Microscopic Basis of the Interacting Boson Model

Abstract

The microscopic basis of the IBM is discussed in this paper, presenting a derivation of the IBM system from the multi-nucleon system. Although there could be different approaches to this goal as stated in the preface of this supplement, we focus on two approaches. One is the Otsuka-Arima-Iachello mapping, which works for the spherical and near-spherical nuclei. The other is a mapping for deformed nuclei. In this paper, we discuss mapping methods for deriving the Interacting Boson Model (IBM). l) We first present a mapping method for spherical and near-spherical nuclei, usually referred to as the Otsuka-Arima-Iachello (OAI) mapping. 2 ), 3 ) The OAI mapping is based on the seniority scheme as will be discussed in detail. This mapping has been developed so that realistic calculations can be carried out as presented in a subsequent paper. In this paper, the basic concepts of the mapping are discussed rather in detail. Furthermore, the proton-neutron Interacting Boson Model (IBM-2) is discussed as a natural consequence of this mapping. 2 ), 3 ) In the second half of this paper, a mapping method for strongly deformed nuclei 8 ) will be reviewed. Although this mapping is for deformed nuclei, it is somewhat related to the OAI mapping. The work on deformed nuclei is much before any sort of completion, and considerable effort should be made in the future. For this purpose, the Quantum Monte Carlo Diagonalization method proposed recently 4 )- 7 ) may be useful. When the IBM was proposed from the phenomenological viewpoint by Arima and Iachello, the microscopic picture of bosons of this model was not known as pointed out in the preface of this supplement. The microscopic theory has made a crucial contribution even to phenomenological studies by the IBM, also as mentioned in the preface. Before starting rather detailed discussions, it may be useful to overview relevant properties of the effective nucleon-nucleon interactions. The short-range nuclear force favors two nucleons lying close to each other. This means that, if the wave functions of the two neutrons have large spatial overlap, the matrix element of this interaction becomes larger. On the other hand, two identical fermions cannot occupy the same quantum state, and this is the case for two neutrons. The next optimum case for gaining energy is that the two neutrons are moving on the same orbital but in opposite directions. Because the direction is opposite, the quantum states of the two neutrons are different. In this case, the total angular momentum of the two-neutron system is zero, because the rotation is completely cancelled. In fact, the