Relationship between the Bohr Collective Hamiltonian and the Interacting-Boson Model

The version of the interacting-boson model (IBM) which treats neutrons and protons symmetrically can be converted into a Bohr Hamiltonian description in three steps: (1) Mapping the IBM pairing bosons onto a quadrupole particle-hole-type boson under a generalized Holstein-Primakoff transformation; (2) introduction of pseudocanonical coordinates and momenta; (3) expansion in powers of the pseudomomenta, valid for large particle numbers. The limiting symmetries of the IBM emerge directly from a study of the potential-energy surface.