Role of hexadecapole deformation of projectile ${}^{28}\mathrm{Si}$ in heavy-ion fusion reactions near the Coulomb barrier

The vast knowledge regarding the strong influence of quadrupole deformation ${\beta }_2$ of colliding nuclei in heavy-ion sub-barrier fusion reactions inspires a desire to quest the sensitivity of fusion dynamics to higher order deformations, such as ${\beta }_4$ and ${\beta }_6$ deformations. However, such studies have rarely been carried out, especially for deformation of projectile nuclei. In this article, we investigated the role of ${\beta }_4$ of the projectile nucleus in the fusion of the ${}^{28}\mathrm{Si}+{}^{92}\mathrm{Zr}$ system. We demonstrated that the fusion barrier distribution is sensitive to the sign and value of the ${\beta }_4$ parameter of the projectile, ${}^{28}\mathrm{Si}$, and confirmed that the ${}^{28}\mathrm{Si}$ nucleus has a large positive ${\beta }_4$. This study opens an indirect way to estimate deformation parameters of radioactive nuclei using fusion reactions, which is otherwise difficult because of experimental constraints.

Figure 1

A comparison of fusion barrier distributions for the ${}^{28}\mathrm{Si}+{}^{92}\mathrm{Zr}$ system obtained with several coupling schemes for the coupled-channel calculations. The solid line shows the result with the vibrational coupling to the first $2^{+}$ state of ${}^{28}\mathrm{Si}$, along with the vibrational excitation of ${}^{92}\mathrm{Zr}$. The dashed line shows the result of the rotational couplings to the $2^{+}$ state of ${}^{28}\mathrm{Si}$ with deformation parameters of ${\beta }_2=-0.407$ and ${\beta }_4=0.0$. On the other hand, the dashed lines with triangles and crosses are obtained with ${\beta }_2=+0.407$ and ${\beta }_2=-0.407$, respectively, together with ${\beta }_4=0.1$. The experimental data, taken from Ref. [17], are shown with filled circles.

Figure 2

The fusion barrier distribution for the ${}^{28}\mathrm{Si}+{}^{92}\mathrm{Zr}$ system obtained with the rotational coupling scheme for ${}^{28}\mathrm{Si}$ with ${\beta }_2=-0.407$ and ${\beta }_4=0.25$ (the dashed line with triangles) and with ${\beta }_2=-0.407$ and ${\beta }_4=-0.25$ (the dotted line). The meaning of the solid line is the same as in Fig. 1.

Figure 3

A comparison of fusion barrier distributions for the ${}^{28}\mathrm{Si}+{}^{92}\mathrm{Zr}$ system obtained with the rotational coupling scheme with a truncation of the ground-state rotational band of ${}^{28}\mathrm{Si}$ at the $2^{+}$ state (the solid line) and at the $4^{+}$ state (the dashed line with stars) in the coupled-channel calculations.