A Comprehensive Empirical Study of the Critical Point at N/Z = 1.55 in Heavy Nuclides: Six Independent Dimensions of Evidence

Abstract

Whether a universal critical N/Z value governs the stability and decay modes of all heavy nuclides has remained unresolved. Using experimental data from the ENDF/B-VIII.0, NuDat 3.0, ENSDF, and AME2020 public databases, this paper identifies N/Z = 1.55 as a structural break point within the heavy nuclide region (Z > 82, N > 126) through six independent empirical analyses. (1) Piecewise linear regression and the Chow test on 577 heavy nuclides reveal a statistically highly significant structural break in logarithmic half-life at N/Z = 1.55 (p < 0.000001). (2) The doubly magic ²⁰⁸Pb chain and two non-magic control chains (At, Fr) demonstrate that shell stabilization fails once N/Z exceeds 1.55. (3) A survey of 32 nuclides with competing α and β⁻ decay channels reveals a rapid phase transition in decay mode dominance at N/Z = 1.55, with α branching ratios dropping by several orders of magnitude within Δ(N/Z) ≈ 0.01–0.02. (4) In the superthreshold region, β⁻-dominated half-lives obey a power-law scaling T₁/₂ ∝ (N − 1.55Z)^(−γ) with γ ≈ 6.5 (R² = 0.94 for the Pb chain), verified across four isotopic chains. (5) Significant spontaneous fission (branching ratio > 0.1%) occurs exclusively at N/Z ≥ 1.55 among 28 actinides, with zero counterexamples. (6) Neutron separation energies and β-decay Q-values break sharply at N/Z = 1.55, unlike Q_α, confirming the effect is specific to neutron excess. These six independent lines of evidence converge on a single conclusion: within the heavy nuclide region, N/Z = 1.55 constitutes a structural break that subordinates local shell effects and governs the global switching of decay modes, the onset of spontaneous fission, and the behavior of neutron separation energies. A dedicated comparison with the conventional β-stability valley demonstrates that N/Z = 1.55 is physically distinct from a smooth energy minimum. The sharpness, simultaneity, and shell-independence of this transition suggest the possible involvement of a global saturation mechanism. A candidate framework—geometric saturation of the nucleon correlation network—is briefly discussed as a possible interpretive lens, while the empirical findings stand independently. All analyses use publicly available data and standardized statistical methods, and are independently reproducible.