Solve The Universe

Pressure-Based Theory — a mechanical, unified account of gravity, electromagnetism, spin, and entanglement

The Semi-Empirical Mass Formula (Liquid-Drop Model)

What it claims: Proposed by Carl Friedrich von Weizsäcker (1935) and refined by Bethe & Bacher (1936), the semi-empirical mass formula models the nucleus as a liquid drop, predicting binding energy per nucleon from five real physical terms: volume (bulk binding), surface (a drop’s “skin” costs energy, same as surface tension), Coulomb (protons electrostatically repel each other), asymmetry (a quantum-statistical penalty for unequal proton/neutron counts, from the Pauli exclusion principle), and pairing (an extra bonus for even-even nuclei).

Catalog status: Proven Systems. This formula, fit against real measured binding energies, remains a standard teaching and working tool in nuclear physics nearly a century later — accurate to a few percent across most of the periodic table. Its known real limitation is that it’s a smooth model with no shell structure, so it systematically misses “magic number” nuclei (closed nuclear shells, e.g. tin-132, lead-208) that are unusually tightly bound — that gap is what motivated the nuclear shell model (Maria Goeppert Mayer & J. Hans D. Jensen, 1949, shared 1963 Nobel Prize), a real, separate, also-proven refinement.

Where PBT touches this: Paper 13 (currently an unpublished draft, not yet live on this site) re-derives this formula’s structure from PBT’s own “equilibrium bubble” pressure premise — reframing the Coulomb term as protons producing extra outward pressure, and offering a partial (explicitly incomplete, by the paper’s own admission) toy derivation of the asymmetry term’s quadratic form from discrete level-filling. The paper is unusually direct about its own limits: it states plainly that it reproduces the form of established terms rather than deriving electric charge or Pauli exclusion from anything deeper, and that its fitted coefficients (validated out-of-sample against 15 real withheld isotopes, RMSE 0.133 MeV) land within about 8% of the real textbook values — expected for using the correct functional form against real data, not an independent rediscovery of nuclear physics.

References

  1. von Weizsäcker, C.F. (1935). “Zur Theorie der Kernmassen.” Zeitschrift für Physik 96, 431–458.
  2. Bethe, H.A., Bacher, R.F. (1936). “Nuclear Physics A. Stationary States of Nuclei.” Reviews of Modern Physics 8, 82–229.
  3. Mayer, M.G. (1949). “On Closed Shells in Nuclei. II.” Phys. Rev. 75, 1969.
  4. Wang, M. et al. (2021). “The AME 2020 atomic mass evaluation.” Chinese Physics C 45, 030003.