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Deriving an interacting boson model from the fermion SO(8) model.

To see how closely an interacting-boson-model-like model can be approached, we systematically develop a similarity transformation that unitarizes the simple correspondence version of the Dyson boson mapping of the Ginocchio SO(8) model. For a large region of Hamiltonian parameter space, a one-body plus two-body Hermitian boson Hamiltonian of the interacting-boson-model form is achieved. The similarity transformation consists of a dynamical part and a normalizing part. The dynamical transformation results in a one-body plus two-body Hermitian Hamiltonian and simple transition operators. The normalizing transformation commutes with the dynamically transformed Hamiltonian. This enables the transition rates to be calculated without introducing dual bases. However, the resulting boson model differs from the phenomenological interacting boson model in that transition rates are not calculable from the absolute squares of matrix elements. Dynamically transformed operators are given explicitly, and normalizing transformations for SO(6) and seniority limits are obtained in closed form.