Exactly solvable pairing plus mean field model

A mean-field plus extended pairing interaction Hamiltonian that includes multi-pair scattering terms is proposed for describing well-deformed nuclei. Eigenvalues of the model are easily obtained. The investigation shows that even through the extended pairing includes many-body terms, the one- and two-body interactions continue to dominate the dynamics for relatively small values of the pairing strength. As the strength of the pairing interaction grows, however, the higher many-body interaction terms grow in importance. A numerical study of even-odd mass differences in the Yb154-171 isotopes demonstrates the applicability of the theory.