Symmetric and Asymmetric Fission

Abstract

Fission yields have been calculated assuming as a first approximation that they are proportional to the product of the level densities of a pair of binary fission products. The level densities have been calculated with the simplified shell-model methods of Newson and Duncan. The calculations predict a single symmetric peak when the mass of the fissioning nucleus, $A_0<N_1+Z_1+N_2+Z_2=50+28+82+50=210\mathrm{}$ (in agreement with the observed fission yields for bismuth and lighter elements), and three maxima in the fission yield curves for heavier compound nuclei. The peak corresponding to approximately equal-size binary fission products is very much higher than is observed experimentally. This is undoubtedly due to the fact that in asymmetric fission a core corresponding to 82 neutrons and 50 protons remains intact in the heavier fission product, whereas for symmetric fission this core is disrupted at the cost of several Mev. Since correction for this energy effect involves a number of unknown factors, the calculated yields for symmetric fission have been reduced by the same empirical factor in all calculations. An additional parameter, $n$, is introduced in correcting for excitation energy of the fission products and for possible departures from equilibrium. These calculations, which involve only two free parameters, explain most of the fission yield data for all five known cases where the compound nucleus is within an Mev or so of the fission threshold: ${\mathrm{Pu}}^{239}$, ${\mathrm{U}}^{238}$, ${\mathrm{U}}^{235}$, ${\mathrm{U}}^{233}$, and ${\mathrm{Th}}^{232}$, but it is necessary to treat $n$ as a free parameter for each curve to fit the small steep regions on each side of mass number $\frac{1}{2}{A}_0$. The calculated fission yields of the more highly excited compound nucleus, ${\mathrm{Ac}}^{227}$, predict three equally prominent maxima in qualitative agreement with observation.