IBM hamiltonian, Bohr collective hamiltonian and classical limit for an exactly soluble model with the symmetry of O(5)

Interacting boson model (IBM), Bohr collective hamiltonian and adiabatic collective model descriptions are derived from a shell model (describing pairing plus two-dimensional quadrupole-quadrupole interactions) with the symmetry of the Lie algebra O(5). The tools utilized for these purposes are three boson mappings from the fermion pair space, two exact and one approximate. Adiabatic descriptions are derived by two distinct methods. The extension of the methods of this paper to more realistic models is outlined.