The microscopic structure and group theory of the interacting boson model

The chains of groups used in calssifying states of the IBM are compared with the chains used in a composite model with j = 3/2 fermion pairs. Many similarities are found, along with differences due to Pauli principle effects in continuum fermion pairs. The classifications are shown to be characterized by several different seniority numbers, which are physically similar but formally different in the two cases because fermion pair and boson pair states used to define seniority in each model correspond to single bosons and four-fermion clusters, respectively, in the other model. The SO(6) and SO(5) groups which define boson pair seniorities in the boson sextet model are isomorphic, respectively, to SU(4) and Sp(4) which have simple physical interpretations in fermion quartet models. (orig.)