Chapter 1 Present Status of the Microscopic Study of Low-Lying Collective States in Spherical and Transitional Nuclei

It was 1971 when the present authors in collaboration with Kanesaki, Kuriyama and Matsuyanagi tried to construct a microscopic theory which is capable to clarify structure of the anharmonicity effects for the simple phonon picture in a systematic way.n. 2> Since then, some important progress has been made both in developing the theory itself and in clarifying various important physical concepts in connection with experimental facts. One of the main themes was to clarify the very concept of the collective subspace, which is treated as the phonon (boson) space in the phenomenological collective model, from the microscopic point of view. The other one was to investigate dynamical interplay between pairing and quadrupole correlations, which is expected to play a crucial role in the phase transition from the spherical to the deformed shape. The results of investigation on these two themes are reported in Chapters 2, 3, 4 and 5 of this issue. During performing the works, the "new phenomenology" based on the interacting boson model popularized by Arima and Iachello3> has demonstrated the considerable success in fitting experimental spectra and transition probabilities on the collective states. According to the interacting boson model, low-lying nuclear spectra are described in terms of s and d bosons, which are identified with those corresponding to nucleon-pairs coupled to J = 0 and J=2 respectively, by making use of SU(6)-group-theoreticallanguage. Since the interacting boson model has rather large number of the free patrameters (up to eleven), it can incorporate many important limits which correspond to various subgroups of SU (6) and can obtain marvellous agreement with many experimental spectra in spherical, transitional and strongly deformed nuclei. Thus, the new phenomenology based on the interacting boson model