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
49 lines
1.9 KiB
Markdown
49 lines
1.9 KiB
Markdown
# SSM — Spectrum Shape Method
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## Overview
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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).
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## Algorithm
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1. **Compute shape factor components** C_V(W), C_A(W), C_VA(W) from nuclear model
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2. **Build theoretical spectrum** for trial g_A values: N(W; g_A) = PhaseSpace × Fermi × ... × C(W; g_A)
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3. **Compare with experimental spectrum** using χ² minimization
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4. **Extract g_A** from the minimum χ² position
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5. **Estimate uncertainty** from χ² = χ²_min + 1
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## Key Requirements
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- **Forbidden nonunique transition**: The spectral shape must depend on g_A
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- **High-precision measurement**: Low energy threshold (< 10 keV), good energy resolution (< 1 keV)
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- **Accurate nuclear model**: Nuclear shell model (NSM) or MQPM with appropriate valence space
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## g_A Values from Literature
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| Source | g_A^eff | Method | Notes |
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|---|---|---|---|
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| Paulsen et al. (2024) | 1.526(92) | CVC-fixed sNME | Enhanced value |
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| Song et al. (2025) | 1.0–1.2 | ESSM (farCVC) | Quenched value |
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| Suhonen review | ~0.9 | Half-life comparison | Quenched value |
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## Uncertainty Budget
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| Component | Uncertainty on g_A | Relative |
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|---|---|---|
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| Fit method (statistics) | 0.0745 | 4.9% |
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| Coulomb displacement energy | 0.0425 | 2.8% |
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| Nuclear model | 0.0294 | 1.9% |
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| Lepton current treatment | 0.0127 | 0.8% |
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| Fit range | 0.0061 | 0.4% |
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| Endpoint energy | 0.0038 | 0.2% |
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| Radiative corrections | 0.0033 | 0.2% |
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| Atomic exchange | 0.0029 | 0.2% |
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| **Combined** | **0.0919** | **6.0%** |
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## References
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- [[Shape Factor C(W, g_A)]]
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- [[ESSM — Enhanced Spectrum Shape Method]]
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- [[Paulsen et al. (2024)]]
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- [[Song et al. (2025)]]
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