Phenomenological analysis of the interacting boson model

The classical Hamiltonian of the interacting boson model is defined and expressed in terms of the conventional quadrupole variables. This is used in the analyses of the dynamics in the various limits of the model. The purpose is to determine the range and the features of the collective phenomena which the interacting boson model is capable of describing. In the commonly used version of the interacting boson model with one type of the $s$ and $d$ bosons and quartic interactions, this capability has certain limitations and the model should be used with care. A more sophisticated version of the interacting boson model with neutron and proton bosons is not discussed.