Asymmetry in Nuclear Fission

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Abstract
The two-center shell model for fission has been generalized to include asymmetric deformations. The calculation of the potential energy involves four independent shape variables, where only two were required in the symmetric calculations. Potential energy calculations have been carried out for Pb202, Po210, U236, Cm248, Fm252, and Fm264. Asymmetric fission is found to be energetically preferred in U236, Cm248, and Fm252; and symmetric fission is preferred in Pb202, Po210, Fm258, and Fm264. Two of these nuclei, namely U236 and Po210, have been studied in detail. It is seen that the asymmetry in U236 remains almost constant from the second saddle to scission, whereas in Po210 (and also in Pb202), the preferred shape changes from asymmetry in the region of the second saddle to symmetry in the region of scission. The results for Fm isotopes indicate that there is a transition from asymmetric fission in the lighter Fm isotopes to symmetric fission in the heavier Fm isotopes. The preference for symmetric mass division in Fm264 is very strong, since two double-magic Sn8250132 fragments are formed at symmetry. In general, the structures which appear in the potential energy surfaces are the results of an interplay between compound-nucleus shell structure, fragment shell structures, and liquid-drop-model energies. Comparisons of our results with experimental observations indicate that the observed mass distribution is correlated with the potential energy surface in the neighborhood of scission.