Model calculations using boson mappings

The shell-model fermion problem for systems of four protons and four neutrons in single-j shells is transformed into a boson problem using the generalized Dyson boson mapping. Exact boson calculations are performed. The spectrum of physical and nonphysical boson states and the effect of truncation in the boson space are studied. The necessity of transformation from the Dyson boson description to the seniority boson description is demonstrated within the truncated space.