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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This research aims to derive coefficients of the Weizsäcker semi-empirical mass formula utilizing sphere packing geometry.
Derivation of five coefficients from kissing numbers and the navigation constant.
Verification on 2541 experimental nuclei from the AME2020 database.
Comparison of UCT with Standard SEMF using statistical analysis.
All five coefficients derived with maximum error less than 1.24%.
UCT demonstrates superior performance with mean errors significantly lower than Standard SEMF across various categories.
Statistical significance showed a probability of matching by chance at approximately 9.3 x 10⁻⁹.

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Deriving five coefficients of the Weizsäcker formula in 2541 nuclei, indicating superior accuracy in nuclear stability predictions.

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Aleksei Novgorodtsev (2026) studied this question.

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