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Quantum Theory of Collective Motion: Quantized Self-Consistent Collective-Coordinate Method for the Large-Amplitude Nuclear Collective Motion

Toshio Marumori, Fumihiko Sakata, Tsutomu Une +2 more

This is the third in a series of papers which intends to develop a new microscopic theory capable by itself to determine the “maximaldecoupled” collective subspace in the many-particle Hilbert space as well as the collective Hamiltonian specifying the subspace. The fundamental principle to formulate the theory is called the invariance principle of the Schrödinger equation. The main purpose of this paper is to show that, when we positively utilize the invariance principle, we can directly obtain a quantum theory of collective motion going beyond the random phase approximation.This is the third in a series of papers which intends to develop a new microscopic theory capable by itself to determine the “maximaldecoupled” collective subspace in the many-particle Hilbert space as well as the collective Hamiltonian specifying the subspace. The fundamental principle to formulate the theory is called the invariance principle of the Schrödinger equation. The main purpose of this paper is to show that, when we positively utilize the invariance principle, we can directly obtain a quantum theory of collective motion going beyond the random phase approximation.

Progress of Theoretical PhysicsNov 1, 19816 citations

Quantum Theory of Dynamical Collective Subspace for Large-Amplitude Collective Motion

Fumihiko Sakata, Toshio Marumori, M. Ogura

By placing emphasis on conceptual correspondence to the “classical” theory which has been developed within the framework of the time-dependent Hartree-Fock theory, a full quantum theory appropriate for describing large-amplitude collective motion is proposed. A central problem of the quantum theory is how to determine an optimal representation called a dynamical representation; the representation is specific for the collective subspace where the large-amplitue collective motion is replicated as satisfactoryly as possible. As an extension of the classical theory where the concept of an approximate integral surface plays an important role, the dynamical representation is properly characterized by introducing a concept of an approximate invariant subspace of the Hamiltonian.By placing emphasis on conceptual correspondence to the “classical” theory which has been developed within the framework of the time-dependent Hartree-Fock theory, a full quantum theory appropriate for describing large-amplitude collective motion is proposed. A central problem of the quantum theory is how to determine an optimal representation called a dynamical representation; the representation is specific for the collective subspace where the large-amplitue collective motion is replicated as satisfactoryly as possible. As an extension of the classical theory where the concept of an approximate integral surface plays an important role, the dynamical representation is properly characterized by introducing a concept of an approximate invariant subspace of the Hamiltonian.

Progress of Theoretical PhysicsAug 1, 19869 citations

Quantum Theory of the Maximally-Decoupled Collective Motion(大振幅集団運動の微視的理論)

正徳小倉

素粒子論研究Apr 20, 19850 citations

Toward a Quantum Theory of Maximally-Decoupled Collective Motion (「時間依存自己無撞着場の方法と量子化」研究会報告)

司宇根

素粒子論研究Mar 20, 19840 citations

Maximal-Decoupling Variational Principle and Optimal Auxiliary Hamiltonians for Nuclear Collective Motions

Ching‐Teh Li

Springer eBooksJan 1, 19940 citations

Formally exact quantum variational principles for collective motion based on the invariance principle of the Schrödinger equation

Abraham Klein, Toshio Marumori, Tsutomu Une