docs: restructure knowledge base into tree layout + gA extraction module
- Organize into tree structure: corrections/, nuclear-structure/, gA-extraction/, refs/ - Move all correction notes to corrections/ (01-09) - Move nuclear structure to nuclear-structure/ with index - Add gA-extraction/ with SSM algorithm, sNME/ESSM formalism, Tc99 case study, and implementation TODO - Reorganize refs by topic (electromagnetic/, forbidden-decay/) - Update all wikilinks to new paths - Remove radiative_spec.md (code algorithm, not reference) - Lint: all wikilinks verified valid - Comprehensive gA extraction research based on Paulsen et al. (2024) and Song et al. (2025)
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title: "$^{99}$Tc Case Study — gA Extraction Results"
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date: 2026-05-14
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tags:
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- gA/extraction/tc99
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- beta-spectrum/forbidden/second
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status: active
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aliases: [Tc99 gA, 99Tc beta spectrum, SSM Tc99]
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related_notes:
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- gA-extraction/01-ssm-algorithm
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- gA-extraction/02-ssnme
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- refs/2024_Paulsen_T99_beta_spectrum/summary
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- refs/2025_Song_tc99_measurement_for_g_v/summary
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---
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# $^{99}$Tc — The Premier Laboratory for gA Extraction
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## Decay Properties
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| Property | Value |
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|---|---|
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| Transition | $^{99}\text{Tc}(9/2_1^+) \to {}^{99}\text{Ru}(5/2_1^+)$ |
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| Forbiddenness | Second-forbidden nonunique |
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| Branching ratio | 99.99855(30)% |
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| Q-value | 295.82(16) keV (Paulsen et al.) |
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| Half-life | 211.5(1.1) $\times 10^3$ a (ENSDF) |
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| Dominant transition | $2d_{5/2} \to 1g_{9/2}$ (OBTD $\approx 0.478$) |
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| Sub-dominant | $1g_{7/2} \to 1g_{9/2}$ (OBTD $\approx 0.010$) |
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## Two Contradictory Results
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### Result 1: Paulsen et al. (2024) — Enhanced $g_A$
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**Measurement:** MMC at PTB Berlin + LNHB Paris. Two independent setups, consistent results.
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**Method:** Fixed sNME to CVC value (CloseCVC).
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**Result:**
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$$g_A^{\text{eff}} = 1.526(92)$$
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This is an **enhanced** value — significantly above the free-nucleon value of 1.27.
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**Follow-on values:**
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- $g_V^{\text{eff}} = 0.376(5)$ — quenched (via half-life normalization)
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- $g_A^{\text{eff, quenched}} = 0.574(36)$ — quenched
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- $\bar{E}_\beta = 98.51(23)$ keV
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- $\log ft = 12.3478(23)$
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**Key claim:** This resolves an inconsistency — first-forbidden nonunique transitions show $g_A^{\text{eff}} \approx 0.9$, while fourth-forbidden show $g_A^{\text{eff}} \approx 0.9$. The $^{99}\text{Tc}$ result suggests $g_A$ is **enhanced** in second-forbidden decays.
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### Result 2: Song et al. (2025) — Quenched $g_A$
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**Measurement:** MMC at LLNL (KRISS sensor). Independent of Paulsen et al.
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**Method:** ESSM — sNME fitted as free parameter (FarCVC).
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**Result:**
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$$g_A^{\text{eff}} \approx 1.0\text{--}1.2$$
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This is a **quenched** value, consistent with first-forbidden and fourth-forbidden nonunique decays.
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**Best fit:** glekpn Hamiltonian, $g_A^{\text{eff}} = 1.2$, sNME = −0.0698 fm³, $\chi^2_\nu = 1.066$, p-value = 0.22
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**Key claim:** The Paulsen result is an artifact of fixing sNME to CVC. When sNME is fitted, the data prefer quenched $g_A$, consistent with the broader pattern.
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## The Crucial Difference: sNME Treatment
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| Aspect | Paulsen et al. | Song et al. |
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|---|---|---|
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| sNME treatment | Fixed to CVC value | Fitted as free parameter (ESSM) |
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| $g_A^{\text{eff}}$ | 1.526(92) (enhanced) | 1.0–1.2 (quenched) |
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| Nuclear models | NSM (GLEKPN) only | NSM (glekpn, jj45pnb) + MQPM |
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| Half-life constraint | Separate normalization | Simultaneous shape + half-life fit |
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| Consistency with 113Cd, 115In | Inconsistent | Consistent |
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## What This Means for Your Experiment
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The $^{99}\text{Tc}$ case demonstrates that **the treatment of sNME is the dominant theoretical systematic** in gA extraction. The two experiments (Paulsen and Song) measured essentially the same spectrum (Paulsen's data was used as input for Song's analysis) but obtained **contradictory results** because of different theoretical assumptions.
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**For your data analysis:**
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1. **Do not fix sNME to CVC** — treat it as a fitting parameter
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2. **Use ESSM** — simultaneous fit to spectral shape + half-life
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3. **Try multiple nuclear models** — glekpn, jj45pnb, and MQPM (if available)
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4. **Report both sNME solutions** (c and f) for each model
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5. **The "optimal" choice** (closest to CVC) is theoretically motivated but requires experimental validation
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## Your Polynomial Fit: Connecting to SSM
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You've fitted $C(W) = A \cdot W + B \cdot W^{-1} + C \cdot W^2$. This empirical parametrization can be **cross-checked** against the SSM prediction:
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1. Compute $C_{\text{SSM}}(W; g_A)$ for a range of $g_A$ values
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2. Fit each SSM curve to the polynomial form $aW + bW^{-1} + cW^2$ over your fit range
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3. Extract the effective $(A, B, C)$ as a function of $g_A$
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4. Compare your fitted $(A, B, C)$ to the $g_A$-dependent curve to identify which $g_A$ range is consistent
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This provides a **model-independent bridge** between your empirical fit and the physical $g_A$ extraction.
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## References
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| Ref | Citation |
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|---|---|
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| [Paulsen2024] | Paulsen et al., *Phys. Rev. C* **110**, 055503 (2024) |
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| [Song2025] | Song et al., arXiv:2506.17544 (2025) |
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| [Kostensalo2017] | Kostensalo & Suhonen, *Phys. Rev. C* **96**, 024317 (2017) |
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| [ESSM] | Kumar et al., *Eur. Phys. J. A* **57**, 225 (2021) |
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