Precision $Q_{\mathrm{EC}}\text{-value}$ measurement of ${}^{23}\mathrm{Mg}$ for testing the Cabibbo-Kobayashi-Maskawa matrix unitarity

We report a new direct measurement of the transition energy $Q_{EC}$ of the ${}^{23}\mathrm{Mg}$ ${\beta }^{+}$ decay, using the TITAN Penning-trap mass spectrometer. This value is found to agree with the latest atomic mass evaluation while being four times more precise. The increase in precision changes the uncertainty contribution of the $Q_{EC}$ value on the statistical rate function $f_v$ from $11\%$ to $0.6\%$, an improvement by a factor of 18. This enables a more robust determination of the corrected $\mathcal{F}t$ value of this mirror transition to the required precision, making possible further test of the Cabibbo-Kobayashi-Maskawa matrix unitarity.

Figure 1

Typical quadrupole (a) and Ramsey (b) resonances of ${}^{23}\mathrm{Mg}$${}^{+}$ with the fitted theoretical line shapes [45, 46]. The quadrupole excitation time is $T_{RF}$ = 977 ms, while the Ramsey excitation scheme cycle ratio is 200:577:200 ms. The full width half maximum is indicated by the arrows.

Figure 2

Respective relative contribution to the $f_{v}t$ value of the branching ratio BR, half-life $t_{1/2}$, and statistical rate function $f_v$ in the case where either the AME12 [18] or TITAN $Q_{EC}$ of ${}^{23}\mathrm{Mg}$ used to calculate $f_v$. Since the $f_v\text{-value}$ uncertainty is significantly reduced, the relative contributions of the BR and $t_{1/2}$ uncertainties are increased.