beta_shape_pnpi/TODO.md

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.

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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/deconvolution routines
  • Convolve theoretical spectrum with detector response for comparison to data
  • Deconvolve measured spectrum to recover true shape (for initial C(W) extraction)
  • Iterative unfolding (Richardson-Lucy or similar)
  • Implemented: convolve() and convolve_batch() 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

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Track B: Package Usability Improvements

B1. Nuclear Data Integration

• Add usage of paceENSDF package to retrieve nuclear data for decays
  • Q-values, half-lives, branch intensities, decay schemes
  • Automated setup of W0, Z, A parameters from ENSDF
  • Support for multiple isotopes without manual input

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

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

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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.

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Current Status

Version: 0.3.0
Implemented: Phase space, Fermi function, finite size, screening, exchange, radiative corrections (with delta_cut resummation). Detector response module with analytical models (Gaussian, Gaussian+tail, Tikhonov), convolution API, declarative config integration. χ² curve fitting framework (CurveFitter) with confidence intervals, profile likelihood, and correlation analysis. C(W) shape factor extraction pipeline (CWExtractor) with Kurie plot analysis, parametrized fitting, and g_V/g_A extraction. CLI interface (bs_pnpi) with paceENSDF integration, structured logging (-v/-vv/-q), --dry-run, --version, --log-file. CSV metadata headers. JSON input with full detector param support. Comprehensive test suite (195 tests). Notebook quality control with nbmake and auto-save plot hooks.

Completed: A2 — detector response function and convolution routines. A4 — fitter routine and C(W) extraction pipeline. B2 — input flexibility (JSON input, ENSDF auto-population). B8 — CLI & output improvements (logging, CSV headers, dry-run, version). B8.2 — CLI refinement: removed --mode, --transition-type, --decay-index flags; clarified units (MeV everywhere); enhanced logging (INFO shows components, DEBUG shows internals); CSV headers use element notation (Tc99 -> Ru99).

Next immediate step: A3 — data processing pipeline for experimental spectra (background subtraction, energy calibration, dead-time correction, pulse pile-up correction).