Introduction

Spontaneous fission plays a significant role in a disintegration process of the superheavy elements (SHE). Microscopically, this phenomenon can be viewed as a many-body tunneling through a potential barrier. Studies of fission barriers are important for the determination of the stability of the heaviest nuclei.

Recently, a number of theoretical calculations of fission barriers of SHE have been carried out. These include calculations based on the microscopic-macroscopic treatment[1,2], the self-consistent approach with the Gogny[3] and Skyrme[4,5,6,7] forces, and also within the relativistic mean-field model[5,8,9].

The objective of this contribution is to study static fission barriers of the even-even SHE in the Skyrme-Hartree-Fock (SHF) approach with a seniority pairing force treated in the BCS approximation. We focus on two regions of SHE: (i) the deformed nuclei with $100\leq Z \leq 110$, and (ii) spherical isotones with $N$=184.

The calculations have been carried out using the code HFODD (v.2.09i)[10,11,12] that solves self-consistent HF equations by using the Cartesian harmonic oscillator (HO) finite basis. This code makes it possible to break all self-consistent symmetries of the nuclear mean field at the same time, including the axial and reflection symmetry, which is of particular interest in the present study.

Particular attention has been paid to symmetry-breaking effects along the fission path. The influence of reflection-asymmetric (for a non-zero octupole mass moment, $Q_{30}\equiv \langle \hat{Q}_{30}\rangle \neq 0$) and triaxial degrees of freedom (for $Q_{22} \neq 0$) on the static fission barriers are discussed.