Precision half-life measurement of the ${\beta }^{+}$ decay of ${}^{37}\mathrm{K}$

The half-life of ${}^{37}\mathrm{K}$ has been measured to be $1.23651\left(94\right)\mathrm{s}$, a value nearly an order of magnitude more precise than the best previously reported. The ${\beta }^{+}$ decay of ${}^{37}\mathrm{K}$ occurs mainly via a superallowed branch to the ground state of its $T=1/2$ mirror, ${}^{37}\mathrm{Ar}$. This transition has been used recently, together with similar transitions from four other nuclei, as a method for determining $V_{ud}$, but the precision of its $ft$ value was limited by the relatively large half-life uncertainty. Our result corrects that situation. Another motivation for improving the $ft$ value was to determine the standard-model prediction for the $\beta$-decay correlation parameters, which will be compared to those currently being measured by the TRINAT Collaboration at TRIUMF. The new $ft$ value, $4605\left(8\right)\mathrm{s}$, is now limited in precision by the $97.99\left(14\right)\%$ ground-state branching ratio.

Figure 1

(a) Typical summed decay curve of the dead-time-corrected data obtained from a single run; (b) the corresponding residuals of the fit. The ${}^{37}\mathrm{K}$ decay curve accounts for 99.5% of the data, with 0.27% from the ${}^{35}\mathrm{Ar}$ and ${}^{33,34}\mathrm{Cl}$ contaminants, and the rest from background. The reduced ${\chi }^2$ of the fit was 1.05 with 488 degrees of freedom.

Figure 2

(a) Simultaneous fit to the 21 decay curves of a single run containing a total of 311 cycles combined into groups of 15; (b) the corresponding residual plot. The data here are the same as shown in Fig. 1 except in this case the data are not summed to a single decay curve. Here the reduced ${\chi }^2$ is 1.025 with 10 288 degrees of freedom.

Figure 3

The half-life obtained for ${}^{37}\mathrm{K}$ with different experimental conditions using the two analysis methods. The labels for each run are the detector bias, discriminator setting, degrader thickness, and imposed dead time. The solid line shows the best-fit half-life with the dashed lines representing the statistical uncertainty in the fit.

Figure 4

Test for otherwise undetected short-lived impurities or for possible rate-dependent effects. Each point is the result of a separate fit to one of the runs as the starting time of the fitting range is increased. The solid and dashed lines correspond to the average half-life value and uncertainties given in Fig. 3.

Figure 5

Values of $V_{ud}$ deduced for the four most precisely measured mirror transitions as a function of mass number. The smaller error bars with the filled in region represent the component of the total uncertainty arising from just $\mathcal{F}t$ (the total error bars are all dominated by the correlation measurements). The hatched region represents the fit to the average (${\chi }^2/3=0.7$) yielding $|V_{ud}|=0.9718\left(17\right)$. For comparison, the solid band shows the value of $V_{ud}$ derived from the pure Fermi transitions.