High-precision half-life measurement for the superallowed Fermi ${\beta }^{+}$ emitter ${}^{22}\mathrm{Mg}$

A high-precision half-life measurement for the superallowed Fermi ${\beta }^{+}$ emitter ${}^{22}\mathrm{Mg}$ was performed at the TRIUMF-ISAC facility using a $4\pi$ proportional gas counter. The result of $T_{1/2}=3.87400\pm 0.00079$ s is a factor of 3 more precise than the previously adopted world average and resolves a discrepancy between the two previously published ${}^{22}\mathrm{Mg}$ half-life measurements.

Figure 1

A plot of the 14 precisely measured superallowed $\mathcal{F}t$ values obtained in the most recent evaluation using (a) the SM-WS ${\delta }_C$ corrections of Ref. [1] and (b) the SM-HF ${\delta }_C$ corrections of Ref. [18]. In both panels, the solid line represents the weighted average and the dashed lines represent the $\pm 1\sigma$ uncertainties.

Figure 2

Measurements of the applied dead time with nominal values of (a) 3 $\mu \mathrm{s}$ and (b) 4 $\mu \mathrm{s}$. The weighted average of the data points and corresponding $\pm 1\sigma$ uncertainty are given by the solid and dashed lines, respectively. Measurements performed before the ${}^{22}\mathrm{Mg}$ half-life experiment are given in black and the measurements performed after the experiment are given in blue.

Figure 3

Dead-time-corrected data points (black) and best fit curve (red) for a typical run. The fit to the data includes a ${}^{22}\mathrm{Mg}$ decaying component as well as a constant background component.

Figure 4

Run by run distribution of the half-life measurements. The corresponding ${\chi }^2/\nu$ of the fit for each run is given in the lower panel.

Figure 5

$\gamma$-ray energy spectrum in $\beta \text{−}\gamma$ coincidence recorded with the GRIFFIN spectrometer. The absence of characteristic $\gamma$ rays from potential isobaric contaminants was used to set limits on contributions to the activity in the gas counter.

Figure 6

The half-life of ${}^{22}\mathrm{Mg}$ as a function of the initial count rate in the gas counter. The slope as determined from a weighted linear regression is shown in red and is consistent with zero.

Figure 7

The half-life of ${}^{22}\mathrm{Mg}$ with the removal of leading channels for the data. Since each data point contains all of the data to the right of it, the data points are strongly correlated and are not expected to be scattered about the mean. The removal of 30 channels corresponds to approximately three half-lives of ${}^{22}\mathrm{Mg}$, or $\sim 87.5\%$ of the data. No trend indicative of rate-dependent effects is observed.

Figure 8

Half-life measurements of ${}^{22}\mathrm{Mg}$ grouped according to the different experimental running conditions. No ${\chi }^2/\nu$ is calculated for the dead time and MCS groupings as these data are not statistically independent. The solid red line represents the deduced ${}^{22}\mathrm{Mg}$ half-life while the dashed red lines represent the corresponding $\pm 1\sigma$ uncertainties. Since the ${\chi }^2/\nu$ is greater than 1 for the different bias voltages used, the statistical uncertainty is inflated by $\sqrt{1.44}$ and assigned as a systematic uncertainty.

Figure 9

Half-life measurements for ${}^{22}\mathrm{Mg}$ from Refs. [24] and [23], and the current work. The solid red line represents the weighted average of the two precise measurements and the dashed red lines represent the corresponding $\pm 1\sigma$ uncertainty. The result of Ref. [24] is more than a factor of 10 less precise than the result presented in the current work and is thus excluded from the weighted average [1].