Dynamical Properties of the GCM Rotational Hamiltonian: Dynamics of the Transition from Collective to Noncollective Rotation

Abstract

The general form of the rotational Hamiltonian is derived using the generator coordinate method for a well-deformed intrinsic state without any symmetry property. It is shown that this Hamiltonian can describe the dynamics of the band termination, that is, the transition from collective to noncollective rotation for a simple nuclear system. The spectroscopy of rapidly-rotating nuclei has been extensively developed. In recent years it has become possible to study the whole process of rotational bands, that is, how the nuclear rotation changes its property with increasing angular momentum until the rotational sequence terminates. Theoretical study of the yrast line has been mainly carried out in the framework of the cranking model accompanied by the Strutinsky method. 1 > In this model the nucleus is externally cranked with a constant angular velocity and the classical concept of angular velocity (rotational frequency) plays an essential role. The property of nuclear rotation has been discus­ sed on the basis of the property of the eigenstate of the cranked Hamiltonian. In the low-energy spectrum, nuclear rotation occurs associated with the deformation in the nuclear equilibrium shape, and such a rotation is usually called collective. In gen­ eral, the property of nuclear rotation changes through band crossings, which arise in connection with the self-consistent changes of the mean field in the rotating nucleus, and then the angular momentum is generated partially by nucleons aligned along the rotational axis. We call simply such a quantal motion of nucleons noncollective rotation in this paper. Without band crossings, the property of nuclear rotation changes through the transform of the nuclear shape which is required to guarantee the nuclear self-consistency of the mean field. At the end of the rotational sequence, the nucleus becomes oblate with respect to the axis of rotation and then collective rotation disappears completely. In this paper we will study the dynamics of the change of the nuclear rotational mode along the yrast line, on the basis of the GCM rotational Hamiltonian which is derived on the generator coordinate method (GCM). The properties of the GCM rotational Hamiltonian depend essentially on the choice of the intrinsic state. In this paper, we will construct the intrinsic state on the cranking model as the first step of further investigations, though the cranking model is justified only under some condi­ tions.2> . The GCM rotational Hamiltonian is derived in § 2 for an arbitrarily chosen intrinsic state. In § 3, the explicit form of this Hamiltonian is shown for a simple