MICROSCOPIC ASPECTS OF THE INTERACTING BOSON MODEL.

Abstract

As a phenomenological tool, the Interacting Boson Model (IBM) has been useful and successful in correlating a wide variety of experimental data regarding the collective properties of many nuclei. The original version of the IBM did not distinguish between protons and neutrons and is referred to as the IBM-1. Microscopic investigation of the model revealed the need for explicit proton and neutron degrees of freedom and, thus, the IBM-2 was developed. The net result is a model, the IBM-2, motivated by microscopic theory, which is a boson description of collective features in medium-to-heavy mass even-even nuclei, and which is capable of distinguishing proton and neutron characteristics. A review is presented of the concept of using boson descriptions of many-fermion systems, and the IBM is introduced in a historical context. Next, the use of the IBM-2 as a phenomenological tool is investigated. The model is applied to the even zinc isotopes and the model is found to give a reasonable description of the experimental data. In the phenomenological calculations, the parameters of the IBM-2 Hamiltonian are adjusted until good agreement is obtained with the experimental data. To put the theoretical basis of the IBM-2 on firm ground, it is important to be able to calculate these parameters microscopically. A framework is developed in which such calculations can be performed for non-deformed nuclei. Results are presented for the mercury isotopes and discussed in detail. The calculated parameter values agree for the most part with the values obtained by phenomenological fit but with some exceptions. Similar calculations are performed for the platinum isotopes. The results for these isotopes are then related to the concpet of F-spin multiplets. When the Surface Delta Interaction (SDI) is used, several simplifications can be made in the IBM. In certain schematic situations, the parameters of the IBM-2 Hamiltonian can be related directly to the strength of the SDI. Several interesting results are obtained whose full implication will be investigated in the future. In conclusion, the IBM is discussed in relation with its application to other topics, both within and beyond the realms of nuclear physics. Several appendices are attached in which many algebraic details are shown explicitly. A brief summary is given of the computer codes that have been written in connection with this work.