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

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 ${}^{138}\mathrm{La}\beta$-decay $Q$ value with the $\beta$-decay spectrum end-point energy measured by Quarati et al. using ${\mathrm{LaBr}}_3$ detectors [Appl. Radiat. Isot. 108, 30 (2016)]. Use new precise measurements of the ${}^{138}\mathrm{La}\beta$-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 ${}^{138}\mathrm{La}$, ${}^{138}\mathrm{Ce}$, and ${}^{138}\mathrm{Ba}$ ions from which $\beta$-decay and EC $Q$ values for ${}^{138}\mathrm{La}$ were obtained.

Results: The ${}^{138}\mathrm{La}\beta$-decay and EC $Q$ values were measured to be $Q_{\beta }=1052.42\left(41\right)$ keV and $Q_{\mathrm{EC}}=1748.41\left(34\right)$ 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 ${}^{138}\mathrm{La}\beta$-decay shape factor and EC probabilities. New determinations for the ${}^{138}\mathrm{Ce}$ 2EC $Q$ value and the atomic masses of ${}^{138}\mathrm{La}$, ${}^{138}\mathrm{Ce}$, and ${}^{138}\mathrm{Ba}$ are also reported.

Conclusion: The ${}^{138}\mathrm{La}\beta$-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 ${}^{138}\mathrm{La}\beta$ 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.

Figure 1

Decay scheme for the Ba-La-Ce $A=138$ triplet. $Q_{\beta }^{\mathrm{gs}}$ and $Q_{\mathrm{EC}}^{\mathrm{gs}}$ are the ground-state-to-ground-state $\beta$-decay and EC $Q$ values measured in this work, corresponding to the energy equivalent of the mass difference between parent and daughter atoms. $Q_{\beta }^{(2+)}$ and $Q_{\mathrm{EC}}^{(2+)}$ are the $\beta$-decay and EC $Q$ values to the $2^{+}$ daughter state in ${}^{138}\mathrm{Ce}$ and ${}^{138}\mathrm{Ba}$, calculated as $Q^{(2+)}=Q^{\mathrm{gs}}–{\mathrm{E}}_{\gamma }$. All $Q$ values and $\gamma$ energies are given in keV.

Figure 2

A schematic overview of the sections of the LEBIT facility used for this experiment.

Figure 3

A 2.0-s time-of-flight ion cyclotron resonance for ${}^{138}\mathrm{La}$. The solid line is the theoretical fit to the data [52].

Figure 4

Cyclotron frequency ratio measurements for ${}^{138}\mathrm{La}^{+}/{}^{138}\mathrm{Ce}^{+}$, with the $1\sigma$ uncertainty in $\overline{R}$ shown by the shaded region.

Figure 5

LEBIT ${}^{138}\mathrm{La}\beta$-decay $Q$ value result compared to the AME2012 [33], AME2016 [54], and Quarati et al. [32] values.

Figure 6

LEBIT ${}^{138}\mathrm{Ce}$ 2EC $Q$ value measurements and their weighted average and uncertainty (shown by the dotted line and shaded region) compared to the AME2016 value.

Figure 7

Extraction of experimental shape factor $C_{\text{exp}}$ for ${}^{138}\mathrm{La}\beta$ decay using AME2016 $Q$ value from Ref. [54] and LEBIT $Q$ value from this work. The measured spectrum, shown in black, is from Ref. [32]. The classical theoretical calculation is shown in green. $C_{\text{exp}}$ is applied to the theory to get the adjusted spectrum, shown in red. The inset shows the improvement on $C_{\text{exp}}$ uncertainties due to the high-precision LEBIT $Q$ value determination.

Figure 8

Mass excesses measured in this work, as listed in Table 5, and compared to the AME2016 values, with AME2016 uncertainties indicated by the shaded region.