Abstract
In the past, several schematic nuclear models have been proposed with the symmetry of the Lie algebra SO(5). We derive a set of mappings from the shell model spaces in which these models are defined to suitable boson spaces. The derivations are carried out by two distinct algebraic methods, which are customarily associated with the names Holstein-Primakoff and Dyson, respectively. The relative utility of the two is seen to depend on the particular mapping. The mappings are useful for the study of the collective properties of the various models and of generalizations of each of them. This is illustrated with one of the models. Some algebraic details, some ideas concerning schematic model building, and an extension of the results of this paper are presented in appendices.
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