Introduction

Nuclear fission is one of the best examples of the nuclear large-amplitude collective motion. Microscopically, fission can be viewed as a many-body tunneling through a potential barrier, which is difficult to treat if one wants to go beyond the standard semiclassical approximation[1,2,3]. Various nuclear structure models (including a microscopic-macroscopic approach and self-consistent approaches both nonrelativistic and relativistic) have been applied to the fission barriers, lifetimes, and mass/charge distributions, and a large sensitivity to model details and parametrizations has been found[4]. (For a recent review of self-consistent mean-field models and parametrizations, see Bender et al.[5].)

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 $N$=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 $^{252}$Fm.