Effects of triaxial deformation on the fission barrier in the $Z=118-120$ nuclei

Within the framework of the macroscopic-microscopic model by using potential energy surface (PES) calculations in the three-dimensional space ($\beta_2$, $\gamma$, $\beta_4$), the fission trajectory and fission barrier for $Z=118$(Og), $119, 120$ nuclei have been systematically investigated. The calculated PES includes macroscopic liquid-drop energy, microscopic shell correction and pairing correction. Taking the $^{294}$Og$_{176}$ nucleus as an example, we discuss the next closed shell after $Z=82$ and $N=126$ with the calculated Woods-Saxon single-particle levels. Then, the results of PES in $^{294}$Og is illustrated from the (X, Y) scale to the ($\beta_2$, $\gamma$) scale. The $\gamma$ degree of freedom reveals the shape evolution clearly during the fission process. The structure near the minimum and saddle point of PES in the $Z=118, 119, 120$ nuclei are demonstrated simultaneously. Based on the potential energy curves, general trends of the evolution of the fission barrier heights and widths are also studied. The triaxial deformation in these superheavy mass regions plays a vital role in the first fission barrier, showing a significant reduction in both triaxial paths. In addition, the model-dependent fission barriers of proton-rich nuclei $^{295}$Og, $^{296$119 and $^{297}$120 are analyzed briefly. Our studies could be valuable for synthesizing the superheavy new elements in the forthcoming High Intensity Heavy-ion Accelerator Facility (HAIF) and other facilities.