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Strategic Development Roadmap

Scientific Goal

Extract the shape factor C(W) from the experimentally measured beta spectrum of ⁹⁹Tc, and parametrize C(W) via the vector coupling constant g_V from the theory of beta decay.

This requires repeating the analysis pipeline of Paulsen et al., Phys. Rev. C 110, 055503 (2024), which used Metallic Magnetic Calorimeters (MMCs) to measure the ⁹⁹Tc beta spectrum with sub-keV threshold and ~100 eV resolution.

See docs/refs/2024_Paulsen_T99_beta_spectrum/summary.md for full analysis details.

Package Architecture (v0.4.0 — In Progress)

Current State (v0.3.x)

Everything lives in beta_spectrum/ — a monolithic package where theory, fitting, detector response, and analysis are intermingled. This is becoming unwieldy.

Target Architecture (v0.4.0)

beta_spectrum/              ← theory-only core
├── __init__.py
├── base.py                 ← SpectrumComponent base
├── constants.py            ← physical constants
├── utils.py                ← T_to_W, W_to_T, momentum
├── spectrum.py             ← BetaSpectrum, SpectrumConfig, BranchConfig
├── components/             ← individual correction factors
│   ├── phase_space.py
│   ├── fermi.py
│   ├── finite_size.py
│   ├── screening.py
│   ├── exchange.py
│   ├── radiative.py
│   └── detector_response.py   ← stays here (part of theory)
└── nuclear_data.py         ← paceENSDF integration

exp_data/                   ← experimental data handling
├── __init__.py
├── raw_reader.py           ← raw data loading (ROOT, CSV, ASCII)
├── calibration.py          ← energy calibration, line fitting
├── fitters.py              ← simple Gaussian fitters for cal sources
├── corrections.py          ← dead-time, pile-up, background
└── spectrum.py             ← experimental spectrum container

fitter/                     ← main analysis framework
├── __init__.py
├── model.py                ← theoretical model + detector convolution
├── fit_engine.py           ← multi-parameter fitting orchestration
├── extractor.py            ← C(W), g_V, g_A extraction
├── result.py               ← FitResult, analysis results
# └── report.py               ← PDF report generation (deferred)

output/                     ← output, 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

Rationale

  • beta_spectrum — pure theory. Given a nuclide and corrections, produces a theoretical spectrum. No fitting, no data, no detector convolution.
  • exp_data — experimental data handling. Loading raw detector outputs, calibrating energy scale, fitting calibration peaks, applying instrumental corrections.
  • fitter — the analysis workhorse. Takes theory model + detector response + experimental data → performs convolution + fitting → extracts physics parameters.

Migration Plan

Phase 1: Create exp_data module ✅ COMPLETE

  • exp_data/spectrum.py — ExpSpectrum dataclass: energies, counts, errors, metadata
  • exp_data/calibration.py — EnergyCalibrator + CalibrationResult: linear/quadratic channel→energy
  • exp_data/fitters.py — GaussianFitter + PeakFitter: peak detection and fitting
  • exp_data/corrections.py — DeadTimeCorrection, PileUpCorrection, BackgroundSubtractor
  • 43 tests, ruff + mypy clean

Phase 2: Create fitter module ✅ COMPLETE

  • fitter/model.py — SpectrumModel: wraps BetaSpectrum + DetectorResponse, callable model with convolution
  • fitter/fit_engine.py — SpectrumFitter + FitConfig + FitResult: χ² fitting, covariance, profile likelihood, confidence intervals
  • fitter/extractor.py — CWExtractor + GVAExtractor: C(W) and g_V/g_A extraction
  • fitter/result.py — AnalysisResult + FitSummary: physics-specific result container
  • 34 tests, ruff + mypy clean
  • Detector convolution handles W < 1.0 edge cases

Phase 3: Clean up beta_spectrum ✅ COMPLETE

  • Remove cw_extractor.py (moved to fitter/extractor.py)
  • Remove fitter.py (moved to fitter/fit_engine.py)
  • Clean up __init__.py — only exports theory classes
  • Add CurveFitter general-purpose fitter to fitter/fit_engine.py for backward compat
  • Add CWExtractor.fit_parametrization() and fit_gV_gA() compatibility methods
  • Remove old test_cw_extractor.py (replaced by tests/fitter/test_extractor.py — file was removed)
  • 322 tests pass, ruff + mypy clean on all 26 source files

