Semi-Empirical Mass Formula (Nuclear Binding Energy)

$$\frac{B}{A} = a_V - a_S A^{-1/3} - a_C \frac{Z(Z-1)}{A^{4/3}} - a_A \frac{(N-Z)^2}{A^2}$$

Status: Proven.

This is the standard liquid-drop model of the nucleus (von Weizsäcker, 1935; Bethe & Bacher, 1936), predicting binding energy per nucleon from four physical terms: volume (bulk binding), surface (a “skin” cost, like surface tension), Coulomb (proton-proton electrostatic repulsion), and asymmetry (a Pauli-exclusion penalty for unequal proton/neutron counts).

Real, independent confirmation: see The Semi-Empirical Mass Formula for the full status — this formula, fit against real measured binding energies, remains a standard working tool in nuclear physics nearly a century later, accurate to a few percent across most of the periodic table.

Used in: Paper 13 (unpublished draft), which re-derives this formula’s structure from PBT’s own equilibrium-pressure premise, fits its coefficients from real data with no textbook values assumed, and validates the result out-of-sample (RMSE 0.133 MeV on 15 withheld isotopes) — a genuinely rigorous piece of work. But the paper is explicit about its own limit: the Coulomb term’s functional form is mathematically identical to the standard electrostatic self-energy of a charged sphere, reframed in pressure language, not derived from anything deeper. The formula itself is proven; PBT’s claim to have derived electric charge or its repulsion from subatomic pressure at a deeper level is not — see Asymmetry-Term Ladder Toy Model for the one piece of this paper that does attempt an original, partial derivation.