Precise half-life measurements for the superallowed ${\beta }^{+}$ emitters ${}^{34}\mathrm{Ar}$ and ${}^{34}\mathrm{Cl}$

To contribute meaningfully to any test of the unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) matrix, the measured $\mathit{ft}$ value of a superallowed $0^{+}\to 0^{+}$ ${\beta }^{+}$ transition must be obtained to a precision of 0.1% or better. We have determined the half-life of the superallowed emitter ${}^{34}\mathrm{Ar}$ to be 843.8(4)ms; the quoted precision, 0.05%, is a factor of five improvement on the best previous measurement and meets this demanding requirement. Our measurement employed a high-efficiency gas counter, which was sensitive to positrons from both ${}^{34}\mathrm{Ar}$ and its daughter ${}^{34}\mathrm{Cl}$. We achieved the required precision on ${}^{34}\mathrm{Ar}$ by analyzing the parent-daughter composite decay with a new fitting technique. We also obtained an improved half-life for ${}^{34}\mathrm{Cl}$ of 1.5268(5) s, which has 0.03% precision and is a factor of two improvement on previous results. As a by-product of these measurements, we determined the half-life of ${}^{35}\mathrm{Ar}$ to be 1.7754(11) s.

Figure 1

Electronic chain. Gas-counter signals are amplified by a preamplifier (PA) and a timing-filter amplifier (TFA); then go to a low-level discriminator, whose output is sent to two gate generators (GG), each of which introduces a well defined, but different, dead time. Finally, the gate-generator signals are multiscaled and their width is monitored.

Figure 2

Total time-spectrum recorded for the ${\beta }^{+}$ decay of ${}^{35}\mathrm{Ar}$.

Figure 3

Total time-decay spectrum recorded for the ${\beta }^{+}$ decay of ${}^{34}\mathrm{Cl}$.

Figure 4

Test for possible systematic bias in the ${}^{34}\mathrm{Cl}$ half-life measurement due to the discriminator threshold or detector bias. Full/open symbols represent the two 150 mV/200 mV discriminator settings; circles/squares/triangles represent, respectively, the detection biases 2600 V/2700 V/2800 V.

Figure 5

Test for possible systematic errors in the measurement of the decay of ${}^{34}\mathrm{Cl}$ caused by undetected short-lived impurities or by rate-dependent counting losses. The abscissa represents the time period at the beginning of the counting cycle for which the data were omitted from the fit.

Figure 6

Total time-decay spectrum obtained for the ${\beta }^{+}$ decay of ${}^{34}\mathrm{Ar}$ and its daughter ${}^{34}\mathrm{Cl}$. The dotted/dashed lines represent the calculated ${}^{34}\mathrm{Ar}$/${}^{34}\mathrm{Cl}$ contributions.

Figure 7

Total time-decay spectrum obtained for the ${\beta }^{+}$ decay of ${}^{34}\mathrm{Ar}$ with copper degraders around the source to preferentially reduce the ${}^{34}\mathrm{Cl}$ contribution. There were more than $9\times {10}^6$ combined ${}^{34}\mathrm{Ar}$ and ${}^{34}\mathrm{Cl}$ events. The dashed line shows the contribution of the exponential with the ${}^{34}\mathrm{Cl}$ decay constant.

Figure 8

Typical time-profile of the collected ${}^{34}\mathrm{Ar}$ beam. The initial drop in intensity is generated by the lowering of the gas density as the primary beam heats the gas around its path. A fan located inside the gas-target speeds up the transition to stable conditions.

Figure 9

Test for possible systematic bias in the ${}^{34}\mathrm{Ar}$ half-life measurement due to discriminator threshold or detector bias. Full/open symbols represent the two 150 mV/200 mV discriminator settings; circles/squares/triangles represent respectively the detection biases 2400 V/2550 V/2700 V. The result from each run is compared to the average value for the experiment to which it belongs. Runs 1–40 comprise the first experiment, contain a total of about $180\times {10}^6$ events, and have ${\chi }^2/\mathit{ndf}=54.6/39$; while runs 41–64 comprise the second experiment, contain about $220\times {10}^6$ events, and have ${\chi }^2/\mathit{ndf}=30.6/23$.