# Direct determination of the $^{138}$La $\beta$-decay $Q$ value using Penning trap mass spectrometry

## TL;DR

This study precisely measured the $^{138}$La $eta$-decay $Q$ value using Penning trap mass spectrometry, confirming previous results and significantly reducing uncertainties, thereby improving theoretical decay models and experimental interpretations.

## Contribution

The paper provides the most precise $^{138}$La $eta$-decay $Q$ value measurement to date, enhancing nuclear decay models and experimental data analysis.

## Key findings

- Measured $Q$ value: 1052.42(41) keV
- Improved precision by an order of magnitude
- Confirmed previous $Q$ value with higher accuracy

## Abstract

Background: The understanding and description of forbidden decays provides interesting challenges for nuclear theory. These calculations could help to test underlying nuclear models and interpret experimental data. Purpose: Compare a direct measurement of the $^{138}$La $\beta$-decay $Q$ value with the $\beta$-decay spectrum end-point energy measured by Quarati et al. using LaBr$_3$ detectors [Appl. Radiat. Isot. 108, 30 (2016)]. Use new precise measurements of the $^{138}$La $\beta$-decay and electron capture (EC) $Q$ values to improve theoretical calculations of the $\beta$-decay spectrum and EC probabilities. Method: High-precision Penning trap mass spectrometry was used to measure cyclotron frequency ratios of $^{138}$La, $^{138}$Ce and $^{138}$Ba ions from which $\beta$-decay and EC $Q$ values for $^{138}$La were obtained. Results: The $^{138}$La $\beta$-decay and EC $Q$ values were measured to be $Q$ = 1052.42(41) keV and $Q_{EC}$ = 1748.41(34) keV, improving the precision compared to the values obtained in the most recent atomic mass evaluation [Wang, et al., Chin. Phys. C 41, 030003 (2017)] by an order of magnitude. These results are used for improved calculations of the $^{138}$La $\beta$-decay shape factor and EC probabilities. New determinations for the $^{138}$Ce 2EC $Q$ value and the atomic masses of $^{138}$La, $^{138}$Ce, and $^{138}$Ba are also reported. Conclusion: The $^{138}$La $\beta$-decay $Q$ value measured by Quarati et al. is in excellent agreement with our new result, which is an order of magnitude more precise. Uncertainties in the shape factor calculations for $^{138}$La beta-decay using our new $Q$ value are reduced by an order of magnitude. Uncertainties in the EC probability ratios are also reduced and show improved agreement with experimental data.