOI
10.1143/ptp.71.109

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Progress of Theoretical Physics•Dec 1, 1983•3 citations
It is shown that the ordinary framework of (adiabatic) time-dependent Hartree-Fock method can uniquely specify the collective submanifold and its canonical coordinate system, with the aid of the RPA and the canonicity condition. Some criticism is given to the pesimistic viewpoint concerning the unique specification of collective submanifold within the adiabatic time-dependent Hartree-Fock method. A decisive foundation of the approach developed by Marumori, Maskawa, Sakata and one of the present author (A. K.) is given.
A theory is proposed with the aim of describing large amplitude collective motion and its coupling with intrinsic degrees of freedom.A canonical transformation is investigated in the full time•dependent Hartree•Fock theory, i.e., in the classical image of boson expansion theory.With the aid of the transfor• mation, the whole system is separated into collective and intrinsic degrees of freedom.Under the condition of the unique separation, two types of equations of collective submanifold, which are canonically invariant, are obtained.One is of the same form as that of the conventional equation of collective submanifold.A principle of the specification of coordinate system is discussed.
A theory based on the time•dependent Hartree•Fock theory is proposed with the aim of describing large amplitude collective motion and its coupling with intrinsic degrees of freedom.With the use of time•dependent canonical transformation, the whole system is separated into two types of degrees of freedom.Under the condition of unique separation, two kinds of equations of collective submanifold are obtained.One js for the collective motion and of the same form as that previously given by the present authors.The other is for the intrinsic degrees of freedom and consists of a set of linear partial differential equations.It is reduced to the old one, the form of which is non-linear.
The applicability of the concept of “optimal” collective submanifold determined by the self-consistent collective-coordinate (SCC) method is investigated by using a simple model Hamiltonian. Long-time behavior of the SCC-method trajectories on the optimal collective submanifold is analyzed, by comparing the geometrical structure of the SCC-method trajectories with that of the time-dependent Hartree-Fock (TDHF) trajectories in terms of the Poincaré-mapping method. The concept of the optimal collective submanifold determined by the SCC method turns out to be applicable for a fairly large domain of the TDHF manifold where the separatrix is not included, in the sense that it can represent an approximate time-averaged trajectory of the complicated TDHF trajectories.