Shell Model Structure of the Interacting Boson Model and the Interacting Boson Fermion Model

Abstract

Nuclei are very complex systems composed of a large number of strongly interacting protons and neutrons. One could expect that such systems will have extremely complicated and unwieldy level spectra. However, in spite of their complexity, nuclei exhibit remarkably simple regularities which make their spectra interesting objects of research. Many of these regularities are associated with individual nucleon motion and find their expression in the shell model1. Nuclei with closed shell or with a few nucleons away can be very well described in terms of simple shell model configurations and effective two-body interactions between nucleons2. As we move away from closed shells, the spectra become more complex. Yet in spectra of nuclei with several protons and neutrons outside closed shells, other remarkable regularities emerge. The low-lying levels can be grouped into bands whose energies in many cases correspond to those of a symmetric rotor. In other cases the bands are more vibrational but they are all characterized by strong intra-band E2 transitions. Such rotational or quasi-rotational spectra found a simple and highly successful description in terms of the collective model3.