Deformation of the Transition-State Nucleus in Energetic Fission

Fission-fragment anisotropy ratios, $\frac{W\left(170\mathrm{}°\right)}{W\left(90\mathrm{}°\right)}$ from fission induced by 42.8-MeV helium ions, have been measured for the targets ${\mathrm{Th}}^{230}$, ${\mathrm{Th}}^{232}$, ${\mathrm{Pa}}^{231}$, ${\mathrm{U}}^{233}$, ${\mathrm{U}}^{234}$, ${\mathrm{U}}^{235}$, ${\mathrm{U}}^{236}$, ${\mathrm{U}}^{238}$, ${\mathrm{Np}}^{237}$, ${\mathrm{Pu}}^{239}$, ${\mathrm{Pu}}^{240}$, ${\mathrm{Pu}}^{242}$, ${\mathrm{Am}}^{241}$, ${\mathrm{Am}}^{243}$, ${\mathrm{Cm}}^{244}$, and ${\mathrm{Cf}}^{249}$. By modifying values of the fission-to-neutron level-width ratio $\frac{{\Gamma }_f}{{\Gamma }_n}$ from the literature, first-chance anisotropies were calculated to permit comparison of the targets at nearly uniform and rather high excitation energies. The resulting values of ${K_0}^2$ (the projection $K$ of the total angular momentum $I$ on the nuclear symmetry axis is assumed to have a Gaussian distribution, and ${K_0}^2$ is the squared standard deviation of the Gaussian) associated with first-chance fission in conjunction with the assumptions of rigid moments of inertia permitted evaluation of saddle deformations. The saddle deformations were found to be fairly insensitive to programmed variations in $\frac{{\Gamma }_f}{{\Gamma }_n}$ values based on a semiempirical relation deduced for the ($Z, A$) dependence of the compound nucleus. The unrelieved disparity for the heaviest elements between the experimentally derived saddle deformations and those theoretically deduced from the conventional liquid-drop model has been interpreted to suggest a re-evaluation of the fissionability parameter, ${\left(\frac{Z^2}{A}\right)}_{\mathrm{crit}}$. Qualitative extrapolation of the new data (assuming a nuclear level-density parameter $a=\frac{A}{8}$) yields