Conclusion

The purpose of this work was to study the sensitivity of static fission trajectories in $N$=184 isotones to the choice of pairing interaction in the SHF+BCS model. We found that the results (energies, hexadecapole moments, pairing gaps) are fairly insensitive to the assumed density dependence of the pairing $\delta$-interaction (DI, DDDI, or MIX). On the other hand, we found rather large differences between results obtained in $\delta$-pairing and seniority-pairing variants. This suggests that the isospin dependence of the seniority-pairing strength used is unrealistic. In general, it is always advantageous to consider a more realistic interaction in the pairing channel (such as the density-dependent $\delta$ force) which does not depend explicitly on mass number and neutron excess.

In the second part of the paper, we examined static fission paths calculated within the SHF+BCS($\delta$) framework and MIX pairing parameterization for twelve even-even $N$=184 isotones. We found that the reduction of fission barriers due to the appearance of triaxial deformation strongly depends on $Z$. Furthermore, the analysis of the static fission barriers suggests the increased stability against spontaneous fission for $118\leq Z \leq 124$.