Atsushi Kuriyama

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.

Theory of Collective Excitations in Spherical Odd-Mass Nuclei. III Electromagnetic Properties of the Anomalous Coupling States

Various electromagnetic properties of the anomalous coupling states with spin (j-1) are shown to be well explained by the new viewpoint of the dressed n-quasi-particle modes proposed in a previous paper. In this point of view, the anomalous coupling collective states with spin (j -1) are considered as the dressed three-quasi-particle modes, which are regarded as a kind of elementary excitation modes in odd-mass nuclei. The effects of couplings between dressed three-quasi-particle modes and one-quasi-particle mode~ are also discussed in this connection, including those with spin j, (j-1) and (j-2).

Theory of Collective Excitations in Spherical Odd-Mass Nuclei. I Basic Ideas and Concept of Dressed Three-Quasi-Particle Modes

A new systematic theory of describing the collective excitations in spherical odd-mass nuclei is developed. The theory can be regarded as a direct extension of the conventional quasi-particle-new-Tamm-Dancoff method (i.e. the quasi-particle-random phase approximation) for spherical even-mass nuclei into the case of spherical odd-mass nuclei. In order to conxad struct properly the theory within the framework of the quasi-particle-new-Tamm-Dancoff method, it is shown to be decisive to introduce a new concept which precisely specifies the dressed three-quasi-particle modes. The new concept is recognized in connection with the quasi-spin space which has been introduced through the quasi-spin formalism for the pairing correlations. It is not the purpose of this paper, part I, to go into a clear-cut formulation of the theory and into detailed quantitative calculations, but rather to put an emphasis on the explanation of basic ideas. § I. Introduction Recent accumulation of the experimental data illuminating the structure of low-lying collective excited states in spherical odd-mass nuclei has stimulated the investigation of problems on particle-vibration coupling. An important effect of particle-vibration coupling, which has been neglected for a long time, has been emphasized by Bohr and Mottelson 1 ) in the Tokyo Conference in 1967: In the phenomenological phonon-quasi-particle coupling model, the lowest-order-perturbation effects which contribute to energies of the excited states composed of the odd quasi-particle and the one-phonon, are shown in Figs. lA and lB. The diagrams of type lA are nothing but the conventional ones which have so far been treated as phonon-quasi-particle coupling, while the diagrams of type lB have usually been neglected so far. The physical effect underlying the diagrams lB is that the phonon disassociates into a pair of quasixad particle, one of which reassociates with the odd-quasi-particle while the remainxad ing quasi-particle is now the odd-quasi-particle. Thus this effect is essentially based on the Pauli principle between the quasi-particles composing the phonon and the extra quasi-particle outside the core. The extreme importance of the diagrams of type lB can be recognized as follows. The diagrams of type lA consist of the coupling with the factor (u!u 2 - v 1v 2) which can be quite small,

A Microscopic Theory of Collective and Independent-Particle Motions

A microscopic theory of collective and independent·particle motion in many· fermion system is developed in the framework of the classical theory. The basic idea is an extention of the conventional time-dependent Hartree-Fock method with the use of fermion coherent state representation. Equation to determine collective path and constraints to govern the collective and the independent-particle variables are given. Hamiltonian and other physical quantities given with the original fermion variables are rewritten to the forms expressed in terms of the collective and the independent-particle variables.

A Quantal Theory of Pairing Rotation, Pairing Vibrations and Independent-Particle Motions

A microscopic theory is proposed to describe not only the pairing rotation, the pairing vibrations and the independent· particle motions, but also their mutual couplings in a consistent manner. With the aid of a BCS·type wave packet and a quasi-particle coherent state, the quantal system is translated into a corresponding classical one. First, we develop a canonical form in a classical image. This classical system obeys certain constraints, by which the double counting in the degrees of freedom is avoided. Then, the quantization is performed with the use of the Dirac theory of a canonical system with constraints. The original fermion operators themselves are expressed in terms of three types of degrees of freedom, which correspond to the pairing rotation, the pairing vibrations and the independent-quasi-particle motions, respectively.

A Note on Pairing Vibrational Motion

With the aim of achieving a unified understanding of the pamng correlation for the normal and super systems, the ground and 1st o+ states (called pairing vibrational state) are studied using the two-level model with the pairing force. There exist two kinds of aspects for the classification of states with the same set of seniority { v J} -horizontal and vertical band aspects. The sets of operators are introduced to characterize each aspect, respectively. The former has the direct correspondence between the characteristic behaviour of phase transition and the information from the two-nucleon transfer reactions. However, it can describe only the behaviour of a phase transition, and not its mechanism. In the latter aspect it is possible to specify the four types of operators, each of which plays a characteristic role in the phase transition. It is shown that· this latter set of operators includes the eigenmode operators of pairing vibrational motion for the normal and super systems, that is, the two-boson operator Y;v=XptXn 1 and two-quasi-particle operators Y~v in a unified manner.