Evaporation of 3 to 8 Neutrons in Reactions betweenC12and Various Uranium Nuclides

Cross sections for the production of ${}_{}{}^{242}{}_{}{}^{}\mathrm{Cf}$, ${}_{}{}^{243}{}_{}{}^{}\mathrm{Cf}$, ${}_{}{}^{244}{}_{}{}^{}\mathrm{Cf}$, ${}_{}{}^{245}{}_{}{}^{}\mathrm{Cf}$, and ${}_{}{}^{246}{}_{}{}^{}\mathrm{Cf}$ in reactions between ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{233}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{234}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{236}{}_{}{}^{}\mathrm{U}$, and ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ have been measured in the energy range 60-110 MeV for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$. A good fit is obtained to the peaks of the cross-section curves. The fit involved (1) calculation of the compound nucleus cross section by the use of the parabolic approximation to the real part of the optical model, (2) modification of Jackson's formula for $P_x$ to include fission and angular-momentum effects, and (3) use of the $\frac{{\Gamma }_n}{{\Gamma }_f}$ formula due to Fujimoto and Yamaguchi. The analysis suggests that the value of ${〈\frac{{\Gamma }_n}{{\Gamma }_f}〉}_{\mathrm{av}}$ is independent of the energy of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$. The formula by Fujimoto and Yamaguchi reproduces the experimental ${〈\frac{{\Gamma }_n}{{\Gamma }_f}〉}_{\mathrm{av}}$ values with a standard deviation of 16%.