Abstract
It is shown that under some conditions the operators of the Quasiparticle Phonon Nuclear Model (QPM) and their commutators close the SU (m) algebra and the graded SU (m/n) algebra, respectively, for even-even and odd-even nuclei. The SU (m/n) generators and their matrix representation are then derived from the QPM operators. The generalized Dyson realization for the QPM operators is obtained. Microscopic expressions for the parameters of the IBM-1 and IBFM-1 Hamiltonians are derived.
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