Low-energy nuclear reaction of the ${}^{14}\mathrm{N}+{}^{169}\mathrm{Tm}$ system: Incomplete fusion

Excitation functions of reaction residues produced in the ${}^{14}\mathrm{N}+{}^{169}\mathrm{Tm}$ system have been measured to high precision at energies above the fusion barrier, ranging from $1.04V_B$ to $1.30V_B$, and analyzed in the framework of the statistical model code pace4. Analysis of $\alpha$-emitting channels points toward the onset of incomplete fusion even at slightly above-barrier energies where complete fusion is supposed to be one of the dominant processes. The onset and strength of incomplete fusion have been deduced and studied in terms of various entrance channel parameters. Present results together with the reanalysis of existing data for various projectile-target combinations conclusively suggest strong influence of projectile structure on the onset of incomplete fusion. Also, a strong dependence on the Coulomb effect $\left(Z_P{Z}_T\right)$ has been observed for the present system along with different projectile-target combinations available in the literature. It is concluded that the fraction of incomplete fusion linearly increases with $Z_P{Z}_T$ and is found to be more for larger $Z_P{Z}_T$ values, indicating significantly important linear systematics.

Figure 1

Typical $\gamma$-ray spectra obtained for the ${}^{14}\mathrm{N}+{}^{169}\mathrm{Tm}$ system at $E_{\mathrm{lab}}=82.16\pm 0.84$ MeV. $\gamma$ peaks indicating CF and/or ICF residues are marked by arrows.

Figure 2

Comparison of experimental and theoretical EFs of $xn/pxn$ channels. Dashed and solid line(s) drawn through the data points represent best fits to the pace4 predictions for level density parameter $a=A/8{\mathrm{MeV}}^{-1}$.

Figure 3

CF cross sections as a function of $1/E_{\mathrm{lab}}$ found to reproduce the Coulomb barrier for ${}^{14}\mathrm{N}+{}^{169}\mathrm{Tm}$ system. The dashed line through the data points is achieved by a best-fitting procedure on the data.

Figure 4

(a) Experimentally measured EFs of ERs ${}^{177}\mathrm{W}$ $\left(\alpha 2n\right)$, ${}^{176}\mathrm{W}$ $\left(\alpha 3n\right)$, ${}^{175}\mathrm{W}$ $\left(\alpha 4n\right)$, and ${}^{174}\mathrm{W}$ $\left(\alpha 5n\right)$ are compared with the pace4 predictions at level density parameter $K=8$. (b) The dashed line through the experimental data points is the best fit to the sum of all experimentally measured $\alpha xn$ channels $(\sum {\sigma }_{\alpha }xn)$, and the solid line represents pace4 prediction for $K=8$ for these channels.

Figure 5

Total fusion probability $(\sum {\sigma }_{\mathrm{TF}})$ is plotted with the sum of all CF $\left({\sum }_{\mathrm{CF}}\right)$ and ICF $(\sum {\sigma }_{\mathrm{ICF}})$ channels. Increasing separation between $\sum {\sigma }_{\mathrm{TF}}$ and $\sum {\sigma }_{\mathrm{CF}}$ with incident projectile energy reflects the ICF fraction. Lines and curves are drawn to guide the eyes.

Figure 6

The ICF strength function for the ${}^{14}\mathrm{N}+{}^{169}\mathrm{Tm}$ system (see text for description). Lines are drawn to guide the eyes.

Figure 7

The values of $F_{\mathrm{ICF}}$ obtained for ${}^{12}\mathrm{C},{}^{14}\mathrm{N},{}^{16}\mathrm{O}+{}^{169}\mathrm{Tm}$ reactions are plotted as a function of normalized projectile energies. Lines drawn through the data points guide the eyes [24].

Figure 8

The values of $F_{\mathrm{ICF}}$ for different projectile-target combinations as a function of entrance channel mass asymmetry $\left({\mu }_A\right)$ at a constant relative velocity (i.e., $v_{\mathrm{rel}}=0.053c$). The lines drawn through the data points guide the eyes for individual $({}^{12}\mathrm{C}$, ${}^{14}\mathrm{N}$, ${}^{16}\mathrm{O})$ projectiles.

Figure 9

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