Breakup and fusion of ${}^6\mathrm{Li}$ and ${}^6\mathrm{He}$ with ${}^{208}\mathrm{Pb}$

The effect of ${}^6\mathrm{Li}$ and ${}^6\mathrm{He}$ breakup on the fusion cross section of these nuclei with ${}^{208}\mathrm{Pb}$ is investigated by means of continuum-discretized coupled-channels (CDCC) calculations. For ${}^6\mathrm{Li}$ the calculations describe reasonably well the experimental data for elastic scattering, ${}^6\mathrm{Li}\to \alpha +d$ breakup and the absorption cross section given by the sum of the ${}^6\mathrm{Li}$ fusion and the $\alpha$ production cross section not attributed to breakup. The effect of ${}^6\mathrm{Li}$ breakup on the calculated absorption cross section is found to depend strongly on the imaginary part of the diagonal bare potential. A combination of the CDCC technique and the barrier penetration model generates results close to the measured fusion cross section. For ${}^6\mathrm{He}$ the calculated absorption cross section is much larger than the measured ${}^6\mathrm{He}+{}^{209}\mathrm{Bi}$ complete fusion cross section values. However, it is found to be relatively independent of the form of the imaginary part of the bare potential. The complete fusion cross section is again found to be reasonably well described by the CDCC∕BPM combination.

Figure 1

(a) Angular distribution of the differential cross section (ratio to Rutherford cross section) for ${}^6\mathrm{He}+{}^{208}\mathrm{Pb}$ elastic scattering [13]. The curves show results of one-channel and the full CDCC calculations with the set A of the input cluster-target potentials. (b) Results of the CDCC test calculations with different width of the continuum bins. See text for details.

Figure 2

Angular distribution of the differential cross section (ratio to Rutherford cross section) for ${}^6\mathrm{Li}+{}^{208}\mathrm{Pb}$ elastic scattering. The data are from Keeley et al. [7]. The curves show results of various calculations with the two sets, A and B, of input cluster-target potentials. One-channel no coupling calculations are plotted as dashed curves while the calculations with ${}^6\mathrm{Li}\to \alpha +d$ breakup couplings included are plotted as solid curves, see text for details.

Figure 3

Data for the exclusive ${}^6\mathrm{Li}$ breakup from $\alpha +d$ and $\alpha +p$ coincidences measured by Signorini et al. [9] (filled circles) and for the sequential ${}^6\mathrm{Li}\to \alpha +d$ breakup via the $3^{+}$ resonant state of ${}^6\mathrm{Li}$ obtained by Gemmeke et al. [8] (triangles) compared with the CDCC calculations. See text for details.

Figure 4

(a) Experimental data for ${}^6\mathrm{Li}+{}^{208}\mathrm{Pb}$ (filled circles) [10] and ${}^6\mathrm{Li}+{}^{209}\mathrm{Bi}$ fusion (stars) [2] compared to the absorption cross sections obtained from the CDCC A and CDCC B calculations. The filled triangles represent the sum of the fusion cross section and the so called stripping breakup, the difference between the total $\alpha$ production cross section and the exclusive breakup cross section as discussed in Ref. 9. (b) Experimental data for the ${}^6\mathrm{He}+{}^{209}\mathrm{Bi}$ complete fusion cross section (filled circles) [4] compared with the absorption cross sections obtained from the CDCC A and CDCC B calculations for ${}^{208}\mathrm{Pb}$ target.

Figure 5

Real $\left(V_p\right)$ and imaginary $\left(W_p\right)$ parts of the dynamic polarization potential $\left(U_p\right)$ corresponding to the two different CDCC calculations at $E_{\mathrm{c.m.}}=28.2\mathrm{MeV}$ for ${}^6\mathrm{Li}+{}^{208}\mathrm{Pb}\to (\alpha +d)+{}^{208}\mathrm{Pb}$ breakup. The imaginary parts of the respective ${}^6\mathrm{Li}+{}^{208}\mathrm{Pb}$ bare potentials $\left(U_{\text{bare}}\right)$ are plotted by the dashed curves.

Figure 6

(a) Fusion cross sections for ${}^6\mathrm{Li}+{}^{208}\mathrm{Pb}$ (filled circles) [10] plotted as a function of the $\mathrm{c.m.}$ energy (ratio to the Coulomb barrier height). The curves show the results of calculations using a combination of CDCC and BPM techniques with the bare and effective potentials. See text for details. (b) Fusion cross sections for ${}^6\mathrm{He}+{}^{209}\mathrm{Bi}$ (filled circles) [4]. The curves show the results of calculations using a combination of CDCC and BPM techniques with the bare and effective potentials. See text for details.

Figure 7

Dynamic polarization potentials corresponding to the two different CDCC calculations as in Fig. 5 but for ${}^6\mathrm{He}+{}^{208}\mathrm{Pb}$ at $E_{\mathrm{c.m.}}=28.8\mathrm{MeV}$ .