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)

docs/nuclear-structure/01-shape-factors.md

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+---
+title: "10 – Nuclear Structure Effects"
+date: 2026-04-26
+tags:
+  - beta-spectrum/nuclear-structure
+status: active
+aliases: [Shape Factor, C(Z,W), Form Factors]
+cssclasses: []
+related_components: [[corrections/06-recoil]], 
+---
+
+# Nuclear Structure Effects — The Shape Factor $C(Z,W)$
+
+## Overview
+
+Nuclear structure effects are encapsulated in the shape factor $C(Z,W)$ which multiplies the phase space × Fermi function. This is distinct from electrostatic finite size corrections ([[corrections/02-finite-size]]) — it describes how nuclear form factors and matrix elements modify the spectrum beyond simple point-nucleus Coulomb interaction.
+
+$$N(W)\,dW \propto p W (W_0 - W)^2 F(Z,W) C(Z,W) \tag{79}$$
+
+## Two Formalisms Compared
+
+| Approach | Style | Strengths |
+|---|---|---|
+| **Behrens-Bühring** (BB) | Couples leptonic + nuclear parts; rigorous expansion in $r^2$, $(m_eR)^a$, $(WR)^b$, $(\alpha Z)^c$ with tabulated functions $I(k_e,m,n,\rho)$ | Most precise, established computational machinery |
+| **Holstein** (HS) | Decouples leptonic + nuclear parts; manifestly covariant form factors | Clean symmetry properties, intuitive classification |
+
+Hayen et al. adopt BB's computational approach but present results in Holstein notation for clarity. See Appendix E of Hayen paper for detailed comparison.
+
+## Multipole Expansion (Eq. 78)
+
+Form factors $F_{KLs}(q^2)$ describe nuclear structure model-independently:
+
+$$\langle f | V_\mu - A_\mu | i \rangle \propto \sum_{KMs} \sum_{L=K-1}^{K+1} (-1)^{J_f-M_f+M} (-i)^L F_{KLs}(q^2) $$
+$$\times \sqrt{4\pi(2J_i+1)} \begin{pmatrix} J_f & K & J_i \\ -M_f & M & M_i \end{pmatrix} \frac{(qR)^L}{(2L+1)!!}$$
+
+Since $(qR)^2$ is very small for beta decay, expansion typically stops after first order.
+
+## Impulse Approximation (Eq. 80–81)
+
+Nucleons treated as non-interacting particles coupling to weak vertex as free particles:
+
+$$O_{KLs} = \sum_{\alpha,\beta} \langle \alpha | O_{KLs} | \beta \rangle a^\dagger_\alpha a_\beta \tag{80}$$
+$$\langle f | O_{KLs} | i \rangle = \sum_{\alpha,\beta} \langle \alpha | O_{KLs} | \beta \rangle \langle f | a^\dagger_\alpha a_\beta | i \rangle \tag{81}$$
+
+The one-body density matrix elements $\langle f | a^\dagger_\alpha a_\beta | i \rangle$ are calculable via shell model methods.
+
+> [!warning] Limitations
+> The impulse approximation neglects many-body effects:
+> - **Meson exchange**: long history (Blin-Stoyle, Chemtob & Rho)
+> - **Core polarization**: nuclear medium modifications
+> 
+> For allowed decays, results largely hold due to cancellations between core-polarization and meson exchange (Morita 1985), but individual effects can reach ~40%.
+
+## Induced Currents — Form Factor Classification
+
+See [[corrections/06-recoil]] for detailed equations. Key points:
+
+### First-Class Currents (CVC/PCAC)
+- **Vector** $g_V$: conserved, from EM data via CVC
+- **Weak magnetism** $(g_M - g_V)/2M$: determined by CVC from M1 transitions
+- **Axial-vector** $g_A$: measured in neutron decay
+- **Induced pseudoscalar** $g_P/2M$: PCAC predicts ~−229, quenched ~80% in nuclei
+
+### Second-Class Currents (G-parity forbidden)
+- **Induced scalar** $g_S/2M$: excluded by CVC for Fermi transitions
+- **Induced tensor** $g_{II}/2M$: experimental null results; reduces to first-class component only
+
+## Nuclear Matrix Element Operators (Table V of Hayen)
+
+| Operator | Symbol | Type | $\Delta J$ |
+|---|---|---|---|
+| $M_F$ | Fermi matrix element | Vector | 0 |
+| $M_{GT}$ | Gamow-Teller matrix element | Axial-vector | 0,1 (not 0→0) |
+| $M_L$ | Longitudinal vector | — | depends on K |
+| $M_{T}, M_{TL}$ | Transverse multipoles | — | depends on K |
+
+## Validity of Impulse Approximation
+
+- **Vector current**: conserved via CVC → impulse approximation reliable
+- **Axial current**: broken by PCAC → quenching effects significant (up to 80% for $g_P$)
+- Mesonic degrees of freedom absorbed into nuclear potential (Wilkinson 1974)
+
+## Nuclear Deformation Correction $D_C(Z,W,\beta^2)$
+
+The nuclear structure analogue of the electrostatic deformation correction ([[corrections/02-finite-size]]):
+- Accounts for non-spherical nuclear shape in convolution terms
+- Partially cancels with $DFS$ correction (electrostatic)
+- Relevant for deformed nuclei ($\beta_2 \neq 0$)
+
+## Calculator Status
+
+> [!info] Not yet implemented
+> The shape factor $C(Z,W)$ is NOT part of the current calculator. This note documents the theory for future implementation. For superallowed Fermi transitions, $C(Z,W) = |M_F|^2 \approx 1$ (isospin symmetry), so it can be approximated as unity in many cases.

docs/nuclear-structure/index.md

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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