Incomplete fusion studies in the ${}^{19}\mathrm{F}+{}^{159}\mathrm{Tb}$ system at low energies and its correlation with various systematics

The excitation functions of reaction residues populated via the complete fusion and incomplete fusion process in the interaction of the ${}^{19}\mathrm{F}+{}^{159}\mathrm{Tb}$ system have been measured at energies $\approx 4–6$ MeV/nucleon, using off-line $\gamma$-ray spectroscopy. The analysis of data was done within the framework of statistical model code pace4 (a compound nucleus model). A significant fraction of incomplete fusion was observed in the production of reaction residues involving $\alpha$ particle(s) in the exit channels, even at energies as low as near the Coulomb barrier. The incomplete fusion strength function was deduced from the experimental excitation functions and the dependence of this strength function on various entrance channel parameters was studied. The present results show a strong dependence on the projectile $\alpha$-Q value that agrees well with the existing data. To probe the dependence of incomplete fusion on entrance channel mass asymmetry, the present work was compared with the results obtained in the interaction of ${}^{12}\mathrm{C}, {}^{16}\mathrm{O}$, and ${}^{19}\mathrm{F}$ with nearby targets available in the literature. It was observed that the mass asymmetry linearly increases for each projectile separately and turns out to be a projectile-dependent mass-asymmetry systematics. The deduced incomplete fusion strength functions in the present work are also plotted as a function of $Z_P{Z}_T$ (Coulomb effect) and compared with the existing literature. A strong dependence of the Coulomb effect on the incomplete fusion fraction was observed. It was found that the fraction of incomplete fusion linearly increases with $Z_P{Z}_T$ and was found to be more for larger $Z_P{Z}_T$ values indicating significantly important linear systematics.

Figure 1

Typical gamma ray spectrum of ${}^{19}\mathrm{F}+{}^{159}\mathrm{Tb}$ interaction at energy $\approx 105.44 \pm$ 1.56 MeV, where $\gamma$ lines are assigned to different reaction products expected to be populated by complete fusion and/or incomplete fusion processes.

Figure 2

Experimentally measured excitation functions of all xn/pxn channels populated in the ${}^{19}\mathrm{F}+{}^{159}\mathrm{Tb}$ system. The solid lines through the experimental data points are the pace4 calculations as discussed in the text.

Figure 3

(a) Sum of experimentally measured excitation functions of all $\alpha$-emitting channels compared with the predictions of corresponding statistical model code pace4. The line through the blue dot points is drawn to guide the eyes. (b) Comparison of ${\sigma }_{\mathrm{TF}}, {\sigma }_{\mathrm{CF}}$, and ${\sigma }_{\mathrm{ICF}}$ cross sections for the ${}^{19}\mathrm{F}+{}^{159}\mathrm{Tb}$ system with the incident laboratory energy. The lines are drawn to guide the eyes.

Figure 4

A comparison of incomplete fusion strength function ($F_{\mathrm{ICF}}$) in terms of the $\alpha$-Q value of the projectile at a constant $v_{\mathrm{rel}}$ (= $0.053\mathrm{c})$ for different projectiles on the same target ${}^{159}\mathrm{Tb}$. The data were taken from Ref. [27].

Figure 5

Incomplete fusion strength function ($F_{\mathrm{ICF}}$) of various systems (see text) as a function of mass asymmetry ($\mu$). The dashed lines are drawn to guide the eyes.

Figure 6

Incomplete fusion strength function ($F_{\mathrm{ICF}}$) of various systems (see text) as a function of $Z_P{Z}_T$. The dashed line is drawn to guide the eyes.