Asymmetry in Nuclear Fission

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 ²⁰²Pb, ²¹⁰Po, ²³⁶U, ²⁴⁸Cm, ²⁵²Fm, and ²⁶⁴Fm. Asymmetric fission is found to be energetically preferred in ²³⁶U, ²⁴⁸Cm, and ²⁵²Fm; and symmetric fission is preferred in ²⁰²Pb, ²¹⁰Po, ²⁵⁸Fm, and ²⁶⁴Fm. Two of these nuclei, namely ²³⁶U and ²¹⁰Po, have been studied in detail. It is seen that the asymmetry in ²³⁶U remains almost constant from the second saddle to scission, whereas in ²¹⁰Po (and also in ²⁰²Pb), 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 ²⁶⁴Fm is very strong, since two double-magic ₅₀¹³²Sn₈₂ 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.