Systematic study of incomplete-fusion dynamics below 8 MeV/nucleon energy

An attempt has been made to provide crucial information about the dependence of incomplete-fusion dynamics on various entrance channel parameters below 8 MeV/nucleon energy. The forward recoil range distributions of several evaporation residues produced in the ${}^{13}\mathrm{C}+{}^{175}\mathrm{Lu}$ system have been measured at $\approx 88$-MeV energy and examined in the framework of the code SRIM. Owing to the fractional linear momentum transfer from the projectile to the target nucleus, incomplete-fusion (ICF) products are observed to be trapped at lower cumulative thickness than that of complete fusion products. In order to study the incomplete-fusion behavior with various entrance channel parameters, the incomplete-fusion fraction ($F_{\mathrm{ICF}}$) has also been deduced and compared with those obtained for the systems available in the literature. The reinvestigation of the Coulomb factor $\left(Z_P{Z}_T\right)$ dependence of incomplete fusion indicates that it is somehow projectile structure dependent. No systematic trend is observed with the target deformation parameter $\left({\beta }_2\right)$ dependent study of ICF. A systematic linear growth in the incomplete-fusion probability function ($F_{\mathrm{ICF}}$) is observed with increasing the parameters $Z_P{Z}_T{\beta }_2$ and $Z_P{Z}_T/(1-{\beta }_2)$, but separately for $\alpha$- and non-$\alpha$-cluster structured projectiles with different targets. The present findings explore the role of Coulomb interaction on ICF dynamics more effectively. Moreover, the projectile $\alpha -Q$ value is found to be a suitable parameter which explains effectively the observed trend in the study of ICF with the above-mentioned parameters. The incomplete-fusion existence below critical angular momentum (${\ell }_{\mathrm{crit}}$), i.e., $\ell \le {\ell }_{\mathrm{crit}}$, is also observed for the present ${}^{13}\mathrm{C}+{}^{175}\mathrm{Lu}$ system.

Figure 1

Experimentally measured FRRDs for the residues (a) ${}^{184}\mathrm{Ir}$ ($4n$), (b) ${}^{183}\mathrm{Ir}$ ($5n$), (c) ${}^{182}\mathrm{Ir}$ ($6n$), (d) ${}^{183}\mathrm{Os}$ ($p4n$), and (e) ${}^{182}\mathrm{Os}$ ($p5n$) populated in the ${}^{13}\mathrm{C}+{}^{175}\mathrm{Lu}$ system.

Figure 2

Experimentally measured FRRDs for the residues (a) ${}^{183}\mathrm{Re}$ ($\alpha n$), (b) ${}^{181}\mathrm{Re}$ ($\alpha 3n$), and (c) ${}^{179}\mathrm{Re}$ ($\alpha 5n$) populated in the ${}^{13}\mathrm{C}+{}^{175}\mathrm{Lu}$ system.

Figure 3

Experimentally measured FRRDs for the residues (a) ${}^{178m}\mathrm{Ta}$ ($2\alpha 2n$), (b) ${}^{177}\mathrm{Ta}$ ($2\alpha 3n$), and (c) ${}^{176}\mathrm{Ta}$ ($2\alpha 4n$) populated in the ${}^{13}\mathrm{C}+{}^{175}\mathrm{Lu}$ system.

Figure 4

The $F_{\mathrm{ICF}}$ (%) deduced from the present FRRD analysis along with those obtained for earlier studied systems as a function of Coulomb factor $\left(Z_P{Z}_T\right)$ at the same relative velocity ($v_{\mathrm{rel}}=0.074c$). The color lines drawn through the data points are just to guide the eyes.

Figure 5

The deduced $F_{\mathrm{ICF}}$ (%) for (a) ${}^{12}\mathrm{C}$ induced reactions and (b) ${}^{13}\mathrm{C}$ induced reactions as a function of target deformation parameter $\left({\beta }_2\right)$ at the same relative velocity ($v_{\mathrm{rel}}=0.074c$).

Figure 6

The $F_{\mathrm{ICF}}$ (%) deduced from the present FRRD analysis along with those obtained for earlier studied systems as a function of parameter $Z_P{Z}_T{\beta }_2$. The color lines drawn through the data points are just to guide the eyes.

Figure 7

The $F_{\mathrm{ICF}}$ (%) deduced from the present FRRD analysis along with those obtained for earlier studied systems as a function of parameter $Z_P{Z}_T/(1-{\beta }_2)$ at relative velocity (a) $v_{\mathrm{rel}}=0.074c$ and (b) $v_{\mathrm{rel}}=0.053c$. The color lines drawn through the data points are just to guide the eyes.

Figure 8

The comparison of deduced $F_{\mathrm{ICF}}$ (%) from the present FRRD analysis along with those obtained earlier from the EF analysis (Kumar et al. [21]) and FRRD analysis (Kumar et al. [41]) at the same relative velocity ($v_{\mathrm{rel}}=0.074c$).

Figure 9

The comparison between $F_{\mathrm{ICF}}$ (%) deduced using the tightly bound projectiles (${}^{12}\mathrm{C}$ and ${}^{13}\mathrm{C}$) and loosely bound projectiles (${}^6\mathrm{Li}$ and ${}^7\mathrm{Li}$) as a function of parameter $Z_P{Z}_T/(1-{\beta }_2)$ at relative velocity $v_{\mathrm{rel}}=0.074c$. The color lines drawn through the data points are just to guide the eyes.

Figure 10

Fusion $\ell$ distributions for the ${}^{12}\mathrm{C}+{}^{175}\mathrm{Lu}$ and ${}^{13}\mathrm{C}+{}^{175}\mathrm{Lu}$ systems calculated using the ccfull code [67] and by incorporating the coupled-channel calculations at $\approx 88$-MeV energy.