unzhakov
dc8e26403b
Remove gA-extraction notes, nuclear-structure notes, paper-summary refs, detector-response correction note and the finished test migration checklist. Rewrite the vault index for the single-package theory calculator; repoint dangling wiki-links in surviving notes to inline citations; refresh docs_check.py (drop bs_exp CLI check, register removed files). Literature and nuclear-structure research resumes in dedicated projects; the removed notes are recoverable from history.
85 lines
4.2 KiB
Markdown
85 lines
4.2 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 is the scientific reference behind the **beta-spectrum shape calculator** (`beta_spectrum`). Since v0.5.0 the repository is dedicated solely to high-precision spectrum-shape *calculation*: detector response, data calibration, and fitting/extraction analyses are separate projects, and their literature was removed from this vault.
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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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Key external references (cited inline in the notes): Hayen et al., *Rev. Mod. Phys.* **90**, 015008 (2018); Sirlin (1967–2011); Hayen et al., *J. Phys. G* (2019) on first-forbidden transitions. Nuclear-structure shape-factor theory is external to this repository.
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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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├── test-architecture.md ← Test organization & strategy
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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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│ ├── 08-atomic-overlap.md ← Atomic mismatch r(Z,W)
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│ └── 09-chemical-effects.md ← Molecular environment
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└── (refs removed; literature research resumes in dedicated projects)
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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 component) → corrections/06-recoil.md (not yet implemented)
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BetaSpectrum (spectrum.py) — multiplicative composition + from_config()
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BetaSpectrumAnalyzer (output/core.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 | — | C(Z,W) is an input parameter (external nuclear-structure theory) | out of scope |
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| 9 | Atomic overlap | — | r(Z,W) | documentation only |
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| 10 | Chemical effects | — | molecular environment | documentation only |
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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. (2018).
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