7 - The interacting boson models-3 and -4

Summary

Introduction

The techniques discussed in Parts I and II can be extended to include other degrees of freedom, if necessary. These extensions will be generically called interacting boson models-k. In them, particularly important is the extension to include isospin degrees of freedom, since it allows one to treat light nuclei where protons and neutrons occupy the same single-particle orbits and thus where isospin plays a major role. There are two versions of this model, introduced by Elliott and White (1980) and Elliott and Evans (1981) which we shall call interacting boson models-3 and -4. Although, in principle, one should repeat for these models the entire discussion of Parts I and II, we shall confine ourselves to a brief account only, since most properties of the interacting boson models-3 and -4 can be deduced from those of the models-1 and -2.

The interacting boson model-3

This model is devised to describe the situation in light nuclei, where protons and neutrons occupy the same orbits, Fig. 7.1. Elliott and White (1980) have suggested that in order to treat the isospin degree of freedom properly, one must introduce in these nuclei a third boson, called δ, formed by a proton–neutron (pn) pair, in addition to those of the interacting boson model-2, called π and ν, formed by proton–proton (pp) and neutron–neutron (nn) pairs. The new bosons, with angular momenta and parities J^P = 0⁺ and J^P = 2⁺, will be denoted by s_δ, d_δ.