Systematic study of low-energy incomplete fusion: Role of entrance channel parameters

An attempt has been made to investigate the role of various entrance channel parameters in low-energy ($\approx 4\text{–}7$ MeV/nucleon) incomplete fusion reactions through excitation function measurements. The analysis of measured excitation functions, in the framework of statistical model code pace4, reveals that the $xn$/$pxn$ channels are populated, predominantly, via complete fusion processes. However, in the production of $\alpha$-emitting channels, even after correcting for the precursor decay contribution, a significant enhancement as compared to statistical model predictions has been observed, which may be attributed due to the contribution of breakup processes. The observed enhancement is found to increase with projectile energy. Further, the comparison of present work with literature data reveals the dependence of incomplete fusion on mass-asymmetry of interacting partners, $\alpha \text{−}Q$ value of the projectile, and also on $Z_P{Z}_T$ (the Coulomb factor). From the present analysis, it may be concluded that a single entrance channel parameter (i.e., mass asymmetry or $Z_P{Z}_T$ or $\alpha \text{−}Q$ value) is not able to explain, completely, the yields of the low-energy incomplete fusion component. Therefore, a combination of these parameters and/or a parameter which can incorporate all gross features of interacting partners should be chosen to get a systematics for such reactions.

Figure 1

A typical $\gamma$-ray spectrum obtained at $87.62\pm 0.38$ MeV beam energy in ${}^{13}\mathrm{C}+{}^{159}\mathrm{Tb}$ interactions. Some of the identified $\gamma$ lines corresponding to different CF and/or ICF residues are labeled. The inset of this figure shows the decay curve of ${}^{168}\mathrm{Lu}$ ($t_{1/2}=5.5$ min) residues populated via the $4n$ channel.

Figure 2

Experimentally measured EFs of ${}^{169}\mathrm{Lu}\left(3n\right)$, ${}^{168}\mathrm{Lu}^{g+m}\left(4n\right)$, ${}^{167}\mathrm{Lu}\left(5n\right)$, and ${}^{167}\mathrm{Yb}\left(p4n\right)$ residues populated in the ${}^{13}\mathrm{C}+{}^{159}\mathrm{Tb}$ system. The lines through the data points are predictions done using the pace4 code (for details see text).

Figure 3

Experimentally measured EFs of $\alpha$-emitting channels are compared with the pace4 predictions. Solid blue lines represent pace4 predictions performed for $a={A/8\text{MeV}}^{-1}$. See text for explanation.

Figure 4

The comparison of $F_{ICF}$ values for different projectiles on same target ${}^{159}\mathrm{Tb}$. The $x$ axis is normalized by their corresponding Coulomb barriers (for details see text).

Figure 5

The incomplete fusion fraction $F_{ICF}$ for various systems are compared in terms of the mass asymmetry ($\mu$) of the interacting partners at a constant $E_{\mathrm{lab}}/V_b$ value. The lines are linear fits to data, separately for each projectile (see text for explanation).

Figure 6

A comparison of incomplete fusion fraction $F_{ICF}$ in terms of the $\alpha \text{−}Q$ value of the projectile at a constant $E_{\mathrm{lab}}/V_b$ value for different projectiles on the same target, ${}^{159}\mathrm{Tb}$.

Figure 7

The comparison of incomplete fusion fraction $F_{ICF}$ values for various systems as a function of $Z_P{Z}_T$ at a constant $E_{\mathrm{lab}}/V_b$ value. The dashed line is drawn just to guide the eyes. Systems with same or almost same $Z_P{Z}_T$ values are marked by vertical boxes (see text for explanation).

Figure 8

Comparison of ICF fraction for different systems, at a constant $E_{\mathrm{lab}}/V_b$=1.35, with same or almost same $Z_P{Z}_T$ values.