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

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 ${\sigma }_{\mathrm{CF}}$ for the complete fusion mechanism is found to be well below the total-reaction cross section ${\sigma }_R$ 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${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$, and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$. Assuming only first-chance fission, the ratio $\frac{{\Gamma }_f}{{\Gamma }_n}$ has been calculated for the system ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$+${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$→${}_{}{}^{213}{}_{}{}^{}\mathrm{Fr}$*.