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
38 lines
1.5 KiB
Markdown
38 lines
1.5 KiB
Markdown
# 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)]]
|