Breakup and $n$-transfer effects on the fusion reactions ${}^{6,7}\mathrm{Li}+{}^{120,119}\mathrm{Sn}$ around the Coulomb barrier

This paper presents values of complete fusion cross sections deduced from activation measurements for the reactions ${}^6\mathrm{Li}+{}^{120}\mathrm{Sn}$ and ${}^7\mathrm{Li}+{}^{119}\mathrm{Sn}$, and for a projectile energy range from 17.5 to 28 MeV in the center-of-mass system. A new deconvolution analysis technique is used to link the basic activation data to the actual fusion excitation function. The complete fusion cross sections above the barrier are suppressed by about $70\%$ and $85\%$ with respect to the universal fusion function, used as a standard reference, in the ${}^6\mathrm{Li}$ and ${}^7\mathrm{Li}$ induced reactions, respectively. From a comparison of the excitation functions of the two systems at energies below the barrier, no significant differences can be observed, despite the two systems have different $n$-transfer $Q$ values. This observation is supported by the results of coupled reaction channels (CRC) calculations.

Figure 1

Sketch of the experimental setup for the activation procedure. The beam passes through a thin Au foil in order to monitor the beam current using Rutherford scattering. A catcher foil follows the Sn target in order to stop recoiling evaporation residuals.

Figure 2

X-ray spectra measured offline, 20 minutes, 13 hours and 5 days after the end of the irradiation, for the reaction ${}^6\mathrm{Li}+{}^{120}\mathrm{Sn}$ at 25 MeV. Together with the $k_{\alpha }$ and $k_{\beta }$ x-rays emitted in the EC decay of iodine produced in the CF reactions, it is possible to distinguish the x-rays emitted in the EC decay antimony produced in reactions with the target. See text for details.

Figure 3

Typical activity curves (a) for the ${}^6\mathrm{Li}+{}^{120}\mathrm{Sn}$ reaction and (b) for the ${}^7\mathrm{Li}+{}^{119}\mathrm{Sn}$ reaction. The continuous line is the best fit of the activity curve.

Figure 4

ER production yields for ${}^6\mathrm{Li}+{}^{120}\mathrm{Sn}$ at three different energies, compared with the prediction of the statistical model cascade [53].

Figure 5

(a) Typical $\alpha$-particle residual energy spectrum and (b) the corresponding deduced thickness distribution profile, $w\left(t\right)$, for one of the Sn targets.

Figure 6

Beam energy probability distribution $D\left(E,t_0\right)$ inside the first (a) and last (b) targets of the second stack (see Table 2) in the ${}^6\mathrm{Li}+{}^{120}\mathrm{Sn}$ reaction.

Figure 7

Fusion excitation function for (a) ${}^6\mathrm{Li}+{}^{120}\mathrm{Sn}$ and (b) ${}^7\mathrm{Li}+{}^{119}\mathrm{Sn}$ systems extracted with the deconvolution procedure (continuous line) using the Wong function and its associated uncertainty (colored band). The symbols represent the measured cross sections plotted in the usual way, i.e., as $({\sigma }_{\mathrm{mean}},\overline{E})$ and $({\sigma }_{\mathrm{mean}},E_{\mathrm{eff}})$. Circles are used for points measured with stacked targets and squares are used for single foil measurements. See text for details.

Figure 8

Fusion excitation function for (a) ${}^6\mathrm{Li}+{}^{120}\mathrm{Sn}$ and (b) ${}^7\mathrm{Li}+{}^{119}\mathrm{Sn}$ systems extracted with Eq. (11) (continuous line) and its associated uncertainty (colored band). The symbols represent the measured cross sections plotted in the usual way, i.e., as $({\sigma }_{\mathrm{mean}},\overline{E})$ and $({\sigma }_{\mathrm{mean}},E_{\mathrm{eff}})$. Circles are used for points measured with stacked targets and squares are used for single foil measurements. See text for details.

Figure 9

Ratio between ${\sigma }_{\mathrm{calc}-\mathrm{mean},i}$ and ${\sigma }_{\mathrm{mean},i}$ for the reactions ${}^6\mathrm{Li}+{}^{120}\mathrm{Sn}$ (a) and ${}^7\mathrm{Li}+{}^{119}\mathrm{Sn}$ (b) using the Wong function. See text for details.

Figure 10

Ratio between ${\sigma }_{\mathrm{calc}-\mathrm{mean},i}$ and ${\sigma }_{\mathrm{mean},i}$ for the reactions ${}^6\mathrm{Li}+{}^{120}\mathrm{Sn}$ (a) and ${}^7\mathrm{Li}+{}^{119}\mathrm{Sn}$ (b) using Eq. (11). See text for details.

Figure 11

Comparison of CF reduced cross section for the ${}^6\mathrm{Li}+{}^{120}\mathrm{Sn}$ and ${}^7\mathrm{Li}+{}^{119}\mathrm{Sn}$ systems with the UFF. The experimental data reported in the figure correspond to $({\sigma }_{\mathrm{mean},i},E_{\mathrm{dec},i})$, where $E_{\mathrm{dec},i}$ is the energy point of the deconvolution curve which corresponds to the measured cross section ${\sigma }_{\mathrm{mean},i}$. See text for details.

Figure 12

Couplings scheme for the projectile overlaps.

Figure 13

Couplings scheme for the target overlaps.

Figure 14

Comparison of the experimental CF cross sections for the ${}^7\mathrm{Li}+{}^{119}\mathrm{Sn}$ system with the results obtained from CC and CRC calculations.