Deformation of the Transition-State Nucleus in Energetic Fission

Fission-fragment anisotropy ratios, $\frac{W(170\ifmmode^\circ\else\textdegree\fi{})}{W(90\ifmmode^\circ\else\textdegree\fi{})}$ 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 $\frac{{\ensuremath{\Gamma}}_{f}}{{\ensuremath{\Gamma}}_{n}}$ 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 $\frac{{\ensuremath{\Gamma}}_{f}}{{\ensuremath{\Gamma}}_{n}}$ 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, ${(\frac{{Z}^{2}}{A})}_{\mathrm{crit}}$. Qualitative extrapolation of the new data (assuming a nuclear level-density parameter $a=\frac{A}{8}$) yields ${(\frac{{Z}^{2}}{A})}_{\mathrm{crit}}\ensuremath{\approx}44\ensuremath{-}453$ for saddle deformations based on first-chance anisotropies computed from experimental data (deleting higher chance fission contributions). This value compares favorably with results of a modification of the conventional liquid-drop model, which allows the surface tension to vary with the curvature of the nuclear surface.