Abstract
An extensive application of the Holstein-Primakoff boson expansion to both single-particle angular momentum and total angular momentum provides an algebraic solution, which gives a good approximation to the exact results for the particle-rotor model with one high-j nucleon coupled to a triaxially deformed core. Two kinds of quantum numbers classify the rotational bands characteristic of the particle-rotor model and lead the selection rules for the interband and intraband transitions. The algebraic solution is compared with the experimental data for the odd mass isotopes $^{163,165,167}\mathrm{Lu}$ as testing grounds.
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