# 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

1. **Compute shape factor components** C_V(W), C_A(W), C_VA(W) from nuclear model
2. **Build theoretical spectrum** for trial g_A values: N(W; g_A) = PhaseSpace × Fermi × ... × C(W; g_A)
3. **Compare with experimental spectrum** using χ² minimization
4. **Extract g_A** from the minimum χ² position
5. **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%** |

## References

- [[Shape Factor C(W, g_A)]]
- [[ESSM — Enhanced Spectrum Shape Method]]
- [[Paulsen et al. (2024)]]
- [[Song et al. (2025)]]