beta_shape_pnpi/docs

title, date, tags, status

title	date	tags	status
Beta Spectrum Wiki	2026-04-26	vault/overview	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 of m_e c^2 (natural units, m_e = 1)
• T or E_{\text{kin}} — kinetic energy (keV or MeV)
• W_0 — endpoint total energy
• Z_{\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.