With an improved Boltzmann-Uehling-Uhlenbeck model, the deformation en
ergy surfaces in reactions leading to the formation of toroidal and bu
bble nuclei are examined for central Mo-92+Mo-92 collisions. We found
that the potential maximum, or the fragmentation barrier, occurs at ti
mes close to the times when these exotic shapes are formed. However, d
ue to the dynamics of large amplitude compression and expansion, the f
ragmentation barriers are significantly higher than those estimated fr
om the liquid-drop models.