Conclusion

The Skyrme energy density functional with the SLy4 parametrization has been applied to study static fission barriers of even-even SHE with $100\leq Z \leq 110$ and even-even spherical isotones with $N$= 184. Our calculations take into account axial- and reflection-symmetry-breaking effects along the static fission paths.

For all the nuclei investigated, the appearance of triaxial deformations reduces the inner barrier by up to 3MeV. It has also been found that the strongest reflection-symmetry-breaking effects appear in $^{258}$Sg, $^{254,256}$Rf, and in the Fm and No isotopes (excluding $^{264}$Fm and $^{264}$No). In all remaining cases, purely reflection-symmetric fission paths have been predicted. The analysis of the static fission barriers of even-even nuclei with $N$=184 hints at an increased stability against spontaneous fission for $Z$= 118 and 120.