Effects of ${\beta }_6$ deformation and low-lying vibrational bands on heavy-ion fusion reactions at sub-barrier energies

We study fusion reactions of ${}^{16}\mathrm{O}$ with ${}^{154}\mathrm{Sm},$ ${}^{186}\mathrm{W},$ and ${}^{238}\mathrm{U}$ at sub-barrier energies by a coupled-channels framework. We focus especially on the effects of ${\beta }_6$ deformation and low-lying vibrational excitations of the target nucleus. It is shown that the inclusion of ${\beta }_6$ deformation leads to a considerable improvement of the fit to the experimental data for all of these reactions. For the ${}^{154}\mathrm{Sm}$ and ${}^{238}\mathrm{U}$ targets, the octupole vibration significantly affects the fusion barrier distribution and the optimum values of the deformation parameters. The effect of $\beta$ band is negligible in all the three reactions, while the $\gamma$ band causes a non-negligible effect on the barrier distribution at energies above the main fusion barrier. We compare the optimum values of the deformation parameters obtained by fitting the fusion data with those obtained from inelastic scatterings and the ground state mass calculations. We show that the channel coupling of high multipolarity beyond the quadrupole coupling is dominated by the nuclear coupling and hence higher order Coulomb coupling does not much influence the optimum values of ${\beta }_4$ and ${\beta }_6$ parameters. We also discuss the effect of two neutron transfer reactions on the fusion of ${}^{16}\mathrm{O}$ with ${}^{238}\mathrm{U}.$