Complete-Fusion Cross Sections for the Reactions of Heavy Ions with Cu, Ag, Au, and Bi

Abstract

Mica track detectors were used to detect recoil nuclei from the reactions of $^{12}\mathrm{C}$, $^{16}\mathrm{O}$, and $^{20}\mathrm{Ne}$ projectiles with Cu, Ag, Au, and Bi targets. The observed track-length distributions and angular distributions together with detector-threshold information indicate that the observed recoils result from complete fusion of the target and projectile nuclei. The cross section ${\ensuremath{\sigma}}_{\mathrm{CF}}$ for the complete fusion mechanism is found to be well below the total-reaction cross section ${\ensuremath{\sigma}}_{R}$ at the higher projectile energies. A sharp-cutoff model is employed to extract values of ${J}_{\mathrm{crit}}$, the maximum angular momentum of the compound nuclei formed in complete-fusion reactions. Using those values, complete-fusion cross sections are calculated as a function of the mass of the complete-fusion product for reactions induced by$\phantom{\rule{0ex}{0ex}}^{16}\mathrm{O}$, $^{20}\mathrm{Ne}$, and $^{40}\mathrm{Ar}$. Assuming only first-chance fission, the ratio $\frac{{\ensuremath{\Gamma}}_{f}}{{\ensuremath{\Gamma}}_{n}}$ has been calculated for the system $^{197}\mathrm{Au}$+$^{16}\mathrm{O}$\ensuremath{\rightarrow}$^{213}\mathrm{Fr}$*.