Phase 4: Update package structure ✅ COMPLETE

  • pyproject.toml auto-discovers all 4 packages via setuptools.packages.find
  • beta_spectrum.cli keeps CLI entry point (no re-exports needed)
  • All imports updated across 26 source files
  • 322 tests pass
  • README updated with new architecture diagram and Quick Start examples
  • Version bumped to 0.4.0
  • Decide: restore or delete the detector_response module — it was removed from beta_spectrum/components/ together with its tests, but fitter/model.py keeps a duck-typed optional hook and DEFAULT_JSON_SCHEMA keeps the detector keys; restore from git history (commits up to 5f99566) if convolution is needed again

Track A: ⁹⁹Tc Spectrum-Shape Analysis

A1. Research & Data Collection

  • Parse additional PDF sources on ⁹⁹Tc beta decay and spectrum-shape method
    • Kostensalo & Suhonen, Phys. Rev. C 96, 024317 (2017) — theoretical spectrum shape predictions
    • Suhonen, Frontier. Phys. 5, 55 (2017) — review of g_A quenching
    • Haaranen et al., Phys. Rev. C 93, 034308 (2016) — effective coupling constants
    • Additional experimental ⁹⁹Tc spectra (historical data for comparison)
  • Research methods to extract g_V from fitted C(W) shape
    • Study the relationship between C(W) parametrization and g_V, g_A effective values
    • Understand how CVC (Conserved Vector Current) constrains g_V
    • Review the spectrum-shape method formalism (Behrens-Bühring + shell model)
  • Document the full analysis pipeline: experimental data → theoretical model → C(W) extraction → g_V extraction

A2. Detector Response Function

  • Implement analytical detector response function for 4π semiconductor detector
    • Gaussian core with low-energy tail (charge collection effects)
    • Parameters: energy resolution σ(E), tail fraction, tail shape
    • Energy-dependent resolution σ(E) = a + b·√E
    • Implemented: Gaussian, Gaussian+tail, Tikhonov models with energy-dependent resolution and Fano factor
  • Implement convolution routines
    • Convolve theoretical spectrum with detector response for comparison to data
    • Implemented: convolve() with tabulated response support
  • Monte Carlo simulation (GEANT4) — out of scope for this project but noted for future
    • Full detector geometry simulation
    • Energy loss in source, dead layers, absorber
    • Response matrix for unfolding (as done in Paulsen et al. with EGSNRC)

A3. Data Processing & Analysis

  • Data processing pipeline for 1-hour run spectra
    • Background subtraction
    • Energy calibration (using known X-ray/gamma lines)
    • Dead-time correction
    • Pulse pile-up correction
  • Endpoint fitting and energy calibration
    • Kurie plot analysis for endpoint determination
    • Polynomial calibration using known spectral lines
    • Linearity correction across energy range
  • Data quality assessment procedures
    • Residual analysis (data vs model)
    • χ²/ndf evaluation
    • Consistency checks across multiple runs
    • Statistical combination of long-exposure spectra

A4. Fitter for C(W) Extraction

  • Implement fitter routine to extract experimental C(W) from data
    • χ² minimization: theoretical spectrum (with all corrections) vs measured spectrum
    • Free parameters: C(W) shape parameters, endpoint energy, normalization, background
    • Covariance matrix and uncertainty propagation
    • Implemented: CurveFitter with least_squares optimization, FitResult with covariance, chi2, residuals
  • Parametrize C(W) in terms of g_V (and g_A)
    • Fit C(W) data to theoretical parametrization
    • Extract g_V^eff and g_A^eff from the fit
    • Compare with Paulsen et al. results: g_A^eff = 0.574(36), g_V^eff = 0.376(5)
    • Implemented: CWExtractor with Kurie plot analysis, parametrized fitting, g_V/g_A extraction
  • Systematic uncertainty analysis
    • Vary correction implementations within uncertainties
    • Test sensitivity to detector response model
    • Background model dependence

Track B: Package Usability Improvements

B1. Nuclear Data Integration

  • paceENSDF integration for automated nuclear data retrieval
    • get_decay_info_from_paceENSDF(nuclide, decay_type) — retrieves Q-value, half-life, spin/parity, branches, forbiddenness from ENSDF
    • decay_info_to_config() — converts DecayInfo to SpectrumConfig with branch support
    • create_config_from_source("paceENSDF", nuclide="Tc99") — one-liner config creation
    • _parse_nuclide_symbol() — parses "Tc99" → (Tc, 43, 99) with full Z lookup for Z=1..98
    • _resolve_decay_index() — finds correct decay index (ground state by default)
    • _get_decay_mode_symbol() — maps beta_minus→BM, beta_plus/ec→ECBP
    • FORBIDDENNESS_MAP — translates paceENSDF codes (0A, 1F, 2F, …) to transition_type
    • CLI --nuclide Tc99 uses paceENSDF automatically
    • Branch intensities, log_ft, level energies, transition types all populated from ENSDF
    • Tested with Tc99 (2 branches, F2) and Co60 (multi-branch)

