Effect of breakup processes on the near-barrier elastic scattering of the ${}^{6,7}$Li + ${}^{232}$Th systems

Elastic scattering angular distribution measurements of the weakly bound ${}^{6,7}$Li projectiles on a ${}^{232}$Th target have been carried out at different bombarding energies close to the Coulomb barrier. The data have been analyzed for both systems using the optical model ecis code with phenomenological Woods-Saxon and Sao Paulo double-folding forms of the optical potentials. The energy dependence of the volume-type real and imaginary parts of the optical potentials are derived from the best fit of the experimental angular distribution data. The usual threshold anomaly has been observed for the ${}^7$Li + ${}^{232}$Th system, whereas there is an indication of a breakup threshold anomaly in case of the ${}^6$Li + ${}^{232}$Th system. Results on total reaction cross sections obtained from the optical model analysis for both systems have been interpreted to understand the role of projectile breakup on the reaction mechanism.

Figure 1

A typical two-dimensional $\Delta E$ vs $E_{\mathrm{res}}$ spectrum for the ${}^7$Li + ${}^{232}$Th system at $E_{\mathrm{lab}}=44$ MeV and ${\theta }_{\mathrm{lab}}$ = 60${}^{\circ }$. The projection of the ${}^7$Li elastic peak of the bi-parametric $\Delta E$ vs $E_{\mathrm{res}}$ spectrum is shown in the inset.

Figure 2

Experimental elastic scattering cross section (${\sigma }_{El}$) normalized to the Rutherford cross section (${\sigma }_{\mathrm{Ruth}}$) as a function of ${\theta }_{\mathrm{c}.\mathrm{m}.}$ for the ${}^7$Li + ${}^{232}$Th system (solid circles) (suitably scaled up for each energy) and their best fits from optical model calculations (solid lines). The curves correspond to the best fits obtained by using the ecis code.

Figure 3

Experimental elastic scattering cross section (${\sigma }_{El}$) normalized to the Rutherford cross section (${\sigma }_{\mathrm{Ruth}}$) as a function of ${\theta }_{\mathrm{c}.\mathrm{m}.}$ for the ${}^6$Li + ${}^{232}$Th system (solid circles) (suitably scaled up for each energy) and their best fits from optical model calculations (solid lines). The curves correspond to the best fits obtained by using the ecis code.

Figure 4

Several potentials that produce similar fits of the data, for 44 MeV. The crossing point are the derived real (a) and imaginary (b) sensitivity radii.

Figure 5

Energy dependence of the real and imaginary potentials at $R_s=12.14$ fm and 11.27 fm for ${}^6$Li + ${}^{232}$Th and ${}^7$Li + ${}^{232}$Th systems, respectively. The straight line segments represent various fits of imaginary potential $W\left(E\right);$ the corresponding curves for real potential $V\left(E\right)$ were obtained from these by using the dispersion relation. Panels (a) and (b) correspond to the real and imaginary potential curves for the ${}^7$Li + ${}^{232}$Th system, whereas (c) and (d) represent the ${}^6$Li + ${}^{232}$Th system.

Figure 6

Energy dependence of the normalization factors $N_R$ and $N_I$, for the real and imaginary potentials, corresponding to the Sao Paulo potential with two free parameters, for the ${}^6$Li + ${}^{232}$Th and ${}^7$Li + ${}^{232}$Th systems. The lines represent possible behaviors of $N_R$ and $N_I$ that are compatible with the dispersion relation [2, 10]. Panels (a) and (b) correspond to the real and imaginary potential curves for the ${}^7$Li + ${}^{232}$Th system, whereas (c) and (d) represent the ${}^6$Li + ${}^{232}$Th system.

Figure 7

The total fusion cross sections (${\sigma }_{\mathrm{fus}}$) calculated by ccfull and total reaction cross sections (${\sigma }_R$) for the ${}^{6,7}$Li + ${}^{232}$Th systems obtained by using (a) the ecis code and (b) the SPP calculation, plotted as a function of the bombarding energy. The total fission cross sections (${\sigma }_{\mathrm{fis}}$) [33] and the total fusion cross sections for the ${}^{6,7}$Li + ${}^{232}$Th systems are plotted in (c).

Figure 8

Reduced total reaction cross section vs reduced projectile energy for the ${}^{6,7}$Li + ${}^{232}$Th reactions using the prescription given in Ref. [40].