Fusion reactions of ${}^{58,64}\mathrm{Ni}+{}^{124}\mathrm{Sn}$

Measurements of fusion excitation functions of ${}^{58}\mathrm{Ni}+{}^{124}\mathrm{Sn}$ and ${}^{64}\mathrm{Ni}+{}^{124}\mathrm{Sn}$ are extended towards lower energy to cross sections of 1 $\mu \mathrm{b}$ and are compared to detailed coupled-channels calculations. The calculations clearly show the importance of including transfer reactions in a coupled-channels treatment for such heavy systems. This result is different from the conclusion made in a previous article which claimed that the influence of transfer on fusion is not important for fusion reactions of $\mathrm{Ni}+\mathrm{Sn}$. In the energy region studied in this experiment no indication of fusion hindrance has been observed, which is consistent with a systematic study of this behavior.

Figure 1

Cross sections of excitation functions for the system ${}^{58}\mathrm{Ni}+{}^{124}\mathrm{Sn}$ plotted as functions of the c.m. energy. Black circles: Fusion cross sections measured in this experiment. Red triangles and red open triangles: Cross sections of fusion and fusion-fission reactions from Lesko et al. [25]. Green squares and green open squares: Cross sections of fusion and fusion-fission reactions from Wolfs et al. [26]. The red solid line is a fit with the Wong formula to fusion data with cross sections larger than 0.1 mb. The black dashed line represents the average fusion-fission cross sections used to obtain the total capture cross sections.

Figure 2

Cross sections of excitation functions for the system ${}^{64}\mathrm{Ni}+{}^{124}\mathrm{Sn}$ plotted as functions of the c.m. energy. Black circles: Fusion cross sections measured in this experiment. Red triangles and red open triangles: Cross sections of fusion and fusion-fission reactions from Lesko et al. [25]. The red solid line is a fit with the Wong formula to fusion data with cross sections larger than 0.1 mb. The black dashed line represents the average fusion-fission cross sections used to obtain the total capture cross sections.

Figure 3

Fusion excitation functions for various $\mathrm{Ni}+\mathrm{Sn}$ systems plotted as functions of $E-V_C$ where $E$ is the c.m. energy and $V_C$ is the Coulomb barrier taken from Table 1. The curves are fits to the Wong formula. Insert: Average excitation energies of neutron pickup reactions calculated from the $Q$-value systematics for the same systems. Except for the systems ${}^{58,64}\mathrm{Ni}+{}^{124}\mathrm{Sn}$ the cross sections are identical to the ones shown in Figs. 3(c) and 3(d) of Ref. [21].

Figure 4

(a) Plot of the energy $E_s$, where a maximum of the $S$ factor is observed versus $\zeta$ [=$Z_1{Z}_2\sqrt{A_1{A}_2/(A_1+A_2)}$]. The dot-dashed line is from Eq. (2). (b) Plot of the fusion cross sections ${\sigma }_s$ measured at $E_s$ as a function of $\zeta$ for the same systems shown in Fig. 4(a). The two lines give the range of ${\sigma }_s$. Neutron-deficient (closed-shell) systems are concentrated towards larger ${\sigma }_s$ values while neutron-rich systems have smaller values of ${\sigma }_s$. The green symbols are the values of $E_s$ and ${\sigma }_s$ expected for the ${}^{58,64}\mathrm{Ni}+{}^{124}\mathrm{Sn}$ systems. See text for details.

Figure 5

Coupled-channels calculations for the fusion reaction ${}^{58}\mathrm{Ni}+{}^{124}\mathrm{Sn}$ as a function of the c.m. energy, covering the full energy range.

Figure 6

Coupled-channels calculations for the fusion reaction ${}^{64}\mathrm{Ni}+{}^{124}\mathrm{Sn}$ as a function of the c.m. energy, covering the full energy range.

Figure 7

Coupled-channels calculations for the fusion reaction ${}^{58}\mathrm{Ni}+{}^{124}\mathrm{Sn}$ in the sub-barrier energy region.

Figure 8

Coupled-channels calculations for the fusion reaction ${}^{64}\mathrm{Ni}+{}^{124}\mathrm{Sn}$ in the sub-barrier energy region.