Effect of channel coupling on the elastic scattering of lithium isotopes

Herein, we investigated the channel coupling (CC) effect on the elastic scatterings of lithium (Li) isotopes ($A=6$–9) for ${}^{12}\mathrm{C}$ and ${}^{28}\mathrm{Si}$ targets at $E/A=50$–60 MeV. The wave functions of the Li isotopes were obtained using the stochastic multi-configuration mixing method based on the microscopic-cluster model. The proton radii of the ${}^7\mathrm{Li}$, ${}^8\mathrm{Li}$, and ${}^9\mathrm{Li}$ nuclei became smaller as the number of valence neutrons increased. The valence neutrons in the ${}^8\mathrm{Li}$ and ${}^9\mathrm{Li}$ nuclei exhibited a glue-like behavior, thereby attracting the $\alpha$ and $t$ clusters. Based on the transition densities derived from these microscopic wave functions, the elastic-scattering cross section was calculated using a microscopic coupled-channel method with a complex $G$-matrix interaction. The existing experimental data for the elastic scatterings of the Li isotopes and ${}^{10}\mathrm{Be}$ nuclei were well reproduced. The Li isotope elastic cross sections were demonstrated for the ${}^{12}\mathrm{C}$ and ${}^{28}\mathrm{Si}$ targets at $E/A=53$ MeV. The glue-like effect of the valence neutrons on the Li isotope was clearly demonstrated by the CC effect on elastic scattering. Finally, we realize that the valence neutrons stabilized the bindings of the core parts and the CC effect related to core excitation was indeed reduced.

Figure 1

Excitation energy of the experimental data and calculated results for the Li isotopes. The experimental data are taken from a previous study [51].

Figure 2

Elastic cross section for the ${}^6\mathrm{Li}+{}^{12}\mathrm{C}$ system at $E/A=53$ MeV. The experimental data are taken from a previous study [58].

Figure 3

Same as Fig. 2 but for the ${}^{28}\mathrm{Si}$ target.

Figure 4

Elastic cross section for the ${}^7\mathrm{Li}+{}^{12}\mathrm{C}$ system at $E/A=50$ MeV. The experimental data are taken from a previous study [59].

Figure 5

Same as Fig. 4 but for the ${}^{28}\mathrm{Si}$ target.

Figure 6

Quasi-elastic cross section for the ${}^9\mathrm{Li}+{}^{12}\mathrm{C}$ system at $E/A=60$ MeV. The experimental data are taken from a previous study [60].

Figure 7

Elastic cross section for the ${}^{10}\mathrm{Be}+{}^{12}\mathrm{C}$ and ${}^9\mathrm{Li}+{}^{12}\mathrm{C}$ systems at $E/A=59.4$ MeV. The experimental data for the ${}^{10}\mathrm{Be}+{}^{12}\mathrm{C}$ system are taken from previous research [61, 62].

Figure 8

Elastic scattering of the ${}^7\mathrm{Li}$, ${}^8\mathrm{Li}$, and ${}^9\mathrm{Li}$ nuclei for the ${}^{12}\mathrm{C}$ target at $E/A=53$ MeV.

Figure 9

Same as Fig. 8 but for the ${}^{28}\mathrm{Si}$ target.