Fusion reaction of a weakly bound nucleus with a deformed target

We discuss the role of deformation of the target nucleus in the fusion reaction of the ${}^{15}\mathrm{C}+{}^{232}\mathrm{Th}$ system at energies around the Coulomb barrier, in which ${}^{15}\mathrm{C}$ is a well-known one-neutron halo nucleus. To this end, we construct the potential between ${}^{15}\mathrm{C}$ and ${}^{232}\mathrm{Th}$ with the double folding procedure, assuming that the projectile nucleus is composed of the core nucleus, ${}^{14}\mathrm{C}$, and a valence neutron. In addition, we also take into account the coupling to the one-neutron transfer process to the ${}^{14}\mathrm{C}+{}^{233}\mathrm{Th}$ configuration. We show that such calculation simultaneously reproduces the fusion cross sections for the ${}^{14}\mathrm{C}+{}^{232}\mathrm{Th}$ and the ${}^{15}\mathrm{C}+{}^{232}\mathrm{Th}$ systems, implying an important role of the transfer coupling in fusion of neutron-rich nuclei.

Figure 1

Fusion cross sections for the ${}^{14}\mathrm{C}+{}^{232}\mathrm{Th}$ system. The dashed line denotes cross sections in the absence of the deformation effect of the target nucleus ${}^{232}\mathrm{Th}$ while the solid line is obtained by taking into account the deformation effect with a deformed Woods-Saxon potential. The experimental data are taken from Ref. [30].

Figure 2

The density distribution of the ${}^{15}\mathrm{C}$ nucleus (the solid line). The dashed and the dot-dashed lines denote the contributions of the core nucleus and the valence neutron, respectively.

Figure 3

The potential between the valence neutron in ${}^{15}\mathrm{C}$ and the target nucleus ${}^{232}\mathrm{Th}$ for the ${}^{15}\mathrm{C}+{}^{232}\mathrm{Th}$ reaction. The top, the middle, and the bottom panels are for $V_0\left(r\right), V_2\left(r\right)$, and $V_4\left(r\right)$ in Eq. (9), respectively. The black solid lines show the results of the double folding potential, while the red dashed lines show fits with the Woods-Saxon function.

Figure 4

The total potentials (the sum of the nuclear and the Coulomb potentials) for the ${}^{14}\mathrm{C}+{}^{232}\mathrm{Th}$ and ${}^{15}\mathrm{C}+{}^{232}\mathrm{Th}$ systems for $\theta =0^{\circ }$ and $\theta ={90}^{\circ }$. The solid and the dotted lines are for the ${}^{15}\mathrm{C}+{}^{232}\mathrm{Th}$ system, for which the solid line corresponds to $\theta =0^{\circ }$ and the dashed line corresponds to $\theta ={90}^{\circ }$. The dashed and the dot-dashed lines are the same as the solid and the dotted lines, but for the ${}^{14}\mathrm{C}+{}^{232}\mathrm{Th}$ system.

Figure 5

Fusion cross sections for the ${}^{15}\mathrm{C}+{}^{232}\mathrm{Th}$ system. The dot-dashed line shows fusion cross sections obtained by scaling the potential for the ${}^{14}\mathrm{C}+{}^{232}\mathrm{Th}$ system with the mass number of the colliding nuclei. The dotted line shows fusion cross sections with the double folding potential, which takes into account the halo structure of the ${}^{15}\mathrm{C}$ nucleus, while the solid line shows the result of the coupled-channels calculation with the transfer coupling. For comparison, the figure also shows the theoretical fusion cross sections for the ${}^{14}\mathrm{C}+{}^{232}\mathrm{Th}$ system by the dashed line. The experimental data are taken from Ref. [30].