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Progress of Theoretical Physics

Canonicity Condition and Its Favourite Form of Collective Hamiltonian

A. Kuriyama, M. Yamamura

Published Dec 1, 1983• 3 citations
Publisher

Abstract

The role of canonicity condition in fixing a proper canonical coordinate system of collective submanifold is investigated. We take up two typical forms of canonicity condition, which favour two typical forms of collective Hamiltonian, respectively. We show a beautiful harmony and mutual aid between the canonicity and the so-called RPA boundary condition.

DOI
10.1143/ptp.70.1675

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The role of canonicity condition in fixing a proper canonical coordinate system of collective submanifold is investigated. We take up two typical forms of canonicity condition, which favour two typical forms of collective Hamiltonian, respectively. We show a beautiful harmony and mutual aid between the canonicity and the so-called RPA boundary condition.
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 of collective submanifold, recently, developed by the present authors (M. Y. and A. K.) is applied to a classical many-body system, the Hamiltonian of which depends on the relative coordinates. The solution enables the separation of the total degrees of freedom into the collective and the intrinsic ones, which may be called the generalized center of mass and the relative motions. The results can be applied to the large amplitude collective motion and its couplings with the intrinsic degrees of freedom, which cannot be given in the HF plus RPA method.
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.
With the purpose of clarifying characteristic difference of the optimum collective submanifolds between in nonresonant and resonant cases, we propose an improved method of solving the basic equations of the self-consistent collective-coordinate (SCC) method, which describes optimum (“maximally-decoupled”) large-amplitude collective motion within the time-dependent Hartree-Fock theory. It is shown that, in the resonant cases, there inevitably arise essential coupling terms which break the maximal-decoupling property of the collective motion, so that we have to extend the optimum collective submanifold so as to properly treat the degrees of freedom bringing about the resonances. An illustrative example is given with a simple model Hamiltonian.