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Comprehensive documentation on parameterizing the shape factor C(Z,W) via g_A for forbidden nonunique beta decays, based on: - Kostensalo et al. PRC 95, 044313 (2017) - SSM introduction - Kostensalo & Suhonen PRC 96, 024317 (2017) - gA-driven evolution - Paulsen et al. PRC 110, 055503 (2024) - 99Tc high-precision MMC measurement Covers: shape factor decomposition, fitting algorithm, uncertainty budget, implementation plan for ShapeFactorGA module, and literature summary.
title, date, tags, status
| title | date | tags | status | |
|---|---|---|---|---|
| Beta Spectrum Wiki | 2026-04-26 |
|
active |
Beta Spectrum Calculator — Knowledge Base
This Obsidian vault serves as the scientific reference and development workspace for the beta-spectrum calculator project (beta_shape_pnpi).
Purpose
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.
Source Material
| Reference | Type | Location |
|---|---|---|
| Hayen et al., RevModPhys 90, 015008 (2017) | Review article | pdf_source/Hayen2017.pdf / Hayen2017_summary |
Notes Structure
All notes are flat in this directory, linked via wikilinks.
Core Theory
- 00-beta-spectrum-overview — Master equation and overview of all corrections
- 02-phase-space — Baseline spectral shape
pW(W_0-W)^2
Correction Components (mapped to calculator modules)
| # | Note | Calculator Module | Status |
|---|---|---|---|
| 1 | 01-fermi-function | components/fermi.py |
✓ implemented |
| 2 | 03-finite-size | components/finite_size.py |
✓ implemented |
| 3 | 04-screening-correction | components/screening.py |
✓ implemented |
| 4 | 05-exchange-correction | components/exchange.py |
✓ implemented |
| 5 | 06-radiative-corrections | components/radiative.py |
✓ implemented |
| 6 | 07-recoil-effects | components/recoil.py |
✗ not yet implemented |
Nuclear Structure & Atomic Effects
- 10-nuclear-structure — Shape factors, form factors, impulse approximation
- 11-isospin-breakdown — Shake-off/shake-up processes, endpoint shift
- 12-atomic-overlap — Bahcall correction, bound-state β decay
- 13-chemical-effects — Molecular environment influence on spectrum
References
- refs/hayen2017 — Metadata and key equations from Hayen et al. (2017)
Calculator Architecture
SpectrumComponent (ABC, base.py)
├── PhaseSpace → phase_space.py
├── FermiFunction → fermi.py
├── FiniteSizeL0 → finite_size.py
├── ChargeDistributionU → finite_size.py
├── ScreeningCorrection → screening.py
├── ExchangeCorrection → exchange.py
└── RadiativeCorrection → radiative.py
BetaSpectrum (spectrum.py) — multiplicative composition + from_config()
BetaSpectrumAnalyzer (spectrum.py) — plotting, CSV export
Key Variables and Units
W— total electron energy in units ofm_e c^2(natural units,m_e = 1)TorE_{\text{kin}}— kinetic energy (keV or MeV)W_0— endpoint total energyZ_{\text{parent}},Z_{\text{daughter}}— atomic numbers\alpha \approx 1/137.036— fine structure constant\gamma = \sqrt{1 - (\alpha Z)^2}
Conversion: W = 1 + T / m_e c^2, with m_e c^2 = 510.998950 keV.