Suppression of the elastic scattering cross section for the ${}^{17}\mathrm{Ne}+{}^{208}\mathrm{Pb}$ system

We investigated the elastic scattering, inelastic scattering, breakup reactions, and total fusion reactions of the ${}^{17}\mathrm{Ne}+{}^{208}\mathrm{Pb}$ system using the extended optical model (OM) and a coupled channel (CC) approach. The aim of this study is to elucidate the suppression of the elastic cross section that is invisible in proton-rich nuclei, such as ${}^8\mathrm{B}$ and ${}^{17}\mathrm{F}$ projectiles, but appears in neutron-rich nuclei, such as ${}^{11}\mathrm{Li}$ and ${}^{11}\mathrm{Be}$ projectiles. The simultaneous ${\chi }^2$ analysis of the ${}^{17}\mathrm{Ne}+{}^{208}\mathrm{Pb}$ system revealed that this suppression was primarily caused by the nuclear interaction between the projectile and the target nucleus, rather than the strong Coulomb interaction observed in neutron-rich nuclei. Moreover, the contributions of the Coulomb excitation interaction due to the two low-lying $E2$ resonance states were relatively small. In addition, the contribution of the direct reaction, comprising the inelastic scattering and breakup reaction cross sections, accounted for almost half of the total reaction cross section. Finally, we performed the CC calculation using the parameters obtained from the OM calculation; however, the present CC calculations could not properly explain the ${}^{15}\mathrm{O}$ production cross section.

Figure 1

Bare potentials for the ${}^{17}\mathrm{Ne}+{}^{208}\mathrm{Pb}$ system. The dashed red line shows the SPP made using nuclear densities for both ${}^{17}\mathrm{Ne}$ and ${}^{208}\mathrm{Pb}$ nuclei. The solid black line represent a newly parametrized SPP potential in the Woods-Saxon form, obtained through the ${\chi }^2$ fitting. The dotted blue and dash-dotted green lines represent the potentials, respectively, as provided by Akyuz-Winther [26] and Ref. [17].

Figure 2

(a) $P_{\text{el}}$ ratios and (b) angular distributions of the breakup (${}^{15}\mathrm{O}$ production) cross section for the ${}^{17}\mathrm{Ne}+{}^{208}\mathrm{Pb}$ system. The dashed blue and solid black lines denote the theoretical ratios $P_{\text{el}}$ and angular distributions using the parameter sets (A) and (B) in Table 2, respectively. The solid red circles denote the experimental data at $E_{\text{lab}}=136\mathrm{MeV}$ taken from Ref. [17]. Note that the dotted magenta line indicates $P_{\text{el}}$ ratio only based on the $V_0+U_{\text{F}}$ in Eq. (2), where $U_{\text{F}}$ has been extracted through set (B). To perform these calculations, we used the ${\frac{3}{2}}^{-}$ state [$E_x=1.288\mathrm{MeV}$ and $B\left(E2\right)=41 e^2{\text{fm}}^4$] for the inelastic interaction and the ${\frac{5}{2}}^{-}$ state [$E_x=1.764\mathrm{MeV}$ and $B\left(E2\right)=72 e^2{\text{fm}}^4$] and ${\frac{3}{2}}^{-}$ state [$E_x=2.692\mathrm{MeV}$ and $B\left(E2\right)=59 e^2{\text{fm}}^4$] for the breakup one. Note that these values correspond to the minimum value of $B\left(E2\right)$ introduced in Refs. [17, 18, 19].

Figure 3

Similar to Fig. 2, the graphs show the contribution of each channel. $P_{\text{el}}$ ratios obtained from the (a) single channel and (b) two channel coupling for the ${}^{17}\mathrm{Ne}+{}^{208}\mathrm{Pb}$ system. The dashed blue lines denote the theoretical $P_{\text{el}}$ ratios obtained from $V_0\left(r\right)+U_{\text{F}}\left(r\right)$ potential. In the left panel, the dotted green, dash-dotted magenta, short dashed cyan, and solid black lines represent the $P_{\text{el}}$ ratios when the potential corresponding to each single channel is switched on at $V_0\left(r\right)+U_{\text{F}}\left(r\right)$ potential. Conversely, in the right panel, the dotted green, dash-dotted magenta, short dashed cyan, and solid black lines represent the $P_{\text{el}}$ ratios when the potential corresponding to two channel coupling is switched on at $V_0\left(r\right)+U_{\text{F}}\left(r\right)$ potential.

Figure 4

Similar to Fig. 2, the graphs show the results of the CC calculations. The dashed blue and solid black lines represent the theoretical angular distribution of the breakup cross sections obtained from the CC calculations using sets (A) and (B) with two nuclear deformation lengths (${\delta }_1+{\delta }_2$) in Table 2, respectively. The dotted magenta and short-dotted violet lines represent those obtained from the CC calculations using the set (B) with double and quadruple of two nuclear deformation lengths, respectively.