unzhakov
876e1e3ab8
- Add neutrino mass parameter to SpectrumConfig and CLI interface - Update PhaseSpace component to handle neutrino mass effects properly - Update CSV headers to show basic endpoint and all transition types - Add --csv-verbosity option to CLI with 'full' and 'concise' options - Fix comparison plots to properly show linear scale variations - Add comprehensive tests for neutrino mass functionality
1.9 KiB
1.9 KiB
SSM — Spectrum Shape Method
Overview
The Spectrum Shape Method (SSM) is a technique for determining the effective axial-vector coupling constant g_A by comparing theoretically computed β spectral shapes with experimental measurements. It is applicable to forbidden nonunique β decays, where the spectral shape depends nontrivially on g_A through the shape factor C(W; g_A).
Algorithm
- Compute shape factor components C_V(W), C_A(W), C_VA(W) from nuclear model
- Build theoretical spectrum for trial g_A values: N(W; g_A) = PhaseSpace × Fermi × ... × C(W; g_A)
- Compare with experimental spectrum using χ² minimization
- Extract g_A from the minimum χ² position
- Estimate uncertainty from χ² = χ²_min + 1
Key Requirements
- Forbidden nonunique transition: The spectral shape must depend on g_A
- High-precision measurement: Low energy threshold (< 10 keV), good energy resolution (< 1 keV)
- Accurate nuclear model: Nuclear shell model (NSM) or MQPM with appropriate valence space
g_A Values from Literature
| Source | g_A^eff | Method | Notes |
|---|---|---|---|
| Paulsen et al. (2024) | 1.526(92) | CVC-fixed sNME | Enhanced value |
| Song et al. (2025) | 1.0–1.2 | ESSM (farCVC) | Quenched value |
| Suhonen review | ~0.9 | Half-life comparison | Quenched value |
Uncertainty Budget
| Component | Uncertainty on g_A | Relative |
|---|---|---|
| Fit method (statistics) | 0.0745 | 4.9% |
| Coulomb displacement energy | 0.0425 | 2.8% |
| Nuclear model | 0.0294 | 1.9% |
| Lepton current treatment | 0.0127 | 0.8% |
| Fit range | 0.0061 | 0.4% |
| Endpoint energy | 0.0038 | 0.2% |
| Radiative corrections | 0.0033 | 0.2% |
| Atomic exchange | 0.0029 | 0.2% |
| Combined | 0.0919 | 6.0% |