docs: restructure knowledge base into tree layout + gA extraction module

- Organize into tree structure: corrections/, nuclear-structure/, gA-extraction/, refs/
- Move all correction notes to corrections/ (01-09)
- Move nuclear structure to nuclear-structure/ with index
- Add gA-extraction/ with SSM algorithm, sNME/ESSM formalism, Tc99 case study, and implementation TODO
- Reorganize refs by topic (electromagnetic/, forbidden-decay/)
- Update all wikilinks to new paths
- Remove radiative_spec.md (code algorithm, not reference)
- Lint: all wikilinks verified valid
- Comprehensive gA extraction research based on Paulsen et al. (2024) and Song et al. (2025)
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---
title: "Nuclear Structure — Overview"
date: 2026-05-14
tags:
- beta-spectrum/nuclear-structure
status: active
aliases: [Nuclear Theory, Shape Factor, NME]
---
# Nuclear Structure Effects in β Decay
## Overview
Nuclear structure enters the β spectrum through the **shape factor** $C(Z,W)$, which encodes how the nuclear wave functions and transition matrix elements modify the spectrum beyond the point-nucleus Coulomb interaction.
## Contents
- [[nuclear-structure/01-shape-factors]] — Shape factor $C(Z,W)$: decomposition, multipole expansion, impulse approximation, induced currents
## Key Concepts
- **Shape factor decomposition:** $C(W) = g_V^2 C_V(W) + g_A^2 C_A(W) + g_V g_A C_{VA}(W)$
- **Forbidden decays:** Nonunique transitions are sensitive to $g_A$ → basis for SSM
- **sNME:** Small relativistic vector NME — critical for precision but hard to compute
## Related
- [[gA-extraction/01-ssm-algorithm]] — How to extract $g_A$ from shape factor
- [[corrections/06-recoil]] — Weak magnetism, induced currents, recoil effects