# ESSM — Enhanced Spectrum Shape Method

## Overview

The Enhanced Spectrum Shape Method (ESSM) extends the standard SSM by treating the small relativistic vector nuclear matrix element (sNME) as a free parameter alongside g_A. This allows simultaneous fitting of both the spectral shape AND the experimental half-life.

## Motivation

The sNME is difficult to compute accurately in nuclear shell model because it involves contributions outside the valence shell. The CVC prediction gives a "canonical" value, but this assumes a perfect many-body theory — which finite valence spaces are not.

## Algorithm

1. Fix g_A at a trial value
2. Vary sNME to simultaneously fit the experimental half-life
3. Because the half-life depends quadratically on sNME, there are typically **two solutions** for each g_A:
   - **sNME(c)**: closer to the CVC value (closeCVC)
   - **sNME(f)**: further from the CVC value (farCVC)
4. Compare both solutions' spectral shapes with the data

## sNME Values for ⁹⁹Tc

| Model | g_A^eff | sNME(c) [fm³] | sNME(f) [fm³] | CVC sNME [fm³] |
|---|---|---|---|---|
| jj45pnb | 1.0 | 0.0666 | −0.0687 | −0.1705 |
| glekpn | 1.0 | 0.1140 | −0.0202 | −0.0080 |

## Results from Song et al. (2025)

- **Best fit**: glekpn with g_A^eff = 1.2, sNME(f) = −0.0698 fm³, χ²_ν = 1.066
- **Conclusion**: Quenched g_A = 1.0–1.2 with farCVC sNME provides the best agreement with data

## References

- [[SSM — Spectrum Shape Method]]
- [[Shape Factor C(W, g_A)]]
- [[Song et al. (2025)]]
- [[Kumar et al. (2021)]]