Structural Coherence in Nuclear Fission: Tracking Correlation Collapse Along the ²⁵⁶Fm Fission Path

Structural Coherence in Nuclear Fission: Tracking Correlation Collapse Along the ²⁵⁶Fm Fission Path Overview This work introduces Structural Coherence ($S_c$), a new quantitative measure that captures the correlated behavior of pairing dynamics and neck geometry along nuclear fission paths. Key Concept We define: $$S_c = \frac{\Delta \cdot Q_N}{\Delta_{\max} \cdot Q_{N,\max}}$$ where: $\Delta$ = pairing gap (MeV) $Q_N$ = neck parameter (dimensionless) Normalization ensures $S_c \in [0, 1]$ This single quantity tracks where pairing and geometric collectivity are maximally correlated, and where this correlation breaks down—signaling the approach to scission. Main Results (²⁵⁶Fm, Gogny D1S) Quantity Compact Fission (CF) Elongated Fission (EF) $S_c$ peak $Q_2 = 30$ b, $S_c = 0.842$ $Q_2 = 50$ b, $S_c = 0.676$ Neck cliff $Q_2 = 60$ b — Two-Stage Physical Picture Coherent Regime ($Q_2 \lesssim 30$ b) Pairing gap $\Delta$, fluctuation $\langle\Delta N^2\rangle$, and neck parameter $Q_N$ all peak together $S_c$ reaches maximum → maximal correlation between pairing and geometry Collapse ($Q_2 \gtrsim 60$ b) Neck parameter drops sharply ("cliff") $S_c \to 0$ as the nucleus approaches scission By $Q_2 = 100$ b: neck ruptured, $Q_N = 0$, $S_c = 0$ Auxiliary Measure An independent pairing sharpness diagnostic: $$S_{\mathrm{pair}} = \frac{\Delta^2}{\langle\Delta N^2\rangle}$$ peaks at the same deformation ($Q_2 = 30$ b), reinforcing the robustness of the correlation. Data Sources Variable Source Reference $Q_N(Q_2)$ Warda et al. Fig.3(d) arXiv:nucl-th/0203057 $\Delta(Q_{20})$ Zdeb et al. Fig.7(c) arXiv:2507.00664 $\langle\Delta N^2\rangle(Q_{20})$ Zdeb et al. Fig.7(d) arXiv:2507.00664 Note: The CF/EF paths (Warda) and LA path (Zdeb) are not identical but traverse qualitatively similar deformation sequences. The correspondence is illustrative but structurally consistent. Significance This is the first work to: Define a single quantitative measure ($S_c$) for pairing–geometry correlation in fission Identify the "cliff" position where structural coherence collapses Provide a unified two-stage picture: coherence → collapse The framework is extensible to other actinides and fissioning systems. Package Contents File Description v12_structural_coherence.pdf Main manuscript (5 pages) v12_structural_coherence.tex LaTeX source 256Fm_unified_v12_corrected.csv Complete dataset (21 points, 20–120 b) 256Fm_v12_corrected.png Summary figure (5 panels) README.md Package description Keywords nuclear fission · structural coherence · pairing gap · neck parameter · fermium-256 · Gogny D1S · density functional theory · scission License CC BY 4.0 Author Takayuki TakagiIndependent Researcher, Higashimatsuyama, Saitama, JapanORCID: 0009-0003-5188-2314