Summary

We analyzed the static spontaneous-fission valleys in $^{256,258,260}$Fm within the self-consistent SHF+BCS framework. For all the nuclei investigated, we found the symmetric-compact, symmetric-elongated, and asymmetric-elongated static paths to fission, leading to symmetric-spherical, symmetric-elongated, and asymmetric-elongated fragment splits at the scission point, respectively.

In the $^{256}$Fm isotope, we found the asymmetric (aEF) path to be most favorable. In the case of $^{258}$Fm, the two symmetric (sCF and sEF) paths take over. This, together with a small asymmetric contribution from the aEF path, explains the bimodal fission observed in this isotope. For the heaviest $^{260}$Fm isotope, we found a purely symmetric fission leading to nearly spherical scission fragments. To what extent will dynamical effects [8] modify this picture? The answer to this question will be provided in forthcoming studies.