Characteristics of the Transition-State Spectra for U234, U236, and Pu240 from (d,pf) and (t,pf) Angular-Correlation Experiments

Fission-fragment angular correlations have been measured as a function of the excitation energy of the fissioning nucleus for the reactions ${}_{}{}^{233}{}_{}{}^{}\mathrm{U}\mathrm{}(d,pf)\mathrm{}$, ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}\mathrm{}(d,pf)\mathrm{}$, ${}_{}{}^{239}{}_{}{}^{}\mathrm{Pu}\mathrm{}(d,pf)\mathrm{}$, and ${}_{}{}^{234}{}_{}{}^{}\mathrm{U}\mathrm{}(t,pf)\mathrm{}$. A simplified microscopic model is developed and used to fit the experimental results in the energy range up to the neutron binding energy. From these fits, the positions of vibrational bands with $K=0^{+},2^{+},0^{-},1^{-}, \mathrm{and} 2^{-}$ are determined for the transition-state spectrum of ${}_{}{}^{234}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{236}{}_{}{}^{}\mathrm{U}$, and ${}_{}{}^{240}{}_{}{}^{}\mathrm{Pu}$. Above the neutron binding energy, the angular correlations are analyzed with a statistical model, and the pairing energy for a highly deformed transition nucleus is determined. Values obtained for the pairing gap are $2{\Delta }_0=2.10\mathrm{}\pm 0.15$ MeV for ${}_{}{}^{236}{}_{}{}^{}\mathrm{U}$ and $2{\Delta }_0=1.98\mathrm{}\pm 0.15$ MeV for ${}_{}{}^{240}{}_{}{}^{}\mathrm{Pu}$.