174 lines
8.1 KiB
Markdown
174 lines
8.1 KiB
Markdown
# Strategic Development Roadmap
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## Scientific Goal
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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.
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This requires repeating the analysis pipeline of [Paulsen et al., Phys. Rev. C **110**, 055503 (2024)](https://doi.org/10.1103/PhysRevC.110.055503), which used Metallic Magnetic Calorimeters (MMCs) to measure the ⁹⁹Tc beta spectrum with sub-keV threshold and ~100 eV resolution.
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See `docs/refs/2024_Paulsen_T99_beta_spectrum/summary.md` for full analysis details.
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______________________________________________________________________
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## Track A: ⁹⁹Tc Spectrum-Shape Analysis
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### A1. Research & Data Collection
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- [ ] Parse additional PDF sources on ⁹⁹Tc beta decay and spectrum-shape method
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- Kostensalo & Suhonen, Phys. Rev. C **96**, 024317 (2017) — theoretical spectrum shape predictions
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- Suhonen, Frontier. Phys. **5**, 55 (2017) — review of g_A quenching
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- Haaranen et al., Phys. Rev. C **93**, 034308 (2016) — effective coupling constants
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- Additional experimental ⁹⁹Tc spectra (historical data for comparison)
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- [ ] Research methods to extract g_V from fitted C(W) shape
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- Study the relationship between C(W) parametrization and g_V, g_A effective values
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- Understand how CVC (Conserved Vector Current) constrains g_V
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- Review the spectrum-shape method formalism (Behrens-Bühring + shell model)
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- [ ] Document the full analysis pipeline: experimental data → theoretical model → C(W) extraction → g_V extraction
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### A2. Detector Response Function
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- [ ] Implement analytical detector response function for 4π semiconductor detector
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- Gaussian core with low-energy tail (charge collection effects)
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- Parameters: energy resolution σ(E), tail fraction, tail shape
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- Energy-dependent resolution σ(E) = a + b·√E
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- [ ] Implement convolution/deconvolution routines
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- Convolve theoretical spectrum with detector response for comparison to data
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- Deconvolve measured spectrum to recover true shape (for initial C(W) extraction)
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- Iterative unfolding (Richardson-Lucy or similar)
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- [ ] Monte Carlo simulation (GEANT4) — out of scope for this project but noted for future
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- Full detector geometry simulation
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- Energy loss in source, dead layers, absorber
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- Response matrix for unfolding (as done in Paulsen et al. with EGSNRC)
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### A3. Data Processing & Analysis
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- [ ] Data processing pipeline for 1-hour run spectra
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- Background subtraction
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- Energy calibration (using known X-ray/gamma lines)
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- Dead-time correction
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- Pulse pile-up correction
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- [ ] Endpoint fitting and energy calibration
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- Kurie plot analysis for endpoint determination
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- Polynomial calibration using known spectral lines
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- Linearity correction across energy range
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- [ ] Data quality assessment procedures
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- Residual analysis (data vs model)
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- χ²/ndf evaluation
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- Consistency checks across multiple runs
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- Statistical combination of long-exposure spectra
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### A4. Fitter for C(W) Extraction
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- [ ] Implement fitter routine to extract experimental C(W) from data
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- χ² minimization: theoretical spectrum (with all corrections) vs measured spectrum
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- Free parameters: C(W) shape parameters, endpoint energy, normalization, background
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- Covariance matrix and uncertainty propagation
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- [ ] Parametrize C(W) in terms of g_V (and g_A)
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- Fit C(W) data to theoretical parametrization
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- Extract g_V^eff and g_A^eff from the fit
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- Compare with Paulsen et al. results: g_A^eff = 0.574(36), g_V^eff = 0.376(5)
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- [ ] Systematic uncertainty analysis
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- Vary correction implementations within uncertainties
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- Test sensitivity to detector response model
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- Background model dependence
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______________________________________________________________________
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## Track B: Package Usability Improvements
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### B1. Nuclear Data Integration
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- [ ] Add usage of `paceENSDF` package to retrieve nuclear data for decays
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- Q-values, half-lives, branch intensities, decay schemes
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- Automated setup of W0, Z, A parameters from ENSDF