B2. Input Flexibility

  • Generalize parameter inputs via custom input file (YAML/JSON)
    • Declare isotope, transition type, detector parameters
    • Toggle corrections on/off per-component
    • Reproducible calculation configurations
    • Implemented: load_json_input(), json_to_config(), DEFAULT_JSON_SCHEMA with full detector param support, CLI --input flag
  • Retrieve parameters directly from ENSDF database
    • Auto-populate W0, Z, A, transition type from isotope name
    • Reduce manual configuration errors
    • Implemented: get_decay_info_from_paceENSDF() returns DecayInfo with Z_parent, Z_daughter, A_number, endpoint_MeV, transition_type, forbiddenness_code, half_life, branches; CLI --nuclide uses this automatically

B3. Multiple Branch Decays

  • Add support for multiple branch decays
    • Calculate total spectral shape weighted by branch intensities
    • Handle decays with significant branching to excited states
    • Sum contributions from all branches with proper weighting
    • Implemented: BranchConfig dataclass, multi-branch BetaSpectrum with per-branch calculators
    • Branch data from paceENSDF: intensity, endpoint (Q-value - excitation energy), transition type
    • Intensity normalization to 100% across all branches
    • CSV export: total spectrum, per-branch spectra, per-branch components (PhaseSpace, Radiative), universal components (Fermi, Screening, etc.)
    • Plot: total spectrum + individual branches with legend (transition type, endpoint energy)
    • Debug plot: vertical layout with per-branch panels, universal components panel
    • Energy grid extends to max branch endpoint, per-branch spectra masked beyond their endpoint
    • Single-branch = trivial case of multi-branch (no separate mode)
    • Per-branch transition types extracted from ENSDF (not defaulting to 'A')
    • --intensity-cutoff CLI option to filter out negligible branches
    • Branch spectra plotted as raw (un-normalized) contributions so total = sum of branches

B4. Beta+ Decay Support

  • Modify corrections to support β⁺ decays
    • Fermi function sign change for positrons
    • Radiative corrections for β⁺ (Sirlin corrections differ for e⁻ vs e⁺)
    • Screening correction for positrons (different atomic interaction)
    • Exchange correction (negligible for β⁺ but check)

B5. Neutrino Spectrum Support

  • Add convenience analyser methods for plotting neutrino spectra
    • Convert electron spectrum to neutrino spectrum
    • Plot both on same figure with proper scaling
  • Adopt corrections that differ for neutrino spectrum
    • Implement neutrino radiative correction h(W̃, W0) per Sirlin 2011
    • Conversion formula: f_ν(W_ν) = f_e(W̃) · [1 + (α/2π)(h − g)]
    • Neutrino-specific corrections (no Fermi function, different radiative terms)

B6. Neutrino Mass Effects

  • Implement option to produce spectra with non-zero neutrino mass
    • Modify phase space: (W0 − W)² → (W0 − W)² · √(1 − m_ν²/(W0−W)²)
    • Add kink feature near endpoint for spectral distortion
    • Useful for neutrino mass search applications
  • Research and document implications of significant neutrino mass
    • Which corrections need m_ν as input parameter?
    • Impact on radiative corrections (mass singularities)
    • Impact on endpoint fitting procedures

B7. Automated Report Generation

  • Implement extensive procedurally generated PDF report
    • Comprehensive details of the calculation
    • Component plots (phase space, Fermi, each correction factor)
    • Total spectrum with all corrections applied
    • Residual analysis, fit quality metrics
    • Parameter table with uncertainties
    • References to theoretical sources
  • Extend report generation to fitters
    • Fit results with covariance matrix
    • Parameter correlations
    • Confidence intervals
    • Goodness-of-fit statistics

