Exploring contributions from incomplete fusion in ${}^{6,7}\mathrm{Li}+{}^{209}\mathrm{Bi}$ and ${}^{6,7}\mathrm{Li}+{}^{198}\mathrm{Pt}$ reactions

We use the breakup absorption model to simultaneously describe the measured cross sections of complete fusion (CF), incomplete fusion (ICF), and total fusion (TF) in nuclear reactions induced by weakly bound nuclei ${}^{6,7}\mathrm{Li}$ on ${}^{209}\mathrm{Bi}$ and ${}^{198}\mathrm{Pt}$ targets. The absorption cross sections are calculated using the continuum discretized coupled channels (CDCC) method with different choices of short-range imaginary potentials to get the ICF, CF, and TF cross sections. It is observed that the cross sections for deuteron ICF / deuteron capture and $\alpha$ ICF / $\alpha$ capture are of similar magnitude, in the case of the ${}^6\mathrm{Li}$ projectile, while the cross sections for the triton ICF / triton capture is more dominant than that of $\alpha$ ICF / $\alpha$ capture in the case of the ${}^7\mathrm{Li}$ projectile. Both these observations are also corroborated by the experimental data. The ratio of ICF to TF cross sections, which defines the value of fusion suppression factor, is found to be in agreement with the data available from the literature. The cross-section ratios of CF/TF and ICF/TF show opposite behavior at below-barrier energies the former decreases while the latter increases as the energy is lowered, which shows the dominance of ICF at below-barrier energies. We have also studied the correlation of the ICF cross sections with the noncapture breakup (NCBU) cross sections as a function of energy, which shows that the NCBU is more significant than ICF at below-barrier energies.

Figure 1

(a) The data of complete fusion (CF), incomplete fusion (ICF), and total fusion, (TF) = CF + ICF + fission, for ${}^6\mathrm{Li}+{}^{209}\mathrm{Bi}$ reaction from Ref. [2] are compared with the calculations. The arrow indicates the position of Coulomb barrier. (b) Comparison of individual ICF contributions from $\alpha$-ICF, $d$-ICF, along with total-ICF with the calculations (see text for details).

Figure 2

Same as Fig. 1 but for ${}^7\mathrm{Li}+{}^{209}\mathrm{Bi}$ reaction.

Figure 3

Same as Fig. 1 but for ${}^6\mathrm{Li}+{}^{198}\mathrm{Pt}$ reaction.

Figure 4

Same as Fig. 1 but for ${}^7\mathrm{Li}+{}^{198}\mathrm{Pt}$ reaction.

Figure 5

The ratio of cross sections, ${\sigma }_{\mathrm{ICF}}/{\sigma }_{\mathrm{TF}},{\sigma }_{\mathrm{CF}}/{\sigma }_{\mathrm{TF}}$, and ${\sigma }_{\mathrm{ICF}}/{\sigma }_{\mathrm{NCBU}}$ derived from the calculations as a function of $E_{\mathrm{c}.\mathrm{m}.}/V_{\mathrm{B}}$ for ${}^{6,7}\mathrm{Li}+{}^{209}\mathrm{Bi}$ and ${}^{6,7}\mathrm{Li}+{}^{198}\mathrm{Pt}$ systems is shown by dashed, dash-dotted, and dotted lines respectively. The symbols are showing the experimental data (see text for details).