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 v1.5 — January 7, 2026 Extends v1.4: DOI 10.5281/zenodo.18173003 What's New in v1.5 Added Appendix B: Extension to ²⁴⁰Pu (lighter actinide test) Key finding: Functional correspondence preserved; numerical values scale systematically with Z Dual scission proxy (A/B): Reveals ~45 b definition dependence (topology vs. density) Figure B1: 3-panel comparison across 6 actinide nuclei (Fm series + Cf + No + Pu) Table B1: Complete extract sheet with sources Total pages: 9 (was 7 in v1.4) Overview This work identifies isotope-independent critical deformations in fermium fission using Gogny D1S calculations from the literature. The analysis spans three fermium isotopes (²⁵⁴Fm, ²⁵⁶Fm, ²⁵⁸Fm), two neighboring actinides (²⁵²Cf, ²⁵⁸No), and now extends to a lighter actinide (²⁴⁰Pu). Key Results Early marker (Q₂,Δ ≈ 30 b for Fm): Functionally preserved across all nuclei Fm: 30 b → Cf/No: 35 b → Pu: 54 b Preservation = functional correspondence, not numerical equality Channel bifurcation: Systematic scaling with Z Fm: ~50 b → Pu: ~110 b (×2.2 factor) Scission: Definition-dependent scaling Fm: ~100 b → Pu: ~295–340 b (×3 factor) A/B proxy gap (45 b) quantifies definition dependence Conclusion The Fermium ruler survives extension to a lighter actinide not as a rigid numerical scale, but as a hierarchy of operationally defined markers: an early pairing-related marker that is functionally preserved, followed by later markers that undergo systematic, nucleus-dependent rescaling. Package Contents File Description v15_fermium_invariants.pdf Main manuscript (9 pages) v15_fermium_invariants.tex LaTeX source v15_appendix_B.tex Appendix B source (²⁴⁰Pu extension) v13_fermium_triangle.png Figure 1: Fermium systematics A_lite_final.png Figure A1: Cf/No comparison Figure_B1_Pu240.png Figure B1: ²⁴⁰Pu extension 254Fm_final.csv ²⁵⁴Fm pairing data 258Fm_QN_CF.csv ²⁵⁸Fm neck data v13_254_256_comparison.csv Isotope comparison data Pu240_extract.csv ²⁴⁰Pu extracted values Keywords nuclear fission · fermium isotopes · geometric invariants · pairing correlations · neck parameter · Gogny D1S · formal causation · californium · nobelium · plutonium-240 · operational definitions License CC BY 4.0 Author Takayuki TakagiIndependent Researcher, Higashimatsuyama, Saitama, JapanORCID: 0009-0003-5188-2314 Related Work v1.4: 10.5281/zenodo.18173003 v1.3: 10.5281/zenodo.18171175 v1.2: 10.5281/zenodo.18162866 v1.1: 10.5281/zenodo.18152763 v1.0: 10.5281/zenodo.18144597 Data Sources for Appendix B Chen et al. (2022) Chinese Physics C 46, 024103 Schunck et al. (2014) Phys. Rev. C 90, 054305 Younes & Gogny (2009) Phys. Rev. C 80, 054313