Influence of higher-order deformations in the ${}^{34}\mathrm{S}{+}^{168}\mathrm{Er}$ fusion reaction

The shape of the measured barrier distribution for the ${}^{34}\mathrm{S}{+}^{168}\mathrm{Er}$ reaction is analyzed using the coupled-channels description. The ${}^{168}\mathrm{Er}$ nucleus is a good candidate to test current fusion models description of deformation since it has a large quadrupole deformation with an insignificant hexadecapole deformation. Coupling to weaker channels, the $2_1^{+}$ state in ${}^{34}\mathrm{S},$ the $3_1^{-}$ state in ${}^{168}\mathrm{Er},$ and the pair neutron transfer channel, all were found to have little influence on the barrier distribution. A successful description of the barrier distribution was only obtained after the hexacontatetrapole deformation term in ${}^{168}\mathrm{Er}\hspace{0.5em}\left({\beta }_6^T\right)$ was included in the coupling scheme. However, a positive value for ${\beta }_6^T$ was needed where the macroscopic-microscopic model predicts a negative one.