Applicability of the orientation average formula in heavy-ion fusion reactions of deformed nuclei

In heavy-ion fusion reactions involving a well-deformed nucleus, one often assumes that the orientation of the target nucleus does not change during the reaction. We discuss the accuracy of this procedure by analyzing the excitation function of the fusion cross section and the fusion barrier distribution in the reactions of ${}^{154}\mathrm{Sm}$ target with various projectiles ranging from ${}^{12}\mathrm{C}$ to ${}^{40}\mathrm{Ar}.$ It is shown that the approximation gradually loses its accuracy with increasing charge product of the projectile and target nuclei because of the effects of finite excitation energy of the target nucleus. The relevance of such inaccuracy in analyzing the experimental data is also discussed.