Nuclear Structure: Weizsäcker Formula Derived from Sphere Packing Geometry Zero-Parameter SEMF Verified on 2541 Nuclei (AME2020, mpmath 150-digit precision)

March 20, 2026Open Access

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Key Points

To derive closed-form expressions for coefficients of the Weizsäcker semi-empirical mass formula without experimental inputs.
Derivation of coefficients from kissing numbers and navigation constant based on sphere packing geometry.
Verification using 2541 experimental nuclei from AME2020 to assess accuracy against standard SEMF methods.
Statistical analysis of fitting coefficients and model performance on various nuclear groups.
All five coefficients derived from geometry showed a maximum error below 1.24%.
UCT outperformed standard SEMF in fitting accuracy, indicating improved predictive capabilities for nuclear stability.
Statistical significance of matching coefficients suggests robust geometrical relationships across 2301 experimental data points.

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This analysis derives coefficients of the semi-empirical mass formula in nuclei, suggesting novel geometric relations in nuclear stability.

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Aleksei Novgorodtsev (2026) studied this question.

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