beta_shape_pnpi/README.md

Beta Spectrum Calculation Toolkit

A modular Python package for calculating high-precision beta decay energy spectra. It models the spectral shape of nuclear transitions by combining well-established physical corrections into a coherent, configurable pipeline.

Features:

• Numerical evaluation from near-zero kinetic energies up to the endpoint
• Selective inclusion of higher-order corrections via SpectrumConfig toggles
• Clean, composable component architecture
• Built-in visualization and CSV export via BetaSpectrumAnalyzer
• Comprehensive scientific reference in docs/

---

Core Concept

The beta spectrum is constructed as a product of independent correction factors:

N(W) \\propto p W (W_0 - W)^2 \\times \\prod_i C_i(W)

Each C_i(W) is an independently implemented and toggleable component.

---

Project Structure

beta_shape_pnpi/
├── pyproject.toml
├── docs/                          # Obsidian knowledge base (physics theory & references)
│   ├── README.md                  # Vault overview + navigation index
│   ├── 00-beta-spectrum-overview.md    # Master equation, all corrections table
│   ├── 01-fermi-function.md           # Fermi function F₀(Z,W)
│   ├── 02-phase-space.md              # Phase space p·W·(W₀−W)²
│   ├── 03-finite-size.md              # L₀, U, DFS corrections
│   ├── 04-screening-correction.md     # Atomic screening S(Z,W)
│   ├── 05-exchange-correction.md      # Electron exchange X(Z,W)
│   ├── 06-radiative-corrections.md    # Outer radiative δᵣ(W,W₀)
│   ├── 07-recoil-effects.md           # Weak magnetism, recoil kinematics
│   ├── 08-detector-response.md        # Detector response models
│   ├── 10-nuclear-structure.md        # Shape factor C(Z,W), BB vs HS formalisms
│   ├── 12-atomic-overlap.md           # Bahcall correction r(Z,W)
│   ├── 13-chemical-effects.md         # Molecular environment effects
├── beta_spectrum/
│   ├── __init__.py          # Public API: constants, utilities, classes
│   ├── base.py              # Abstract SpectrumComponent base class
│   ├── constants.py         # Physical constants (natural units, m_e = 1)
│   ├── utils.py             # Helpers: T<->W conversion, momentum, nuclear radius
│   ├── spectrum.py          # BetaSpectrum + BetaSpectrumAnalyzer classes
│   ├── nuclear_data.py      # paceENSDF integration + JSON input support
│   ├── cli.py               # Command-line interface (bs_pnpi)
│   ├── fitter.py            # χ² curve fitting for C(W) extraction
│   ├── cw_extractor.py      # C(W) shape factor extraction + gV/gA analysis
│   └── components/
│       │   ├── phase_space.py           ✓ Phase space shape (p·W·(W₀−W)²)
│       │   ├── fermi.py                 ✓ Coulomb correction (loggamma for stability)
│       │   ├── finite_size.py           ✓ L0 expansion + charge distribution U term
│       │   ├── screening.py             ✓ Atomic electron screening (ratio method)
│       │   ├── exchange.py              ✓ Hayen-2018 empirical fit coefficients
│       │   ├── radiative.py             ✓ Outer radiative corrections, soft-photon resummation
│       │   └── detector_response.py     ✓ Analytical detector response models
├── tests/
│   ├── test_radiative.py        # Radiative correction tests (24 tests)
│   ├── test_exchange.py         # Exchange correction tests
│   ├── test_fermi.py            # Fermi function tests
│   ├── test_finite_size.py      # Finite size correction tests
│   ├── test_phase_space.py      # Phase space tests
│   ├── test_screening.py        # Screening correction tests
│   ├── test_spectrum.py         # Integration tests
│   ├── test_detector_response.py# Detector response tests
│   ├── test_fitter.py           # Curve fitter tests
│   ├── test_cw_extractor.py     # C(W) extraction tests
│   └── test_nuclear_data.py     # paceENSDF + JSON input tests (23 tests)
└── data/
    ├── exchange_coeff.csv         # Tabulated coefficients for X(Z,W), Z=2..120
    └── custom_input_example.json  # Sample JSON input file

---

Architecture

SpectrumComponent (base class)

Defined in beta_spectrum/base.py. All physics corrections inherit from this abstract base and implement:

def __call__(self, W: np.ndarray) -> np.ndarray

This makes every component stateless (or minimally stateful), vectorized, and composable.

BetaSpectrum

Defined in beta_spectrum/spectrum.py. Orchestrates the calculation:

• Combines components multiplicatively via __call__(W)
• Factory method from_config(config) for declarative setup
• Generates energy grids with get_energy_grid(config)
• Returns individual component values via calculate_components(W)

BetaSpectrumAnalyzer

Also in spectrum.py. Provides debugging and visualization tools:

• total_spectrum(normalize=True/False) — computed spectrum array
• plot_analysis(save_path=None) — 4-panel matplotlib figure (spectrum, components, cumulative effect, deviations from unity)
• export_to_csv(filename) — export via pandas DataFrame
• get_data() — return all numerical data for custom analysis

---

Quick Start

from beta_spectrum import SpectrumConfig, BetaSpectrum, BetaSpectrumAnalyzer

config = SpectrumConfig(
    Z_parent=90,       # Thorium-232 (example)
    Z_daughter=91,
    A_number=232,
    endpoint_MeV=4.8,  # Q-value
    transition_type="A",  # Allowed transition (default)
)

spectrum = BetaSpectrum.from_config(config)
W, E_MeV = spectrum.get_energy_grid(config)
values = spectrum(W)

analyzer = BetaSpectrumAnalyzer(spectrum, config)
analyzer.plot_analysis()          # Show/ save 4-panel figure
analyzer.export_to_csv("output.csv")   # Export data to CSV

---

Components

Component	Module	Status	Description
Phase Space	phase_space.py	✓	Baseline p W (W_0 - W)^2 with transition-type-dependent forbidden factors and optional neutrino mass support
Fermi Function	fermi.py	✓	Relativistic Coulomb correction via scipy.special.loggamma
Finite Size L0	finite_size.py	✓	Low-Z expansion from Hayen et al. with prefactor
Charge Distribution U	finite_size.py	✓	Second-order (1/5)(\alpha Z W R)^2 correction
Screening	screening.py	✓	Ratio method with logistic switching, energy shift V_0
Exchange	exchange.py	✓	Hayen-2018 Table X empirical fit (CSV data for Z=2..120)
Radiative	radiative.py	✓	Outer radiative corrections (Hayen Eq. 47–53), soft-photon resummation at endpoint
Detector Response	detector_response.py	✓	Analytical models: Gaussian, Gaussian+tail, Tikhonov, tabulated

Additional Modules

Module	Description
nuclear_data.py	paceENSDF integration + JSON input for automated SpectrumConfig generation
cli.py	Command-line interface (bs_pnpi) for quick spectrum calculations
fitter.py	χ² curve fitting for C(W) shape factor extraction from experimental data
cw_extractor.py	C(W) extraction pipeline with gV/gA coupling constant analysis