The effect of gamma deformation on the height of the fission barrier in actinides

Systematic calculations of the fission barriers with allowance of triaxial deformation have been performed for the first time within the covariant density functional theory. Pairing is treated within the BCS approximation using seniority zero forces adjusted to empirical values of the gap parameters. Different pairing schemes and their impact on inner fission barriers have been studied in detail. The covariant density functional theory is successful in reproducing the height of the fission barriers at a level of accuracy comparable with the best non-relativistic phenomenological macroscopic+microscopic approaches. Our analysis of the results of calculations shows that allowing triaxial deformation reduces the height of the inner barrier by 1-3 MeV. The fission path between the first and second axially deformed minima goes through the valley characterized by $\gamma$-deformation close to 10$^{\circ}$.