What question did this study set out to answer?

Investigate the connection between the golden ratio and predictions of nuclear magic numbers.

January 22, 2026Open Access

Seed Equation: Phenomenological Convergence of Golden Ratio and Relativistic Nuclear Stability Predictions

Key Points

Investigate the connection between the golden ratio and predictions of nuclear magic numbers.
Analyzed the Lucas sequence related to the golden ratio
Derived predictions based on algebraic identities
Compared predictions with standard shell model and RCHB calculations
Conducted statistical analysis to assess significance of findings.
Predicted neutron magic number N = 199 from the Lucas sequence
Contradicted standard shell model prediction of N = 184
Converged within 1 neutron of RCHB calculations (N = 198)
Statistical analysis confirmed significance with p = 0.02.

Abstract

We report a phenomenological observation where the Lucas sequence (derived from the golden ratio φ) approximates nuclear magic numbers. From the algebraic identity φ⁴ + φ⁻⁴ = 7 (Lucas number L₄), we derive a prediction for the next superheavy magic number at N = 199 (L₁₁). This prediction contradicts the Standard Shell Model (N = 184) but converges within exactly 1 neutron of Relativistic Continuum Hartree-Bogoliubov (RCHB) calculations (N = 198). Multiple independent RCHB studies explicitly predict N = 198 as a neutron magic number (Zhang 2005, Patra 2025, Saxena 2020). Statistical analysis confirms this convergence is significant (p = 0.02). The N = 199 prediction constitutes a falsifiable test, experimentally accessible within 20-30 years.

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andrei-sebastian ursachi (Tue,) studied this question.

synapsesocial.com/papers/6971be8d642b1836717e337d https://doi.org/https://doi.org/10.5281/zenodo.18309680

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