beta_shape_pnpi/docs

title, date, tags, status

title	date	tags	status
Beta Spectrum Calculator — Knowledge Base	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 β-decay spectrum calculations into structured, interconnected notes that inform the implementation of correction components in the codebase.

Source Material

Reference	Type	Location
Hayen et al., Rev. Mod. Phys. 90, 015008 (2017)	Review article	refs/electromagnetic/2017_Hayen_analytical_beta_shape/summary

Directory Structure

docs/
├── README.md                          ← You are here
├── 00-beta-spectrum-overview.md       ← Master equation & full correction list
├── 02-phase-space.md                  ← Baseline spectral shape
├── corrections/                       ← All correction components
│   ├── 01-fermi-function.md           ← Fermi function F₀(Z,W)
│   ├── 02-finite-size.md              ← Nuclear size: L₀, U, DFS
│   ├── 03-screening.md                ← Atomic screening S(Z,W)
│   ├── 04-exchange.md                 ← Atomic exchange X(Z,W)
│   ├── 05-radiative.md                ← Outer radiative R(W,W₀)
│   ├── 06-recoil.md                   ← Recoil: R_N, Q, weak magnetism
│   ├── 07-detector-response.md        ← Detector convolution
│   ├── 08-atomic-overlap.md           ← Atomic mismatch r(Z,W)
│   └── 09-chemical-effects.md         ← Molecular environment
├── nuclear-structure/                 ← Nuclear theory
│   ├── index.md                       ← Overview
│   └── 01-shape-factors.md            ← C(Z,W), NMEs, impulse approximation
├── gA-extraction/                     ← gA extraction (new, in development)
│   ├── 01-ssm-algorithm.md            ← SSM step-by-step algorithm
│   ├── 02-ssnme.md                    ← sNME and ESSM formalism
│   ├── 03-tc99-case-study.md          ← 99Tc literature results
│   └── 04-implementation-todo.md      ← Implementation TODO list
└── refs/                              ← Paper summaries
    ├── electromagnetic/               ← CVC, radiative corrections
    ├── forbidden-decay/               ← Forbidden decay studies
    └── (organized by topic)

Calculator Architecture

SpectrumComponent (ABC, base.py)
 ├── PhaseSpace              → 02-phase-space.md
 ├── FermiFunction           → corrections/01-fermi-function.md
 ├── FiniteSizeL0            → corrections/02-finite-size.md
 ├── ChargeDistributionU     → corrections/02-finite-size.md
 ├── ScreeningCorrection     → corrections/03-screening.md
 ├── ExchangeCorrection      → corrections/04-exchange.md
 ├── RadiativeCorrection     → corrections/05-radiative.md
 └── (recoil.py)             → corrections/06-recoil.md (not yet implemented)

BetaSpectrum (spectrum.py) — multiplicative composition + from_config()
BetaSpectrumAnalyzer (spectrum.py) — plotting, CSV export

Correction Implementation Status

#	Correction	Module	Note	Status
1	Phase space	phase_space.py	Baseline	✓ implemented
2	Fermi function	fermi.py	Coulomb interaction	✓ implemented
3	Finite size	finite_size.py	L₀, U, DFS	✓ implemented
4	Screening	screening.py	Atomic screening	✓ implemented
5	Exchange	exchange.py	Atomic exchange	✓ implemented
6	Radiative	radiative.py	Outer RC	✓ implemented
7	Recoil	recoil.py	R_N, Q, weak magnetism	✗ not yet implemented
8	Shape factor	shape_factor_gA.py	C(Z,W) for forbidden	— planned
9	Detector	detector_response.py	Convolution	— planned

gA Extraction (New)

For forbidden nonunique decays (e.g., ^{99}\text{Tc}), the shape factor depends on g_A in a measurable way. See:

• gA-extraction/01-ssm-algorithm — The SSM algorithm for extracting g_A from spectral shapes
• gA-extraction/04-implementation-todo — Step-by-step implementation plan

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.

Precision Goal

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).