An infinite-dimensional algebraic approach is introduced to derive exact particle-number conserving solutions of the nuclear mean-field plus orbit-dependent pairing Hamiltonian. As an example, exact solutions of a model Hamiltonian for ds-shell nuclei are compared with shell-model and equal strength pairing calculations for isotopes.
Exact solution of the nuclear mean-field plus separable pairing model is reexamined. New auxiliary constraints for solving the Bethe ansatz equations of the model are proposed. By using these auxiliary constraints, the Bethe ansatz form of eigenvectors of the mean-field plus separable pairing Hamiltonian with nondegenerate single-particle energies and nondegenerate separable pairing strengths purposed previously is verified. Since the solutions of the model with one- and two-orbit cases are known, verification of the solutions for these two special cases is made. To demonstrate structure and features of the solution, the model with three orbits in the ds shell is taken as a nontrivial example, of which two-pair results and the ground state of the three-pair case are provided explicitly. Since the number of equations involved increases with the number of orbits and pairs, to solve these equations for a large number of orbits and pairs seems still difficult.
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.