The Interacting Boson Fermion Model and Some Applications

Abstract

In the IBA model, collective states in even-even nuclei are described in terms of a system of interacting s- and d-bosons. This model can be extended to odd-A nuclei by coupling the degrees of freedom of the odd nucleon to the system of bosons1. In general, the Hamiltonian for this coupled system can be written as $$H\, = \,{H_B}\, + \,{H_F}\, + \,{H_{BF}}\,,$$ (1.1) where HB is the usual IBA Hamiltonian which describes the system of s- and d-bosons, and HF is the Hamiltonian of the odd particle. Since only a single odd particle is coupled to the bosons, it is sufficient to consider only the one-body part of HF $${H_F} = \,\mathop \sum \limits_{jm} \,{\varepsilon _j}\,a_{jm}^\dag \,{a_{jm}}\,.$$ (1.2) Here, as well as in the following, the summation index j runs over.the shell model orbits in the valence shell, and ej represents the single particle energy.