unzhakov
030ae3e4b9
- 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)
106 lines
4.9 KiB
Markdown
106 lines
4.9 KiB
Markdown
---
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title: Beta Spectrum Calculator — Knowledge Base
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date: 2026-04-26
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tags:
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- vault/overview
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status: active
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---
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# Beta Spectrum Calculator — Knowledge Base
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This Obsidian vault serves as the scientific reference and development workspace for the **beta-spectrum calculator** project (`beta_shape_pnpi`).
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## Purpose
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Organize the physics theory behind β-decay spectrum calculations into structured, interconnected notes that inform the implementation of correction components in the codebase.
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## Source Material
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| Reference | Type | Location |
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|---|---|---|
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| Hayen et al., *Rev. Mod. Phys.* **90**, 015008 (2017) | Review article | [[refs/electromagnetic/2017_Hayen_analytical_beta_shape/summary]] |
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## Directory Structure
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```
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docs/
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├── README.md ← You are here
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├── 00-beta-spectrum-overview.md ← Master equation & full correction list
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├── 02-phase-space.md ← Baseline spectral shape
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├── corrections/ ← All correction components
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│ ├── 01-fermi-function.md ← Fermi function F₀(Z,W)
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│ ├── 02-finite-size.md ← Nuclear size: L₀, U, DFS
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│ ├── 03-screening.md ← Atomic screening S(Z,W)
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│ ├── 04-exchange.md ← Atomic exchange X(Z,W)
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│ ├── 05-radiative.md ← Outer radiative R(W,W₀)
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│ ├── 06-recoil.md ← Recoil: R_N, Q, weak magnetism
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│ ├── 07-detector-response.md ← Detector convolution
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│ ├── 08-atomic-overlap.md ← Atomic mismatch r(Z,W)
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│ └── 09-chemical-effects.md ← Molecular environment
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├── nuclear-structure/ ← Nuclear theory
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│ ├── index.md ← Overview
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│ └── 01-shape-factors.md ← C(Z,W), NMEs, impulse approximation
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├── gA-extraction/ ← gA extraction (new, in development)
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│ ├── 01-ssm-algorithm.md ← SSM step-by-step algorithm
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│ ├── 02-ssnme.md ← sNME and ESSM formalism
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│ ├── 03-tc99-case-study.md ← 99Tc literature results
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│ └── 04-implementation-todo.md ← Implementation TODO list
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└── refs/ ← Paper summaries
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├── electromagnetic/ ← CVC, radiative corrections
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├── forbidden-decay/ ← Forbidden decay studies
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└── (organized by topic)
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```
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## Calculator Architecture
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```
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SpectrumComponent (ABC, base.py)
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├── PhaseSpace → 02-phase-space.md
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├── FermiFunction → corrections/01-fermi-function.md
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├── FiniteSizeL0 → corrections/02-finite-size.md
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├── ChargeDistributionU → corrections/02-finite-size.md
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├── ScreeningCorrection → corrections/03-screening.md
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├── ExchangeCorrection → corrections/04-exchange.md
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├── RadiativeCorrection → corrections/05-radiative.md
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└── (recoil.py) → corrections/06-recoil.md (not yet implemented)
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BetaSpectrum (spectrum.py) — multiplicative composition + from_config()
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BetaSpectrumAnalyzer (spectrum.py) — plotting, CSV export
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```
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## Correction Implementation Status
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| # | Correction | Module | Note | Status |
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|---|---|---|---|---|
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| 1 | Phase space | `phase_space.py` | Baseline | ✓ implemented |
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| 2 | Fermi function | `fermi.py` | Coulomb interaction | ✓ implemented |
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| 3 | Finite size | `finite_size.py` | L₀, U, DFS | ✓ implemented |
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| 4 | Screening | `screening.py` | Atomic screening | ✓ implemented |
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| 5 | Exchange | `exchange.py` | Atomic exchange | ✓ implemented |
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| 6 | Radiative | `radiative.py` | Outer RC | ✓ implemented |
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| 7 | Recoil | `recoil.py` | R_N, Q, weak magnetism | ✗ not yet implemented |
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| 8 | Shape factor | `shape_factor_gA.py` | C(Z,W) for forbidden | — planned |
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| 9 | Detector | `detector_response.py` | Convolution | — planned |
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## gA Extraction (New)
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For forbidden nonunique decays (e.g., $^{99}\text{Tc}$), the shape factor depends on $g_A$ in a measurable way. See:
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- [[gA-extraction/01-ssm-algorithm]] — The SSM algorithm for extracting $g_A$ from spectral shapes
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- [[gA-extraction/04-implementation-todo]] — Step-by-step implementation plan
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## Key Variables and Units
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- $W$ — total electron energy in units of $m_e c^2$ (natural units, $m_e = 1$)
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- $T$ or $E_{\text{kin}}$ — kinetic energy (keV or MeV)
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- $W_0$ — endpoint total energy
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- $Z_{\text{parent}}$, $Z_{\text{daughter}}$ — atomic numbers
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- $\alpha \approx 1/137.036$ — fine structure constant
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- $\gamma = \sqrt{1 - (\alpha Z)^2}$
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Conversion: $W = 1 + T / m_e c^2$, with $m_e c^2 = 510.998950$ keV.
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## Precision Goal
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The calculator aims for **accurate to a few parts in $10^{-4}$ down to 1 keV** for low-to-medium $Z$ nuclei, following the approach of Hayen et al. (2017).
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