Bohr-Wheeler Fissionability Parameter

$$x = \frac{E_{Coulomb}}{2E_{surface}}, \quad \left(\frac{Z^2}{A}\right)_{crit} = \frac{2a_S}{a_C}$$

Status: Proven.

Proposed by Niels Bohr and John Wheeler (1939) as part of the original liquid-drop theory of nuclear fission: a nucleus becomes unstable against spontaneous fission when its Coulomb (electrostatic repulsion) energy exceeds twice its surface (binding) energy — at that point, splitting into two pieces lowers total energy, and no barrier stops it. This gives a critical value of $Z^2/A$ above which a nucleus can’t be a stable liquid drop at all, expressed directly in terms of the same two coefficients ($a_S$, $a_C$) as the semi-empirical mass formula it’s built from.

Real, independent confirmation: the classical liquid-drop literature places this threshold at roughly 48–51 using standard textbook coefficients; real superheavy nuclei sit close to or exceed it, directionally consistent with these being the most fission-unstable known elements (though real fission barriers also depend on shell and pairing corrections this pure liquid-drop parameter doesn’t capture — the primary reason superheavy elements survive at all despite sitting near this threshold).

Used in: Paper 13 (unpublished draft), which computes a critical value of 44.1 from its own independently-fitted coefficients — a 13.9% difference from the classical ~48–51 range, within the spread seen across published semi-empirical fits using different coefficient sets. A real, checkable result, computed correctly from the paper’s own numbers (independently re-verified in this session’s own audit).