B8. CLI & Output Improvements

  • Implement structured logging system
    • Log to stdout with configurable verbosity levels (-v=INFO, -vv=DEBUG)
    • Visualize workflow steps: data loading, parameter resolution, calculation progress
    • Log all used parameters: Z_parent, Z_daughter, A_number, endpoint, transition type, enabled corrections
    • Optional log file output with timestamped filename
    • Integrate Python logging module with custom formatter
  • Add metadata header to CSV output files
    • Date and time of calculation (ISO 8601 format)
    • Nuclide information: parent/daughter symbol, Z, A
    • Decay/transition info: endpoint energy, transition type, forbiddenness
    • Calculation parameters: energy step, enabled corrections, detector settings
    • Software version and git commit hash (7 chars)
    • Format: YAML-style comments at top of CSV file
  • Optimize CLI argument design and add sanity checks
    • Auto-deduce transition_type from decay_type and nuclear data — remove as explicit CLI parameter
    • Auto-deduce decay_type from Z_parent vs Z_daughter difference — remove as explicit CLI parameter
    • Add sanity checks for custom input:
      • |Z_parent - Z_daughter| must equal 1 (beta decay)
      • For beta_minus: Z_daughter must be Z_parent + 1
      • For beta_plus/ec: Z_daughter must be Z_parent - 1
      • Warn if decay_type contradicts Z values (e.g., beta+ with Z_daughter > Z_parent)
      • Validate endpoint_MeV > 0 and endpoint_MeV > level_energy_keV/1000
      • Cross-check transition_type against ENSDF forbiddenness (if paceENSDF source)
  • Add --dry-run option to validate input and display resolved parameters without calculation
  • Add --version flag
  • Add -q/--quiet flag to suppress terminal output
  • Add ./output/ directory for debug verification artifacts (gitignored except .gitkeep)
  • Add debug verification step to development workflow: bs_pnpi -vv with parameter consistency checks across all components, documented in DEVELOPMENT.md §4.5
  • Add plot output with ID tracking (commit hash + UTC timestamp) and two display modes:
    • Normal mode (default): single spectrum plot with nuclear data header
    • Debug mode (-vv): 4-panel view with all correction factors and deviations

Deferred (Not Planned)

Additional Corrections

Not implementing at this time. Additional corrections (weak magnetism, recoil kinematics, etc.) require a complex implementation with project-wide consequences. This is a far-future plan, irrelevant to the current ⁹⁹Tc analysis goal where the shape factor C(W) absorbs all unmodelled energy-dependent effects.

Nuclear Shape Factors C(Z,W)

Not implementing theoretical shape factor calculations. The entire point of this project is to extract C(W) from experimental data, not to compute it from nuclear theory (shell model, QRPA, etc.). Theoretical shape factor calculations require:

  • Nuclear structure models (NUSHELLX, shell model codes)
  • One-body transition densities (OBTDs)
  • Coulomb displacement energy calculations
  • Multiple effective interactions

These are handled by the nuclear physics community. Our role is to provide the analysis framework that extracts C(W) from data, then compare the extracted shape to theoretical predictions.

Current Status

Version: 0.3.1 → In progress: 0.4.0 — Package restructuring

Completed (v0.3.x)

  • All theoretical corrections: phase space, Fermi function, finite size, screening, exchange, radiative (with delta_cut resummation)
  • Detector response module with analytical models (Gaussian, Gaussian+tail, Tikhonov), convolution API
  • χ² curve fitting framework (CurveFitter) with confidence intervals, profile likelihood, correlation analysis
  • C(W) shape factor extraction pipeline (CWExtractor) with Kurie plot analysis, parametrized fitting, g_V/g_A extraction
  • Multi-branch decay support (unified single/multi-branch)
  • CLI interface (bs_pnpi) with paceENSDF integration (--nuclide), structured logging (-v/-vv/-q), --dry-run, --version, --log-file
  • CSV metadata headers with branch info
  • JSON input with full detector param support
  • paceENSDF integration: get_decay_info_from_paceENSDF() returns DecayInfo with Z, A, endpoint, transition type, half-life, spin/parity, branches
  • Comprehensive test suite (262 tests, including 6 paceENSDF integration tests)
  • Notebook quality control with nbmake and auto-save plot hooks
  • Plot output: unified multi-branch approach, externalized headers, compact legends, consistent titles

Completed (v0.4.0)

  • Track B: Package restructuring — separating into beta_spectrum (theory), exp_data (experimental data), fitter (analysis framework)
    • Phase 1: Create exp_data module (raw_data.py, calibration.py, fitters.py, corrections.py, spectrum.py) — 43 tests
    • Phase 2: Create fitter module (model.py, fit_engine.py, extractor.py, result.py) — 34 tests
    • Phase 3: Clean up beta_spectrum (remove cw_extractor.py, fitter.py, init.py cleanup) — 322 tests
    • Phase 4: Package auto-discovered by setuptools, all imports updated, black formatting applied
  • v0.4.0 is COMPLETE
    • 322 tests pass (262 original + 60 new)
    • ruff + mypy clean on all 26 source files
    • black formatting applied to all new code
    • pyproject.toml auto-discovers all 4 packages: beta_spectrum, beta_spectrum.output, exp_data, fitter
    • README updated with new architecture diagram and Quick Start examples
    • Version bumped to 0.4.0

Next Immediate Step

  • Track A: ⁹⁹Tc spectrum-shape analysis — start real data processing pipeline
    • Data processing pipeline for experimental runs
    • Endpoint fitting and energy calibration
    • Systematic uncertainty analysis
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