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 v1.4 — January 7, 2026 Extends v1.3: DOI 10.5281/zenodo.18171175 What's New in v1.4 Added Sec.2.3: Operational Definitions (reviewer-proof formulations) Added Appendix A: A-lite test on ²⁵²Cf and ²⁵⁸No Key finding: The fermium ruler is preserved at early stages (~30 b) and undergoes systematic rescaling at later stages Figure A1: 3-panel comparison across 5 actinide nuclei Total pages: 7 (was 4 in v1.3) 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, with extension to ²⁵²Cf and ²⁵⁸No in Appendix A. Key Findings Critical Deformation 1: Pairing Activity Peak (Q₂ = 30 ± 5 b) Isotope ⟨ΔN²⟩ peak position Status ²⁵⁴Fm Q₂ = 30 b ✓ ²⁵⁶Fm Q₂ = 30 b ✓ ²⁵²Cf Q₂ = 35 b ✓ ²⁵⁸No Q₂ = 35 b ✓ → PRESERVED across all nuclei (~30-35 b) Critical Deformation 2: Neck Cliff & Scission Isotope Bifurcation Scission Status ²⁵⁶Fm 50 b 100 b baseline ²⁵⁸Fm 50 b 100 b baseline ²⁵²Cf 65 b 130 b scaled ²⁵⁸No 75 b 140 b scaled → SCALED (nucleus-dependent shift at later stages) The Fermium Triangle ²⁵⁴Fm ←—— ⟨ΔN²⟩ @ 30 b ——→ ²⁵⁶Fm ←—— Q_N cliff @ 60 b ——→ ²⁵⁸Fm (pairing) (bridge) (neck) A-lite: Extension to Cf and No The fermium ruler acts as a transferable deformation ruler: Early critical mark (~30 b): universal Later marks (bifurcation, scission): rescale smoothly with nuclear size The observed shifts correlate with increasing Z and A, but no attempt is made to disentangle their individual contributions. Package Contents File Description v13_fermium_invariants_final.pdf Main manuscript (7 pages) v13_fermium_invariants_final.tex LaTeX source v13_fermium_triangle.png Figure 1: Fermium systematics A_lite_final.png Figure A1: Cf/No comparison 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 · californium · nobelium License CC BY 4.0 Author Takayuki TakagiIndependent Researcher, Higashimatsuyama, Saitama, JapanORCID: 0009-0003-5188-2314 Related Work v1.3: 10.5281/zenodo.18171175 v1.2: 10.5281/zenodo.18162866 v1.1: 10.5281/zenodo.18152763 v1.0: 10.5281/zenodo.18144597