Fission Fragment Angular Distributions and Saddle Deformations

Abstract

The fission fragment angular distributions have been measured with solid-state detectors for helium-ion-induced fission of bismuth, lead-206, thallium, and gold. The measurements were made at several helium-ion-projectile energies between 30 and 43 Mev. With 42.8-Mev helium ions the relative differential fission cross sections for gold and bismuth targets were measured at ten angles between 90° and 180° and the resulting angular distributions fitted by a least-squares method with Legendre polynomials. The $\frac{W\left(174.5\mathrm{}°\right)}{W\left(90\mathrm{}°\right)}$ ratios for 42.8-Mev helium-ion-induced fission of bismuth, lead, lead-206, thallium, and gold are 2.26±0.07, 2.47±0.08, 2.46±0.08, 2.53±0.08, and 2.62±0.08, respectively. The relative fission cross sections at 174.5° and 90° were also measured at several lower helium-ion energies for all targets except natural lead. These data are utilized in the calculation of the energy dependence of $K_0$, the standard deviation of the distribution in the angular-momentum projection on the nuclear symmetry axis at the saddle point. The energy dependence of $K_0$ deduced from the experimental anisotropy measurements is similar to the predicted energy dependence from statistical theory if the nuclear temperature at the saddle point is proportional to the square root of the excitation energy. These results indicate that the effective moment of inertia is independent of excitation energy and they differ from heavy element (uranium region) results where it was found that at low excitation energies the experimental $K_0$ values were much reduced from statistical theory presumably due to pairing effects. With the assumption that the effective moment of inertia at the saddle point deformation (which is deduced for each target from the anisotropy measurement at the highest energy) is the rigid-body value, the stretching at the saddle point is calculated for various simple geometric configurations. For a saddle configuration of two equal tangent spheroids, the stretchings necessary to reproduce the observed effective moments of inertia are in good agreement with the liquid drop model calculations of Cohen and Swiatecki. Some comments are made on previous analyses of heavy-ion-induced fission of elements in the vicinity of gold.