The recent accurate measurements of fusion cross sections at subbarrie
r energies have enabled extraction of barrier distributions which coul
d provide a novel test for collective models. We carry out a systemati
c study of subbarrier fusion in rare-earth nuclei using a scheme which
incorporates the interacting boson model for nuclear structure effect
s. The existing data on vibrational and rotational nuclei are fitted w
ith a consistent set of parameters which are then used to predict the
fusion cross sections and distribution of barriers in transitional nuc
lei. Contrary to vibrational and rotational nuclei where the cross sec
tions increase smoothly with increasing deformation or mass number, tr
ansitional nuclei exhibit sharp changes in the barrier distribution du
e to shape-phase transitions. An accurate measurement of fusion cross
sections for Pt and Os nuclei could thus provide a sensitive test for
competing models in this region.