Elastic scattering and total reaction cross sections for the ${}^8\mathrm{Li}+{}^{12}\mathrm{C}$ system

The elastic-scattering angular distribution for ${}^8\mathrm{Li}$ on ${}^{12}\mathrm{C}$ has been measured at $E_{\mathrm{LAB}}=23.9$ MeV with ${}^8\mathrm{Li}$ radioactive nuclear beam produced by the Radioactive Ion Beams in Brazil facility. This angular distribution was analyzed in terms of optical-model with Woods-Saxon and double-folding São Paulo potential. The roles of the breakup and inelastic channels were also investigated with cluster folding and deformed potentials, respectively, through coupled-channels calculations. The angular distribution for the proton-transfer ${}^{12}\mathrm{C}({}^8\mathrm{Li},{}^9\mathrm{Be}){}^{11}\mathrm{B}$ reaction was also measured at the same energy. The spectroscopic factor for the $\langle {}^9\mathrm{Be}|{}^8\mathrm{Li}+p\rangle$ bound system was obtained and compared with shell-model calculations and with other experimental values. Total reaction cross sections for the present system were also extracted from the elastic-scattering analysis. A systematic of the reduced reaction cross sections obtained from the present and published data on ${}^{6,7,8}\mathrm{Li}$ isotopes on ${}^{12}\mathrm{C}$ was performed as a function of energy.

Figure 1

Selected particle identification spectrum [$\Delta E\times E_{\mathrm{total}}$] for the interaction of ${}^8\mathrm{Li}$$+({\mathrm{CH}}_2+\mathrm{Au}$) at $E_{\mathrm{LAB}}=23.9$ MeV measured at ${25}^{°}$. The elastic scattering (${}^8\mathrm{Li}$) and reaction product ${}^9\mathrm{Be}$ are indicated as are the ${}^4\mathrm{He}$, ${}^7\mathrm{Li}$${}^{++}$, and ${}^6\mathrm{He}$ contamination in the secondary beam.

Figure 2

The differential cross sections for elastic scattering (${}^{12}\mathrm{C}$(${}^8\mathrm{Li}$,${}^8\mathrm{Li}$)${}^{12}\mathrm{C}$) at 23.9-MeV incident laboratory energy. The curves are optical-model calculations with the sets of parameters listed in Table . The curve for the São Paulo potential is smeared out by the angular aperture of the detectors.

Figure 3

The differential cross sections for elastic scattering ${}^{12}\mathrm{C}$(${}^8\mathrm{Li}$,${}^8\mathrm{Li}$)${}^{12}\mathrm{C}$ at 23.9-MeV incident laboratory energy. The dashed curve is an optical-model potential with parameters given by WS in Table . The dotted curve is the cluster-folding parametrization of the interaction without the couplings to the continuum while the solid line is the result of the coupling.

Figure 4

The differential cross sections for elastic scattering ${}^{12}\mathrm{C}$(${}^8\mathrm{Li}$,${}^8\mathrm{Li}$)${}^{12}\mathrm{C}$ at 23.9-MeV incident laboratory energy. The dotted curve is an optical-model calculation with SP potential. The dashed curve is the coupled-channels calculation with only the $2^{+}$ first excited state in ${}^{12}\mathrm{C}$ and the solid line is the coupled-channels calculation including also the $1^{+}$ first excited state in ${}^8\mathrm{Li}$. The dotted-dashed curve is the prediction of the inelastic scattering including both first excited states in ${}^8\mathrm{Li}$ and ${}^{12}\mathrm{C}$.

Figure 5

Angular distribution for the ${}^{12}\mathrm{C}$(${}^8\mathrm{Li}$,${}^9\mathrm{Be}$${}_{\mathrm{gs}}$)${}^{11}\mathrm{B}$${}_{\mathrm{gs}}$ proton-transfer reaction at 23.9 MeV incident energy. The curves are indicated in the legend inset. The gray thick line corresponds to experimental error of the spectroscopic factor in the FR-DWBA calculation with SP potential. The curves are smeared out by the angular aperture of the detectors.

Figure 6

The reduced reaction cross sections for the ${}^8\mathrm{Li}+{}^{12}\mathrm{C}$ system obtained in this work together with reduced reaction cross sections of the other lithium isotopes and some weakly bound and tightly bound projectiles on ${}^{12}\mathrm{C}$.