Deformation of the Transition-State Nucleus in Energetic Fission

Fission-fragment anisotropy ratios, W(170^∘)W(90^∘) from fission induced by 42.8-MeV helium ions, have been measured for the targets Th²³⁰, Th²³², Pa²³¹, U²³³, U²³⁴, U²³⁵, U²³⁶, U²³⁸, Np²³⁷, Pu²³⁹, Pu²⁴⁰, Pu²⁴², Am²⁴¹, Am²⁴³, Cm²⁴⁴, and Cf²⁴⁹. By modifying values of the fission-to-neutron level-width ratio ΓfΓₙ 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 K₀² (the projection K of the total angular momentum I on the nuclear symmetry axis is assumed to have a Gaussian distribution, and K₀² 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 ΓfΓₙ 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, (Z²A)crit. Qualitative extrapolation of the new data (assuming a nuclear level-density parameter a=A/8) yields (Z²A)crit≈44-453 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.