Summary

In this study we performed pilot calculations of collective inertia, zero-point quadrupole energy correction, and fission barriers in selected fermi isotopes. The HFODD code employed allows for an arbitrary symmetry breaking; this feature is of crucial importance when discussing spontaneous fission where the reflection-asymmetric and triaxial shapes can play a role. The main conclusion of this work can be summarized as follows:

• The zero-point energy correction is important to include as it can significantly modify the action by lowering the ground state by approximately 1MeV in the nuclei considered.
• The collective quadrupole inertia calculated in the Skyrme SLy4 and SkM$^*$ models have very similar deformation pattern to those in the Gogny D1S model. Our D1S values are very close to those of Ref.[7] and exceed the values obtained in Ref.[9] by a factor of two. The reason for this discrepancy is unknown to the authors.
• The collective inertia obtained in the cranking approximation are about twice as large as the GOA results. In all the cases considered, the collective inertia smoothly decrease at large deformations; they do not exhibit oscillations seen in previous microscopic-macroscopic calculations.
• As discussed earlier, both $V(q)$ and $B(q)$ contribute to the action integral $S$ (1). In general, the fission barriers in the Gogny model are higher as compared to those in SkM$^*$ and the opposite holds for the collective inertia. However, both those effects partly cancel in the product $B(V-E)$ that determines the action and the spontaneous fission lifetime.