Second-order perturbation theory is used to examine the effect of excluding the g boson from the model space of the interacting boson model. Perturbative corrections are calculated in a paired fermion space (in a single $j$-shell approximation) and are mapped onto the interacting boson model Hamiltonian using the imaging techniques of Otsuka, Arima, and Iachello. The resulting renormalization of the boson parameters of the Hamiltonian to account for effects of the $g$ boson depends strongly upon the numbers of valence protons and neutrons, and remains significant throughout the half shell.

NUCLEAR STRUCTURE Interacting boson model, $g$ boson, microscopic calculation using perturbation theory, renormalization of boson parameters.

• Received 1 March 1982

DOI:https://doi.org/10.1103/PhysRevC.26.668