Edef = ES(0)[(Bs − 1) + 2x(Bc − 1)], Bs and Bc the surface area and Coulomb self-energy relative to the sphere. Sharp surface, uniform charge, no shell or pairing energy, no rotation.
Shapes: the (c, h) "funny hills" of Brack et al. at α = 0 (mass-symmetric); c is the half length in units of R0, h controls the neck. Coulomb energy as a double surface integral, azimuth in closed form with elliptic integrals; spheres and spheroids reproduce the closed forms to 10−15, and an independent solver agrees to 5×10−9.
Saddle: lowest pass from the sphere to the scission region on the (c, h) grid, then Newton on ∇E = 0 with the direct energies, accepted only if it converges to a point with exactly one unstable direction. For 1 − x < 10−3, where Newton on the direct energies approaches their rounding floor, the barrier is Bohr and Wheeler's series, Eq. (24); the saddle's location there comes from at most six Newton steps on the direct energies, accepted only if its energy meets the series to 10−4 (down to 1 − x ≈ 4×10−4), and is otherwise extrapolated. A richer shape family (even Legendre terms to P16) finds saddles 0.02 to 3.7% lower: the funny-hills barrier is an upper bound.
Path: steepest descent from the saddle down to the sphere and down to scission, which is taken to be the shape whose neck radius has fallen to 0.02 R0 (the step is cut back so the end point is that shape). The step adapts and is accepted only if the direct energy falls, so no point of the path lies above the saddle; while a slider moves the grid's interpolated energies decide instead and the path is provisional until it stops. For 1 − x below about 4×10−4 the direct energies cannot locate the saddle, and the path drawn there, started from the extrapolated location, is illustrative: its highest point is not the quoted barrier. If the descent does not get there, the drop is not split. What follows scission in the animation, the halves rounding off and flying apart, is illustration on a fixed schedule, not a solution of their Coulomb motion.