Deduction of compound nucleus formation probability from the fragment angular distributions in heavy-ion reactions

The presence of various fissionlike reactions in heavy-ion induced reactions is a major hurdle in the path to laboratory synthesis of heavy and super-heavy nuclei. It is known that the cross section of forming a heavy evaporation residue in fusion reactions depends on the three factors—the capture cross section, probability of compound nucleus formation $P_{\mathrm{CN}}$, and the survival probability of the compound nucleus against fission. As the probability of compound nucleus formation, $P_{\mathrm{CN}}$ is difficult to theoretically estimate because of its complex dependence on several parameters; attempts have been made in the past to deduce it from the fission fragment anisotropy data. In the present work, the fragment anisotropy data for a number of heavy-ion reactions are analyzed and it is found that deduction of $P_{\mathrm{CN}}$ from the anisotropy data also requires the knowledge of the ratio of relaxation time of the $K$ degree of freedom to pre-equilibrium fission time.

Figure 1

Plot showing $P_{\mathrm{NCN}}(t_K/t_f)$ versus ${\chi }_{\mathrm{eff}}$ for the various reactions.

Figure 2

Plot showing ${\chi }_{\mathrm{eff}}$ versus $\alpha$ for various reactions as tabulated in Table 1.

Figure 3

Plot showing $P_{\mathrm{NCN}}(t_K/t_f)$ versus $\alpha$ for the various reactions.

Figure 4

$P_{\mathrm{CN}}$ deduced for the value of ${\sigma }_{\theta }^2=0.06$ from Eq. (7) versus ${\chi }_{\mathrm{eff}}$ for the various reactions analyzed in the present work.