Analysis of elastic, quasielastic, and inelastic scattering of lithium isotopes on a ${}^{28}\mathrm{Si}$ target

The elastic and inelastic cross sections of ${}^6\mathrm{Li}$ on ${}^{28}\mathrm{Si}$ at 240 MeV, and quasielastic cross section of ${}^7\mathrm{Li}$ and ${}^{11}\mathrm{Li}$ on ${}^{28}\mathrm{Si}$ at $177.8$ and 319 MeV, respectively, are analyzed with the coupled-channels method. The collective nuclear level density is used to determine the deformation parameter regarding to the first-excited state of ${}^{28}\mathrm{Si}$. The results are in agreement with the experimental data and indicate the need of using a nuclear structure model such as nuclear level density to reduce the ambiguity between the optical model parameters and the deformation parameter. Additionally, the spin-orbit potential is found to have an important role in reproducing the data of the quasielastic scattering of ${}^7\mathrm{Li}$ and ${}^{11}\mathrm{Li}$ on a ${}^{28}\mathrm{Si}$ target.

Figure 1

The energy of the first-excited state of ${}^{28}\mathrm{Si}$ as a function of deformation parameter.

Figure 2

Angular distribution of the elastic (upper panel) and inelastic (lower panel) cross section for ${}^6\mathrm{Li}+{}^{28}\mathrm{Si}$ scattering at $240\mathrm{MeV}$. The experimental data are taken from Chen et al. [12].

Figure 3

Angular distribution of the elastic cross section for $n+{}^{28}\mathrm{Si}$ scattering at 15.4, 18.9, 21.7, and $25.4\mathrm{MeV}$ compared with the experimental data [53, 54].

Figure 4

Angular distribution of the quasielastic cross section for ${}^7\mathrm{Li}+{}^{28}\mathrm{Si}$ scattering at $177.8\mathrm{MeV}$. The experimental data are taken from Lewitowicz et al. [18].

Figure 5

Angular distribution of the quasielastic cross section for ${}^{11}\mathrm{Li}+{}^{28}\mathrm{Si}$ scattering at $319\mathrm{MeV}$. The experimental data are taken from Lewitowicz et al. [18].