beta_shape_pnpi/docs/gA-extraction/03-tc99-case-study.md

title, date, tags, status, aliases, related_notes

title	date	tags	status	aliases	related_notes
$^{99}$Tc Case Study — gA Extraction Results	2026-05-14	gA/extraction/tc99 beta-spectrum/forbidden/second	active	Tc99 gA 99Tc beta spectrum SSM Tc99	gA-extraction/01-ssm-algorithm gA-extraction/02-ssnme refs/2024_Paulsen_T99_beta_spectrum/summary refs/2025_Song_tc99_measurement_for_g_v/summary

$^{99}$Tc — The Premier Laboratory for gA Extraction

Decay Properties

Property	Value
Transition	^{99}\text{Tc}(9/2_1^+) \to {}^{99}\text{Ru}(5/2_1^+)
Forbiddenness	Second-forbidden nonunique
Branching ratio	99.99855(30)%
Q-value	295.82(16) keV (Paulsen et al.)
Half-life	211.5(1.1) \times 10^3 a (ENSDF)
Dominant transition	2d_{5/2} \to 1g_{9/2} (OBTD \approx 0.478)
Sub-dominant	1g_{7/2} \to 1g_{9/2} (OBTD \approx 0.010)

Two Contradictory Results

Result 1: Paulsen et al. (2024) — Enhanced g_A

Measurement: MMC at PTB Berlin + LNHB Paris. Two independent setups, consistent results.

Method: Fixed sNME to CVC value (CloseCVC).

Result:

g_A^{\text{eff}} = 1.526(92)

This is an enhanced value — significantly above the free-nucleon value of 1.27.

Follow-on values:

• g_V^{\text{eff}} = 0.376(5) — quenched (via half-life normalization)
• g_A^{\text{eff, quenched}} = 0.574(36) — quenched
• \bar{E}_\beta = 98.51(23) keV
• \log ft = 12.3478(23)

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.

Result 2: Song et al. (2025) — Quenched g_A

Measurement: MMC at LLNL (KRISS sensor). Independent of Paulsen et al.

Method: ESSM — sNME fitted as free parameter (FarCVC).

Result:

g_A^{\text{eff}} \approx 1.0\text{--}1.2

This is a quenched value, consistent with first-forbidden and fourth-forbidden nonunique decays.

Best fit: glekpn Hamiltonian, g_A^{\text{eff}} = 1.2, sNME = −0.0698 fm³, \chi^2_\nu = 1.066, p-value = 0.22

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.

The Crucial Difference: sNME Treatment

Aspect	Paulsen et al.	Song et al.
sNME treatment	Fixed to CVC value	Fitted as free parameter (ESSM)
g_A^{\text{eff}}	1.526(92) (enhanced)	1.0–1.2 (quenched)
Nuclear models	NSM (GLEKPN) only	NSM (glekpn, jj45pnb) + MQPM
Half-life constraint	Separate normalization	Simultaneous shape + half-life fit
Consistency with 113Cd, 115In	Inconsistent	Consistent

What This Means for Your Experiment

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.

For your data analysis:

1. Do not fix sNME to CVC — treat it as a fitting parameter
2. Use ESSM — simultaneous fit to spectral shape + half-life
3. Try multiple nuclear models — glekpn, jj45pnb, and MQPM (if available)
4. Report both sNME solutions (c and f) for each model
5. The "optimal" choice (closest to CVC) is theoretically motivated but requires experimental validation

Your Polynomial Fit: Connecting to SSM

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:

1. Compute C_{\text{SSM}}(W; g_A) for a range of g_A values
2. Fit each SSM curve to the polynomial form aW + bW^{-1} + cW^2 over your fit range
3. Extract the effective (A, B, C) as a function of g_A
4. Compare your fitted (A, B, C) to the $g_A$-dependent curve to identify which g_A range is consistent

This provides a model-independent bridge between your empirical fit and the physical g_A extraction.

References

Ref	Citation
[Paulsen2024]	Paulsen et al., Phys. Rev. C 110, 055503 (2024)
[Song2025]	Song et al., arXiv:2506.17544 (2025)
[Kostensalo2017]	Kostensalo & Suhonen, Phys. Rev. C 96, 024317 (2017)
[ESSM]	Kumar et al., Eur. Phys. J. A 57, 225 (2021)