Basic Notions

Abstract

Before the thorough discussions on each particular case, we first present our principal idea. It is often quite reasonable to start with the microscopic calculation of self-consistent mean-field (potential) energy surface with energy density functional (EDF), from which collective spectra and transition rates are derived (cf. Fig. 2.1). Since the energy surface reflects intrinsic deformation, the question arises here: How can we incorporate the energy-surface calculation into the relevant measurable spectroscopic properties with good symmetries? There have been many EDF-based schemes which derive spectroscopic properties from the energy surface, including the generator coordinate method (GCM), collective Hamiltonian approach, etc. 1 These studies are, however, still computationally quite complicated and demanding. Our motivation to employ the interacting boson model (IBM) is twofold: First, IBM can be utilized as an effective theory to generate excitation energies and transition rates with good symmetries in a computationally much moderate way, in comparison to other mean-field based, spectra-generating approaches mentioned above. The second is rather profound. Formulating the IBM by EDF approach should be of certain interest because it may help clarifying the major long-lasting problem of IBM concerning its microscopic foundation.Note that this chapter is not intended to the complete review of the mean-field theory and the IBM. For pedagogical literature of these two models, the interested reader is referred to the textbook by Ring