Isotope-Independent Geometric Invariants in Fermium Fission: Evidence from Pairing and Neck Systematics

Isotope-Independent Geometric Invariants in Fermium Fission: Evidence from Pairing and Neck Systematics Version v1.3 — January 7, 2026 Extends v1.2: DOI 10.5281/zenodo.18162866 Overview This work identifies two isotope-independent critical deformations in fermium fission using Gogny D1S calculations from the literature. The analysis spans three isotopes (²⁵⁴Fm, ²⁵⁶Fm, ²⁵⁸Fm) connected through a "fermium triangle" structure. Key Findings Critical Deformation 1: Pairing Activity Peak (Q₂ = 30 ± 5 b) Isotope ⟨ΔN²⟩ peak position ⟨ΔN²⟩ peak value ²⁵⁴Fm Q₂ = 30 b 33 ²⁵⁶Fm Q₂ = 30 b 34 → The deformation for maximal collective pairing activity is FIXED across isotopes. Critical Deformation 2: Neck Cliff (Q₂ = 60 ± 5 b) Isotope Cliff position Scission EF bifurcation ²⁵⁶Fm Q₂ = 60 b 100 b 50 b ²⁵⁸Fm Q₂ = 60 b 100 b 50 b → The neck geometry follows a geometric ruler independent of neutron number. The Fermium Triangle ²⁵⁴Fm ←—— ⟨ΔN²⟩ @ 30 b ——→ ²⁵⁶Fm ←—— Q_N cliff @ 60 b ——→ ²⁵⁸Fm(pairing) (bridge) (neck) ²⁵⁶Fm serves as the bridge isotope with complete data, connecting: Slice A (Pairing): ²⁵⁴Fm ↔ ²⁵⁶Fm [Zdeb et al.] Slice B (Neck): ²⁵⁶Fm ↔ ²⁵⁸Fm [Warda et al.] Physical Interpretation Fermium fission follows shape-determined dynamics: Critical deformations (pairing peak, neck rupture) are set by nuclear geometry Neutron number modulates magnitudes but not geometric locations This aligns with the concept of formal causation introduced in v1.2 Data Sources Isotope Quantity Source Reference ²⁵⁴Fm Δ, ⟨ΔN²⟩ Zdeb et al. Fig.7 arXiv:2507.00664 ²⁵⁶Fm Δ, ⟨ΔN²⟩ Zdeb et al. Fig.7 arXiv:2507.00664 ²⁵⁶Fm Q_N Warda et al. Fig.3 nucl-th/0203057 ²⁵⁸Fm Q_N Warda et al. Fig.4 nucl-th/0203057 Package Contents File Description v13_fermium_invariants.pdf Main manuscript (4 pages) v13_fermium_invariants.tex LaTeX source v13_fermium_triangle.png Summary figure (4 panels) 254Fm_final.csv ²⁵⁴Fm pairing data 258Fm_QN_CF.csv ²⁵⁸Fm neck data v13_254_256_comparison.csv Isotope comparison data Keywords nuclear fission · fermium isotopes · geometric invariants · pairing correlations · neck parameter · Gogny D1S · formal causation License CC BY 4.0 Author Takayuki Takagi Independent Researcher, Higashimatsuyama, Saitama, Japan ORCID: 0009-0003-5188-2314 Related Work v1.2: 10.5281/zenodo.18162866 — ²⁵⁶Fm single-isotope analysis