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Published January 7, 2026 | Version 1.4
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Isotope-Independent Geometric Invariants in Fermium Fission: Evidence from Pairing and Neck Systematics

Authors/Creators

  • 1. Independent Researcher, Higashimatsuyama,Saitama,Japan

Description

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 Takagi
Independent Researcher, Higashimatsuyama, Saitama, Japan
ORCID: 0009-0003-5188-2314

Related Work

Files

254Fm_final.csv

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Additional details

Related works

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Preprint: 10.5281/zenodo.18171175 (DOI)