Add Obsidian knowledge base (docs/) and update README with docs structure

docs/00-beta-spectrum-overview.md

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+---
+title: "00 – Beta Spectrum Overview"
+date: 2026-04-26
+tags:
+  - beta-spectrum/overview
+status: active
+aliases:
+  - Master Equation
+cssclasses: []
+---
+
+# Beta Decay Spectrum — Full Expression
+
+## The Master Equation
+
+The fully differential allowed β spectrum shape, including all corrections needed for $10^{-4}$ precision (Hayen et al., Eq. 4):
+
+$$N(W)\,dW = \frac{G_V^2 V_{ud}^2}{2\pi^3} \; K(Z,W,W_0,M) \; A(Z,W) \; C'(Z,W) \; p W (W_0 - W)^2 dW$$
+
+or expanded:
+
+$$N(W)\,dW = \frac{G_V^2 V_{ud}^2}{2\pi^3} F_0 L_0 U DFS R R_N Q S X r C D_C \; p W (W_0 - W)^2 dW \tag{4}$$
+
+## Correction Factors
+
+| Symbol | Name | Module / Note | Status |
+|---|---|---|---|
+| $F_0(Z,W)$ | Point charge Fermi function | [[01-fermi-function]] | ✓ |
+| $L_0(Z,W)$ | Electrostatic finite size (uniform sphere) | [[03-finite-size]] | ✓ |
+| $U(Z,W)$ | Charge distribution correction | [[03-finite-size]] | ✓ |
+| $DFS(Z,W,\beta^2)$ | Nuclear deformation correction | [[03-finite-size]] | ✓ |
+| $R(W,W_0) = 1 + \delta_R$ | Outer radiative corrections | [[06-radiative-corrections]] | ✓ |
+| $R_N(W,W_0,M)$ | Recoil kinematic correction | [[07-recoil-effects]] | ✗ |
+| $Q(Z,W,M)$ | Recoil electromagnetic correction | [[07-recoil-effects]] | — |
+| $S(Z,W)$ | Atomic electron screening | [[04-screening-correction]] | ✓ |
+| $X(Z,W)$ | Atomic exchange effect | [[05-exchange-correction]] | ✓ |
+| $r(Z,W)$ | Atomic mismatch / overlap | [[12-atomic-overlap]] | — |
+| $A(Z,W) = S \cdot X \cdot r$ | Combined atomic factors | [[12-atomic-overlap]] | — |
+| $C(Z,W)$ | Nuclear structure shape factor | [[10-nuclear-structure]] | — |
+| $D_C(Z,W,\beta^2)$ | Nuclear deformation (convolution) | [[10-nuclear-structure]] | — |
+
+## Baseline: Phase Space
+
+The uncorrected spectral shape is pure phase space ([[02-phase-space]]):
+
+$$\frac{dN}{dW}\bigg|_{\text{PS}} = p W (W_0 - W)^2$$
+
+with $p = \sqrt{W^2-1}$, $W$ total energy in units of $m_e$, and $W_0$ the endpoint.
+
+## Precision Goal
+
+The paper achieves **accurate to a few parts in $10^{-4}$ down to 1 keV** for low-to-medium $Z$ nuclei — extending previous work by nearly an order of magnitude [[Hayen2017_summary]].
+
+> [!key] Why this matters
+> A precision of ~0.5% is required when determining the Fierz term $b_{\text{Fierz}}$ to improve limits on BSM scalar/tensor couplings. Weak magnetism $b_{wm}$ must be included as experimental precision increases, otherwise it limits BSM sensitivity.
+
+## Three Formalisms Compared
+
+| Approach | Style | Strengths |
+|---|---|---|
+| **Behrens-Bühring** (BB) | Rigorous, numerical Dirac solutions | Most precise results |
+| **Holstein** (HS) | Analytical, manifestly covariant | Clean symmetry properties |
+| **Wilkinson** | Analytical parametrizations | Practical fits for dominant effects |
+
+The Hayen paper combines BB's accuracy with HS's transparency.
+
+## Conventions
+
+- Natural units: $c = \hbar = m_e = 1$ throughout
+- $Z$ is always positive; $\beta^-$ and $\beta^+$ distinguished via upper/lower signs ($\mp$)
+- $W = E/m_ec^2 + 1$, $p = \sqrt{W^2 - 1}$
+- $G_V$: vector coupling strength; $V_{ud} = \cos^2\theta_C$
+
+> [!note] Two types of "finite size"
+> The authors distinguish two corrections conflated under this term:
+> 1. **Electrostatic** ($L_0, U, DFS$): Potential difference from point charge → realistic nuclear shape
+> 2. **Convolution**: Integration of leptonic wave functions over the nuclear volume (appears in $C(Z,W)$)
+
+## Energy Conversion
+
+$$W = 1 + \frac{T}{m_ec^2}, \quad m_ec^2 = 510.998950\text{ keV}$$
+
+In code: see `beta_spectrum/utils.py` → `T_to_W()`, `W_to_T()` functions.
+
+## Calculator Implementation
+
+Each correction factor $C_i(W)$ is a callable class inheriting from `SpectrumComponent`. The total spectrum is the product of all enabled components:
+
+```
+N(W) = PhaseSpace(W0) × FermiFunction(Z) × FiniteSizeL0(Z,A) × ... 
+```
+
+Configuration toggles are defined in `SpectrumConfig` (spectrum.py). See [[README]] for architecture details.