Recently, a number of theoretical calculations of the static fission barriers of nuclei in the actinide and trans-actinide regions have been carried out. These include calculations based on the microscopic-macroscopic treatment[6], the self-consistent approach with the Gogny[7] and Skyrme[8,9] forces, and also within the relativistic mean field model[9].

The aim of this contribution is to calculate static fission barriers for the even-even Fermium isotopes and the even-even superheavy nuclei with =184 using the energy density functional with the Skyrme interaction SLy4[10] and a seniority pairing force treated in the BCS approximation. The calculations were carried out using the Hartree-Fock+BCS code HFODD (v.2.8i) that solves the self-consistent HF equations by using a Cartesian (3D) harmonic oscillator (HO) finite basis.[11] This code makes it possible to break all self-consistent symmetries of the nuclear mean field, including axial symmetry, reflection symmetry, and time reversal. Particular attention has been paid to symmetry-breaking effects along the fission path. The pairing strengths have been adjusted to reproduce the proton and neutron experimental pairing gaps in Fm.