Fission barrier heights of superheavy nuclei to 1 MeV
In plain words
Superheavy elements exist only because shell effects (extra stability from filled nucleon orbits) create an energy barrier against fission. Models disagree by several MeV on how high this barrier is, which changes predicted production rates by orders of magnitude.
Precise statement
For even-even nuclei with $Z = 112 \text{ to } 120$ and $N = 170 \text{ to } 184$, determine the inner fission barrier height $B_f$ to 1 MeV, defined on a multidimensional potential-energy surface including triaxial and reflection-asymmetric shapes. Current macroscopic-microscopic and self-consistent mean-field models differ by several MeV; the answer must be consistent with measured fusion-evaporation survival probabilities and spontaneous-fission half-lives. Because $B_f$ is not directly observable, the answer is a barrier from a microscopic potential-energy surface that, inserted in a stated statistical decay model with no refitting, reproduces measured evaporation-residue cross sections and spontaneous-fission half-lives in this region to within a factor 3.
What would settle it
Model barriers from independent approaches converging to $1\,\mathrm{MeV}$ and reproducing measured survival probabilities of compound superheavy nuclei, or barrier constraints from fission and gamma entry-distribution measurements in the heaviest accessible nuclei, such as 254No.