80 lines
2.9 KiB
Markdown
80 lines
2.9 KiB
Markdown
---
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title: Beta Spectrum Wiki
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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 allowed beta decay spectrum calculations into structured, interconnected notes that directly 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., RevModPhys **90**, 015008 (2017) | Review article | `pdf_source/Hayen2017.pdf` / [[Hayen2017_summary]] |
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## Notes Structure
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All notes are flat in this directory, linked via wikilinks.
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### Core Theory
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- [[00-beta-spectrum-overview]] — Master equation and overview of all corrections
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- [[02-phase-space]] — Baseline spectral shape $pW(W_0-W)^2$
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### Correction Components (mapped to calculator modules)
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| # | Note | Calculator Module | Status |
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|---|---|---|---|
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| 1 | [[01-fermi-function]] | `components/fermi.py` | ✓ implemented |
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| 2 | [[03-finite-size]] | `components/finite_size.py` | ✓ implemented |
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| 3 | [[04-screening-correction]] | `components/screening.py` | ✓ implemented |
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| 4 | [[05-exchange-correction]] | `components/exchange.py` | ✓ implemented |
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| 5 | [[06-radiative-corrections]] | `components/radiative.py` | ✓ implemented |
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| 6 | [[07-recoil-effects]] | `components/recoil.py` | ✗ not yet implemented |
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### Nuclear Structure & Atomic Effects
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- [[10-nuclear-structure]] — Shape factors, form factors, impulse approximation
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- [[11-isospin-breakdown]] — Shake-off/shake-up processes, endpoint shift
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- [[12-atomic-overlap]] — Bahcall correction, bound-state β decay
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- [[13-chemical-effects]] — Molecular environment influence on spectrum
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### References
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- [[refs/hayen2017]] — Metadata and key equations from Hayen et al. (2017)
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## Calculator Architecture
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```
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SpectrumComponent (ABC, base.py)
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├── PhaseSpace → phase_space.py
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├── FermiFunction → fermi.py
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├── FiniteSizeL0 → finite_size.py
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├── ChargeDistributionU → finite_size.py
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├── ScreeningCorrection → screening.py
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├── ExchangeCorrection → exchange.py
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└── RadiativeCorrection → radiative.py
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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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## 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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