Fermion dynamical symmetry and the nuclear shell model

The interacting boson model (IBM) has been very successful in giving a unified and simple description of the spectroscopic properties of a wide range of nuclei, from vibrational through rotational nuclei. The three basic assumptions of the model are that 1) the valence nucleons move about a doubly closed core, 2) the collective low-lying states are composed primarily of coherent pairs of neutrons and pairs of protons coupled to angular momentum zero and two and 3) these coherent pairs are approximated as bosons. In this review the authors shall show how it is possible to have fermion Hamiltonians which have a class of collective eigenstates composed entirely of monopole and quadrupole pairs of fermions. Furthermore the fermion shell model states excluded in the IBM can be classified by the number of fermion pairs which are not coherent monopole or quadrupole pairs. Hence the mixing of these states into the low-lying spectrum can be calculated in a systematic and tractable manner. Thus they can introduce features which are outside the IBM