Investigation of complete and incomplete fusion in the ${}^7\mathrm{Li}+{}^{124}\mathrm{Sn}$ reaction near Coulomb barrier energies

The complete and incomplete fusion cross sections for the ${}^7\mathrm{Li}+{}^{124}\mathrm{Sn}$ reaction were measured using online and offline characteristic $\gamma$-ray detection techniques. The complete fusion (CF) cross sections at energies above the Coulomb barrier were found to be suppressed by $\sim 26\%$ compared to the coupled channel calculations. This suppression observed in complete fusion cross sections is found to be commensurate with the measured total incomplete fusion (ICF) cross sections. There is a distinct feature observed in the ICF cross sections, i.e., $\mathit{t}$ capture is found to be dominant compared to $\alpha$ capture at all the measured energies. A simultaneous explanation of complete, incomplete, and total fusion (TF) data was also obtained from the calculations based on the continuum discretized coupled channel method with short range imaginary potentials. The cross section ratios of CF/TF and ICF/TF obtained from the data as well as the calculations showed the dominance of ICF at below-barrier energies and CF at above-barrier energies.

Figure 1

$\gamma$-ray add-back spectrum from the clover detector at ${125}^{\circ }$ obtained in the ${}^7\mathrm{Li}+{}^{124}\mathrm{Sn}$ reaction at $E_{\mathrm{beam}}=38$ MeV. The $\gamma$ lines from the possible evaporation residues (${}^{126,127,128}\mathrm{I}$) following CF are labeled. Also the $\gamma$ lines following the $\alpha$-capture channel (${}^{126,127}\mathrm{Te}$) and inelastic ${}^{124}\mathrm{Sn}^{*}$ are marked.

Figure 2

Offline $\gamma$-ray spectrum obtained in the HPGe detector for the ${}^7\mathrm{Li}+{}^{124}\mathrm{Sn}$ reaction at $E_{\mathrm{beam}}=33$ MeV. Identified $\gamma$ lines from different residues following CF (${}^{126,128}\mathrm{I}$), $\mathit{t}$ capture (${}^{124,125,126}\mathrm{Sb}$), one-neutron stripping (${}^{125}\mathrm{Sn}$), and one-neutron pickup (${}^{123}\mathrm{Sn}$) are marked.

Figure 3

ER cross sections from online $\gamma$-ray measurement for $3n$ (${}^{128}\mathrm{I}$), $4n$ (${}^{127}\mathrm{I}$), and $5n$ (${}^{126}\mathrm{I}$) channels following CF are represented by open circles, open triangles, and open squares, respectively. The ER data from offline $\gamma$-ray measurements for $3n$ and $5n$ channels are shown by open diamonds and open stars respectively. The results of the statistical model calculations for the corresponding ERs are shown by long-dashed ($3n$), dashed–double-dotted ($4n$), and short-dashed ($5n$) lines.

Figure 4

Typical radioactive decay curves obtained for (a) ${}^{125}\mathrm{Sn}^m$ and (b) ${}^{128}\mathrm{I}$ residues.

Figure 5

Complete fusion cross section (filled circles) for the ${}^7\mathrm{Li}+{}^{124}\mathrm{Sn}$ reaction compared with coupled (dashed lines) and uncoupled (dotted lines) results from ccfull calculations. Solid lines were obtained by multiplying the coupled results by a factor of 0.74.

Figure 6

Measured residue cross sections for (a) $\mathit{t}$-capture process (from offline $\gamma$-ray measurement) (b) $\alpha$-capture process (from online $\gamma$-ray measurement) in the ${}^7\mathrm{Li}+{}^{124}\mathrm{Sn}$ reaction are plotted. The lines are the predictions from statistical model calculations for the corresponding residues (see text for details).

Figure 7

(a) The data of CF, ICF, and TF cross sections for the ${}^7\mathrm{Li}+{}^{124}\mathrm{Sn}$ reaction are compared with the coupled channel calculations. The arrow indicate the position of the Coulomb barrier. (b) Comparison of individual ICF contributions from $\alpha$ capture and $\mathit{t}$ capture along with total ICF with the calculations (see text for details).

Figure 8

The ratios of cross sections, ${\sigma }_{\mathrm{ICF}}/{\sigma }_{\mathrm{TF}}$ and ${\sigma }_{\mathrm{CF}}/{\sigma }_{\mathrm{TF}}$, derived from the calculations as a function of $E_{\mathrm{c}.\mathrm{m}.}/V_{\mathrm{B}}$ for the ${}^7\mathrm{Li}+{}^{124}\mathrm{Sn}$ reaction is shown by dashed and dash-dotted lines respectively. The symbols show the experimental data.