Chapter 2. Outline of the Mode-Mode Coupling Theory

Abstract

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 inter­ 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 phenomenologi­ 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