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Progress of Theoretical Physics

Specification of Collective Submanifold by Adiabatic Time-Dependent Hartree-Fock Method: Coupled Lipkin Model

A. Kuriyama, M. Yamamura, Shinji Iida

Published Dec 1, 1984• 3 citations
Publisher

Abstract

With the use of adiabatic time-dependent Hartree-Fock method, a collective submanifold is specified for the case of the coupled Lipkin model. The energy spectra, which belong to those of collective mode, are well reproduced with the aid of the canonical quantization.
DOI
10.1143/ptp.72.1273

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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.
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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.