Introduction

Another set of degrees of freedom neglected in the interacting boson models -1 and -2 is that of pairs with values of the angular momenta different from 0 and 2 (s and d bosons). We discuss briefly in this chapter those versions of the model which include other pairs. We note that from microscopic considerations, it appears to be important to include JP = 4+ pairs in strongly deformed nuclei. The effects of 4+ pairs (G-pairs) can often be introduced as a renormalization (Otsuka and Ginocchio, 1985) of the parameters of the interacting boson models-1 and -2; for certain properties explicit inclusion of JP = 4+ bosons (g bosons) may be necessary. The corresponding models will be denoted by interacting boson models-1G and -2G.

From another side, negative-parity collective states appear in the spectra of nuclei at an excitation energy ~ 1 MeV. Some of these states can be described by introducing JP = 3- pairs (F-pairs). The effects of these pairs can be taken into account by means of JP = 3- bosons (f bosons). The corresponding models will be denoted by interacting boson models-1F and -2F.

Finally, the presence of subshell gaps in the shell-model levels may cause the occurrence of excited modes with angular momenta JP = 0+ and 2+ which we denote by S′ and D′ and describe by s′ and d′ bosons.