Exact solutions of Nilsson mean-field plus various type of pairing interactions are briefly reviewed. Some even-odd mass differences and moment of inertia of low-lying states for rare earth and actinide nuclei calculated in nearest-orbit pairing and extended pairing models and comparison with the corresponding experimental data are shown. An exact boson mapping of the reduced BCS pairing Hamiltonian is reported. In the mapping, fermion pair operators are mapped exactly to the corresponding bosons. The image of the mapping results in a Bose-Hubbard model with level dependent hopping.

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MEAN-FIELD PLUS VARIOUS TYPES OF PAIRING INTERACTIONS AND AN EXACT BOSON MAPPING OF THE REDUCED BCS PAIRING INTERACTION

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