Toshio Marumori

Self-Consistent Collective-Coordinate Method for the Large-Amplitude Nuclear Collective Motion

This is the second in a series of papers which intends to develop a new microscopic theory capable by itself to select the optimum collective path or, more generally, the optimum collective submanifold in the many-particle Hilbert space. The main content of this paper consists of i) a restatement of the basic equations of the theory, derived from the fundamental principle which leads us to the maximal decoupling between the collective and intrinsic modes and is called the invariance principle of the Schrodinger equation, and ii) a proposal of a method of solving the basic equations in an appropriate way for the largexad amplitude and highly non-linear collective vibrations about the Hartree-Fock ground state with a spherically symmetric equilibrium.

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

Abstract Utilizing the concept of invariant collective subspace of a many-body system (or invariance principle of the time-dependent Schrodinger equation), we derive a number of formally exact variational principles to characterize the subspace. Previous studies based on time-dependent or adiabatic time-dependent Hartree-Fock theory are, in principle, contained as approximations.

Master equations in the microscopic theory of nuclear collective dynamics

Abstract In an isolated finite many-body quantal system as the nucleus in which the self-consistent mean field is realized, collective modes of motion (associated with time evolution of the mean field) are highly involved with non-collective modes of motion in a strongly self-consistent way. By paying attention to this strong self-consistency, a general microscopic framework is given to derive master equations which enable us to investigate various dynamical mechanism of the nuclear large-amplitude collective motion. The theory consists of two ingredients: (i) Introduction of a dynamical canonical coordinate (DCC) system , where the whole nuclear dynamics is optimally described in terms of the collective (relevant) and the non-collective (irrelevant) variables in a self-consistent way on the basis of the self-consistent collective coordinate (SCC) method. (ii) Application of the time-dependent projection operator method of Willis and Picard to the Liouville equation in the DCC system. This application makes it possible to treat both time evolution of a reduced distribution function for the relevant variables and that of a reduced distribution function for the irrelevant variables in a self-consistent way, without introducing any statistical hypothesis for the reduced irrelevant distribution function. The general coupled master equations in the DCC system thus obtained are rich enough to explore the microscopic mechanism responsible for dissipative behaviour of the large-amplitude collective motion, in connection with the stability problem of the collective subspace obtained by the SCC method.

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

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-amplitude collective motion is replicated as satisfactorily 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.

Dissipation Mechanism of the Large-Amplitude Collective Motion Dynamical Evolution of a Collective Budle of Trajectories in the TDHF Phase Space for a Simple Soluble Model

A new microscopic origin responsible for the dissipation process of the large-amplitude collective motion is discussed in terms of the dynamics of distribution function in the time-dependent Hartree Fock (TDHF) phase space. With the use of a simple soluble model, the origin is illustrated by numerically solving the master equation in the microscopic theory of nuclear collective dynamics which has been proposed by the present authors aiming at studying the order-to-chaos transitions of the large-amplitude nuclear collective motion. In this framework, collectivity of the system is expressed by a bundle of trajectories in the TDHF phase space and the dissipation process is related to the diffusive property of the bundle of trajectories. It is clarified that the microscopic dynamics responsible for the dissipation process originates from the dynamical fluctuation part of the coupling between the collective (relevant) and intrinsic (irrelevant) degrees of freedom.

Nuclear spectroscopy and quantum chaos

Abstract In this paper, a recent development of INS-TSUKUBA joint research project on large-amplitude collective motion is summerized. The classical theory of nuclear collective dynamics formulated within the time-dependent Hartree-Fock theory is recapitulated and a decisive role of the level crossing in the single-particle dynamics on the order-to-chaos transition of collective motion is discussed in detail. Extending the basic idea of the classical theory, we discuss a quantum theory of nuclear collective dynamics which allows us to properly define a concept of quantum chaos for each eigenfunction. By using numerical calculation, we illustrate what the quantum chaos for each eigenfunction means and its relation to usual definition based on the random matrix theory.

Chapter 2. Outline of the Mode-Mode Coupling Theory

The main purpose of this chapter is to recapitulate an essential part of the mode-mode coupling theoryu~a> by putting great emphasis on clarifying the basic idea, because it has been published in separate papers in a splitted form. The theory of the dressed n-quasiparticle (nQP) mode was developed for the purpose of taking account of the anharmonicity effects automatically, since it had become dear by means of the boson-expansion method4>. 5> that the anharmonicity effects neglected in the random-phase approximation (RPA) play a decisive role in such a finite quantal system as nuclei. Furthermore it has been developed into a microscopic theory capable to treat the dynamical mutual interplay between the pairing and the quadrupole correlation which are generally considered to be the basic correlations in transitional nuclei. On the other hand, there is a phenomenological approach called the interxad acting boson model (IBM) by Arima and Iachello.6> In this model two kinds of bosons are used; they may be regarded to be introduced in order to embrace the main dyrramical correlations in nuclei. It can successfully classify many experimental data by using a group theoretical language. There have also been some efforts to give a microscopic foundation of the phenomenologixad cal IBM by using the single-j-shell model.n.s> As extensively discussed in Chapter 1, the dynamical interplay between the pairing and the quadrupole degrees of freedom might play a decisive role for the mechanism of the phase transition from spherical to deformed nuclei and the microscopic structure of the collective excited states could be changed from nucleus to nucleus. Such a dynamical interplay can never be described by the simple group theory (e.g. the IBM), where the microscopic structure of the collective boson is supposed to be unchangeable. In order to make clear the structural change of the collective excited states, therefore, we have to construct a theory which can treat the dynamical interplay between the

Toward the Fundamental Theory of Nuclear Matter Physics: The Microscopic Theory of Nuclear Collective Dynamics

Since the research field of nuclear physics is expanding rapidly, it is becoming more imperative to develop the microscopic theory of nuclear matter physics which provides us with a unified understanding of diverse phenomena exhibited by nuclei. An establishment of various stable mean-fields in nuclei allows us to develop the microscopic theory of nuclear collective dynamics within the mean-field approximation. The classical-level theory of nuclear collective dynamics is developed by exploiting the symplectic structure of the time- dependent Hartree-Fock (TDHF)-manifold. The importance of exploring the single-particle dynamics, e.g. the level-crossing dynamics in connection with the classical order-to-chaos transition mechanism is pointed out. Since the classical-level theory is directly related to the full quantum mechanical boson expansion theory via the symplectic structure of the TDHF-manifold, the quantum theory of nuclear collective dynamics is developed at the dictation of what is developed in the classical-level theory. The quantum theory thus formulated enables us to introduce the quantum integrability and quantum chaoticity for individual eigenstates. The inter-relationship between the classical-level and quantum theories of nuclear collective dynamics might play a decisive role in developing the quantum theory of many-body problems.

A MICROSCOPIC THEORY OF DISSIPATIVE NUCLEAR COLLECTIVE MOTIONS

The basic idea of the self-consistent collective coordinate(SCC) method for the dissipative nuclear collective motions is formulated in the framework of time-dependent Hartree-Fock(TDHF) theory. On the basis of the collective subspace defined by the SCC method, an optimum set of canonical variables (dynamical canonical coordinate(DCC) system) is introduced. Making use of the DCC system, a set of coupled master equations is derived to describe the dissipative collective motion accompanied by order-to-chaos transition of the intrinsic motions.