Novel semi-empirical formula and examination for fission barriers of super-heavy nuclei with Z ≥ 100

In this study, we developed a semi-empirical formula for predicting fission barriers of super-heavy nuclei (SHN), which have fissilities χ > 48.5428, based on a former formula proposed by Myers and Swiatecki [1999 Phys. Rev. C 60, 014 606]. We calculated fission barriers for isotopes with Z = 100-135 using our formula and the Lublin-Strasbourg Drop model. It was found that the macroscopic component of the fission barrier is less than 0.2 MeV, which is large enough to be considered with microscopic part for many SHN. These results were compared to each other and to those estimated using other approaches. Through evaluations of theoretical fission barriers, we found that there is a significant difference, up to a few MeV, between the results obtained from different models. In other words, recent fission barrier predictions are very uncertain. Finally, the results of this study are useful for estimating the spontaneous-fission lifetime and production cross sections of unknown super-heavy nuclei.