On the relation between the interacting boson model of Arima and Iachello and the collective model of Bohr and Mottelson

The generator coordinate method is used to relate the interacting boson model of Arima and Iachello and the collective model of Bohr and Mottelson through an isometric transformation. It associates complex parameters to the original boson operators whereas the ultimate collective variables are real. The absolute squares of the collective wave functions can be given a direct probability interpretation. The lowest order Bohr-Mottelson hamiltonian is obtained in the harmonic approximation to the interacting boson model; anharmonic coupling terms render the collective potential to be velocity-dependent.