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- Support for multiple isotopes without manual input
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### B2. Input Flexibility
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- [ ] Generalize parameter inputs via custom input file (YAML/JSON)
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- Declare isotope, transition type, detector parameters
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- Toggle corrections on/off per-component
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- Reproducible calculation configurations
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- [ ] Retrieve parameters directly from ENSDF database
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- Auto-populate W0, Z, A, transition type from isotope name
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- Reduce manual configuration errors
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### B3. Multiple Branch Decays
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- [ ] Add support for multiple branch decays
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- Calculate total spectral shape weighted by branch intensities
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- Handle decays with significant branching to excited states
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- Sum contributions from all branches with proper weighting
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### B4. Beta+ Decay Support
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- [ ] Modify corrections to support β⁺ decays
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- Fermi function sign change for positrons
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- Radiative corrections for β⁺ (Sirlin corrections differ for e⁻ vs e⁺)
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- Screening correction for positrons (different atomic interaction)
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- Exchange correction (negligible for β⁺ but check)
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### B5. Neutrino Spectrum Support
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- [ ] Add convenience analyser methods for plotting neutrino spectra
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- Convert electron spectrum to neutrino spectrum
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- Plot both on same figure with proper scaling
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- [ ] Adopt corrections that differ for neutrino spectrum
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- Implement neutrino radiative correction h(W̃, W0) per Sirlin 2011
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- Conversion formula: f_ν(W_ν) = f_e(W̃) · [1 + (α/2π)(h − g)]
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- Neutrino-specific corrections (no Fermi function, different radiative terms)
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### B6. Neutrino Mass Effects
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- [ ] Implement option to produce spectra with non-zero neutrino mass
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- Modify phase space: (W0 − W)² → (W0 − W)² · √(1 − m_ν²/(W0−W)²)
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- Add kink feature near endpoint for spectral distortion
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- Useful for neutrino mass search applications
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- [ ] Research and document implications of significant neutrino mass
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- Which corrections need m_ν as input parameter?
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- Impact on radiative corrections (mass singularities)
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- Impact on endpoint fitting procedures
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### B7. Automated Report Generation
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- [ ] Implement extensive procedurally generated PDF report
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- Comprehensive details of the calculation
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- Component plots (phase space, Fermi, each correction factor)
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- Total spectrum with all corrections applied
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- Residual analysis, fit quality metrics
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- Parameter table with uncertainties
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- References to theoretical sources
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- [ ] Extend report generation to fitters
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- Fit results with covariance matrix
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- Parameter correlations
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- Confidence intervals
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- Goodness-of-fit statistics
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______________________________________________________________________
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## Deferred (Not Planned)
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### Nuclear Recoil Correction (`recoil.py`)
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Not implementing at this time. The recoil correction (weak magnetism, recoil kinematics) is a small O(q/M_N) effect (~0.1%) that is subdominant to the shape factor C(W) we aim to extract. In the ⁹⁹Tc analysis, the shape factor absorbs all unmodelled energy-dependent effects — including recoil — so implementing recoil explicitly is unnecessary for the scientific goal.
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### Nuclear Shape Factors C(Z,W)
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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:
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- Nuclear structure models (NUSHELLX, shell model codes)
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- One-body transition densities (OBTDs)
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- Coulomb displacement energy calculations
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- Multiple effective interactions
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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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______________________________________________________________________
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## Current Status
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**Version:** 0.2.0\
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**Implemented:** Phase space, Fermi function, finite size, screening, exchange, radiative corrections (with delta_cut resummation). Comprehensive test suite (72 tests).
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**Next immediate step:** A2 — implement detector response function and convolution routines, as this is the bridge between theoretical spectra and experimental data.
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