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/corrections/03-screening.md

@@ -0,0 +1,93 @@
+---
+title: "04 – Screening Correction"
+date: 2026-04-26
+tags:
+  - beta-spectrum/correction/screening
+status: active
+aliases: [Atomic Screening, S(Z,W)]
+cssclasses: []
+related_components: [[corrections/08-atomic-overlap]], [[corrections/09-chemical-effects]]
+---
+
+# Atomic Electron Screening Correction $S(Z,W)$
+
+## Physical Origin
+
+The Fermi function ([[corrections/01-fermi-function]]) assumes the β particle moves in the Coulomb field of a bare nucleus. In reality, atomic electrons partially screen this charge at large distances from the nucleus, modifying the effective potential experienced by the emitted electron/positron. This is particularly important at low kinetic energies where the β particle spends more time far from the nucleus.
+
+## The Screening Correction
+
+Screening is implemented as a ratio method:
+
+$$S(Z,W) = \frac{F_{\text{screened}}(Z, W)}{F_0(Z, W - V_0/m_ec^2)} \tag{144}$$
+
+where $V_0$ is the screening potential (binding energy of the outermost atomic electrons). The denominator evaluates the Fermi function at a shifted energy representing the unscreened case.
+
+### Screening Potential
+
+The screening potential $V_0$ depends on:
+- Atomic number $Z$ (parent atom)
+- Chemical/physical state (neutral atom, ionized molecule)
+- Electronic configuration
+
+For neutral atoms, $V_0$ is typically a few eV to tens of eV — small compared to nuclear potentials but significant at β energies below ~10 keV.
+
+### Molecular Screening Correction
+
+In molecular environments, the screening potential changes:
+
+$$\Delta S_{\text{Mol}} \quad (\text{Eq. 176})$$
+
+Since screening is typically at sub-percent level maximum, molecular deviations are expected at the **few $10^{-4}$** level — relevant for precision work down to 1 keV.
+
+## Energy Dependence
+
+- **Dominant at low energies** (T < ~50 keV): where the β particle's wave function is most affected by atomic electron cloud
+- **Negligible at high energies**: $S(Z,W) \to 1$ as $W \gg V_0$
+- The effect reverses sign between β⁻ and β⁺ (electrons attracted to/repelled from electron cloud differently)
+
+## Shake-Up Effects on Screening
+
+Atomic excitations during β decay modify screening:
+
+> [!warning] Tritium case
+> In tritium β⁻ decay, the screening potential can change by as much as **20%** because only a single electron contributes to atomic Coulomb interaction. For heavier systems, relative changes decrease but scale with $Z$. Neglecting shake-up introduces errors of order $\sim 1 \times 10^{-4}$.
+
+Shake-off (continuum ejection) has smaller effect:
+- With $\Delta Z_{\text{eff}} \approx 0.3$–$0.4$, yields ~**0.1%** relative change in screening potential → few $10^{-5}$ level in spectral shape
+- **Negligible at target precision** for most nuclei
+
+## Calculator Implementation
+
+> [!tip] Code mapping
+> Module: `beta_spectrum/components/screening.py` → `ScreeningCorrection(FermiFunction)` class
+> 
+> Uses ratio method with smooth logistic switching function. The screening potential $V_0$ is passed as a parameter and depends on the parent atom's atomic number.
+
+### API Usage
+
+```python
+from beta_spectrum import ScreeningCorrection, FermiFunction
+
+screen = ScreeningCorrection(
+    FermiFunction(Z_parent=90),  # bare nucleus reference
+    V0=0.015  # screening potential in m_e units (~7.6 keV)
+)
+values = screen(W_grid)
+```
+
+## Size Comparison with Other Corrections
+
+From Hayen et al. Table (Section VIII overview):
+
+| Correction | Magnitude | Energy Range Most Relevant |
+|---|---|---|
+| Screening $S$ | $10^{-3}$ – $10^{-4}$ | T < 50 keV |
+| Exchange $X$ | up to ~20% at lowest E | T < 10 keV |
+| Molecular screening $\Delta S_{\text{Mol}}$ | few $10^{-4}$ | T < 5 keV (molecular) |
+
+## Related Notes
+
+- [[corrections/08-atomic-overlap]] — Atomic mismatch / overlap correction $r(Z,W)$, Bahcall correction
+- [[corrections/09-chemical-effects]] — Molecular environment influence on screening and exchange
+- [[corrections/04-exchange]] — Electron exchange with atomic orbitals (often combined with screening)