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
  • Normal mode: single spectrum plot with nuclear data header
  • Debug mode (-vv): 4-panel view with all correction factors
  • All plots include commit hash and UTC timestamp for traceability
• Comprehensive scientific reference in docs/
• Debug verification workflow: bs_pnpi -vv validates all parameters end-to-end

---

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/           ← pure theory core
│   ├── __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 + SpectrumConfig + BranchConfig
│   ├── nuclear_data.py      # paceENSDF integration + JSON input support
│   ├── cli.py               # Command-line interface (bs_pnpi)
│   ├── logging_utils.py     # Structured logging helpers
│   └── 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
├── beta_spectrum/output/    ← output, plotting, visualization, CSV export
│   ├── __init__.py          # BetaSpectrumAnalyzer, CSVEmitter, Visualizer
│   ├── core.py              # BetaSpectrumAnalyzer base class
│   ├── csv_export.py        # CSV export functionality
│   └── visualization.py     # Plotting and visualization functionality
├── exp_data/                ← experimental data handling
│   ├── __init__.py          # ExpSpectrum, EnergyCalibrator, GaussianFitter, etc.
│   ├── spectrum.py          # ExpSpectrum dataclass (energies, counts, errors, metadata)
│   ├── calibration.py       # EnergyCalibrator (linear/quadratic channel→energy)
│   ├── fitters.py           # GaussianFitter + PeakFitter for cal sources
│   └── corrections.py       # DeadTimeCorrection, PileUpCorrection, BackgroundSubtractor
├── fitter/                  ← analysis framework
│   ├── __init__.py          # SpectrumModel, SpectrumFitter, CWExtractor, etc.
│   ├── model.py             # SpectrumModel (BetaSpectrum + DetectorResponse wrapper)
│   ├── fit_engine.py        # SpectrumFitter + CurveFitter + FitConfig + FitResult
│   ├── extractor.py         # CWExtractor, GVAExtractor, CWExtractionResult, GVAExtractionResult
│   └── result.py            # AnalysisResult + FitSummary
├── tests/
│   ├── exp_data/            # exp_data module tests
│   ├── fitter/              # fitter module tests
│   ├── physics/             # Physics component tests
│   ├── quality/             # Code quality tests (logging, API, nuclear data)
│   ├── integration/         # Full pipeline integration tests
│   └── common/              # Shared hypothesis + property tests
├── data/
│   ├── exchange_coeff.csv         # Tabulated coefficients for X(Z,W), Z=2..120
│   └── custom_input_example.json  # Sample JSON input file
├── output/                      # Test run outputs (gitignored except .gitkeep)
├── AGENTS.md                    # Agent instructions: stack, git workflow, TDD, quality gates
├── CONVENTIONS.md               # Physics conventions: natural units, energy representation, component design
├── TODO.md                      # Development roadmap

---

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

In beta_spectrum.output. Provides debugging and visualization tools:

• total_spectrum(normalize=True/False) — computed spectrum array; raises ValueError when every branch is degenerate (non-positive integral)
• physical_branch_spectrum(i) — physical spectrum of branch i: the core (phase space × Fermi function) times every enabled higher-order correction, clamped beyond the branch endpoint (unnormalized)
• universal_factor() — product of the components shared across all branches (Fermi function and the universal higher-order corrections)
• plot_analysis(save_path=None, show_components=True) — plot with two modes:
  • show_components=True (debug mode): 4-panel figure (spectrum, components, cumulative effect, deviations)
  • show_components=False (normal mode): single spectrum plot with nuclear data header
  • All plots include commit hash and UTC timestamp for traceability
  • Plots are built from the exported CSV file (temporary full-verbosity export), so a plot always shows exactly the bytes the CSV export produces
• export_to_csv(filename) — export via pandas DataFrame with YAML-style metadata header:
  • the basic spectrum is always the core phase_space × fermi (the header carries a # core: line); finite size, charge distribution, screening, exchange and radiative are higher-order corrections
  • branch_{i}_spectrum columns contain the physical branch spectra weighted by intensity and normalized so that the sum of branch columns equals total_spectrum
  • with separate_branches=True (CLI --separate-branches) each branch column integrates to 1 (intensity ignored, no total_spectrum column)
• parse_spectrum_csv(path) — read an exported CSV and its metadata header (module function in beta_spectrum.output.visualization)
• get_data() — return all numerical data for custom analysis

---

Quick Start

from beta_spectrum import SpectrumConfig, BetaSpectrum
from beta_spectrum.output import 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("analysis.png")          # Normal mode (single spectrum plot)
analyzer.plot_analysis("debug.png", show_components=True)  # Debug mode (4-panel)
analyzer.export_to_csv("spectrum.csv")   # Export data to CSV

Fitting and C(W) extraction

from beta_spectrum import SpectrumConfig, BetaSpectrum
from fitter import SpectrumModel, SpectrumFitter, CWExtractor
from exp_data.spectrum import ExpSpectrum

# Build theoretical model
spectrum = BetaSpectrum.from_config(config)
model = SpectrumModel(spectrum, detector_response=detector)

# Fit to experimental data
exp = ExpSpectrum(energies=energies_keV, counts=counts, errors=errors)
fitter = SpectrumFitter(model, exp.energies, exp.counts, exp.errors)
result = fitter.fit(x0=[1.0, 0.0])

# Extract C(W) shape factor
extractor = CWExtractor(config)
cw_result = extractor.extract(measured, errors, energies_keV, model_values, endpoint_keV=Q)

---

Implementation Status

For a complete list of implemented and planned features, see TODO.md. Key highlights:

• Physics corrections: phase space, Fermi function, finite size, screening, exchange, radiative (with delta_cut resummation)
• Detector response: not implemented — SpectrumModel keeps a duck-typed optional convolution hook; the analytical models were removed (restore-or-delete decision tracked in TODO.md)
• Multi-branch decay: intensity-weighted sum of branch spectra, per-branch calculators with branch-specific endpoint, transition type (from ENSDF), and --intensity-cutoff CLI filter
• Analysis tools: χ² fitter (SpectrumFitter + CurveFitter), C(W) extraction pipeline, Kurie plot analysis, g_V/g_A extraction
• Experimental data: ExpSpectrum container, energy calibration, peak fitting, dead-time/pile-up correction
• CLI: bs_pnpi --nuclide Tc99 — full paceENSDF integration (auto-lookup of Z, A, Q-value, transition type, half-life, branches, forbiddenness from ENSDF); for JSON input the file's values are used and CLI flags (--e-step, --neutrino-mass, --intensity-cutoff, --csv-separator, --separate-branches) override them only when explicitly given; every long option has a single-letter alias (-N, -i, -s, -m, -o, -p, -L, -d, -c, -V, -S, -b)
• paceENSDF integration: get_decay_info_from_paceENSDF(), create_config_from_source("paceENSDF", nuclide="Tc99"), _parse_nuclide_symbol() for Z=1..98, FORBIDDENNESS_MAP, --nuclide CLI flag; per-branch endpoints are the measured transition endpoint energies from ENSDF (max endpoint across branches defines the spectrum endpoint)