Nuclear Mass Deficit Calculator

Predict nuclear mass deficits using the alpha-layered restoration model. Enter any nucleus to see how the fine-structure constant α = 1/137 governs nuclear stability.

Calculate Mass Deficit

Enter a nucleus symbol (e.g., He-4, C-12, Fe-56) to calculate its predicted mass deficit using the alpha-layered restoration model.

Quick Examples

About the Model

The alpha-layered restoration model predicts nuclear mass deficits based on the principle that helium-4 (the alpha particle) is the fundamental building block of heavier nuclei. Each alpha particle contributes a baseline restoration of α = 1/137 (the fine-structure constant), with additional compression enhancement that saturates as nuclei get heavier.

The Formula

Δm/m = α × [1 + β₀ × n × exp(-γn)]

  • α = 0.00729735 — Fine-structure constant (1/137), the quantum speed limit for restoration
  • β₀ = 0.0370 — Initial compression enhancement factor
  • γ = 0.0424 — Saturation rate (inverse of ~50 alphas, the periodic table stability limit)
  • n = A/4 — Number of alpha particles in the nucleus

This model explains why gravity is weak by a factor close to 137: the gravitational constant G emerges as G = A(t) × R(t), where the restoration rate R(t) = 0.007594 (helium-4 mass deficit, equal to 1.04α) suppresses the bare gravitational coupling A(t). This connects nuclear physics directly to gravity through helium-4 stability.

Works Best For:

  • Alpha-process nuclei (C-12, O-16, Si-28, Ca-40, Fe-56)
  • Iron peak elements (Fe, Co, Ni)
  • Helium-4 (fundamental unit, matches α exactly)

Limited Accuracy For:

  • Light nuclei (H-2, H-3, He-3, Li-6, Be-9)
  • Odd-A nuclei (require shell corrections)
  • Neutron-rich nuclei (beyond iron peak)

Future Development

We are actively working to extend this model to the entire periodic table by incorporating:

  • Shell closure effects for magic numbers (2, 8, 20, 28, 50, 82, 126)
  • Pairing corrections for odd-A and odd-odd nuclei
  • Neutron excess corrections for neutron-rich nuclei
  • Deformation effects for non-spherical nuclei

These extensions will maintain the core insight: α = 1/137 is the fundamental restoration rate, with corrections accounting for nuclear structure details.

Want to understand the theory behind this calculator?