Precise half-life measurement of the superallowed emitter ${}^{30}\mathrm{S}$

We have measured the half-life of ${}^{30}\mathrm{S}$, the parent of a superallowed $0^{+}\to 0^{+}\beta$ transition, to a high precision using very pure sources and a $4\pi$ proportional gas counter to detect the decay positrons. Our result for the half-life is 1.179 92(34) s. As a by-product of this measurement, we determine the half-life of its daughter, ${}^{30}\mathrm{P}$, to be 2.501(2) min.

Figure 1

Deposited energy versus position as recorded in the PSSD at the MARS focal plane. This result was obtained after the spectrometer had been tuned for ${}^{30}\mathrm{S}$ but before the extraction slits had been narrowed. Vertical lines show the final position of the extraction slits, 6.6 mm apart, which we used during these measurements. The projection on the right is of the counts between the slits. From such spectra recorded periodically during our experiment, we determined that the extracted ${}^{30}\mathrm{S}$ beam included a 0.37(8)% contribution from ${}^{27}\mathrm{Si}$ and 0.050(15)% from ${}^{29}\mathrm{P}$.

Figure 2

Implantation profiles of ${}^{30}\mathrm{S}$ (solid line) and the two contaminant activities, ${}^{29}\mathrm{P}$ and ${}^{27}\mathrm{Si}$ (dashed lines). The beam enters from the left. The shaded region shows the actual thickness of the Mylar collection tape. Our collected source contains only those ions that are stopped inside the tape.

Figure 3

Measured time-decay spectrum for the total of all data obtained from the combined $\beta$ decays of ${}^{30}\mathrm{S}$ and its daughter ${}^{30}\mathrm{P}$. There are 15 000 data points spanning 24 s. Dashed lines show the separate contributions calculated for the parent and daughter decays. The constant background is off scale at 7.3 counts/1.6 ms, more than four orders of magnitude less than the initial source counting rate. Note that counting began about 220 ms after the beam was turned off.

Figure 4

Test for any systematic dependence of our evaluated ${}^{30}\mathrm{S}$ half-life on the initial counting rate. Each symbol represents the average half-life from all 33 runs as obtained from only the portion of each decay spectrum that has a counting rate below a specified value. Diamonds are taken from dead-time channel A; squares, from channel B. Dashed lines give the $1\sigma$ uncertainty limits (statistical only), which correspond to the limiting rate of $9\times {10}^3$ cps. Note that the results are strongly correlated since the plotted symbols are derived from overlapping subsets of the same data.

Figure 5

Test for any systematic bias in the ${}^{30}\mathrm{S}$ half-life measurement due to changes in three detection parameters. Shown are the results from dead-time channel A for (a) five detector biases, (b) three discriminator threshold settings, and (c) two imposed dead times. Each graph includes half-life results from all 33 runs but the runs have been grouped differently for each graph. In all cases, gray bands represent the $\pm \sigma$ limits of the average half-life for a given condition. The average value for all the runs is represented by the solid horizontal line in each graph, with the corresponding dashed lines showing the statistical uncertainty limits. The value of the reduced ${\chi }^2$ for the 33-point average is 0.93.

Figure 6

Test for any systematic bias in the ${}^{30}\mathrm{S}$ half-life results due to otherwise undetected short-lived impurities. Each symbol is the result of a separate fit to the data from dead-time channel A; the abscissa for each symbol represents the time period at the beginning of the counting cycle for which the data were omitted from that particular fit. Dashed lines correspond to the $1\sigma$ uncertainty limits for the full data set. Note that, unlike Fig. 5, this figure uses data without any counting-rate limits applied (see text).

Figure 7

The present measurement (open circle) is compared with the only two previous measurements [5, 6] with subpercentage precision (filled circles). Results are presented in chronological order from left to right. The $\pm \sigma$ limits on the overall average value of 1.179 76(77) s appear as the gray band. Note that the uncertainty of the average has been scaled by a factor of 2.3 as a result of the inconsistency between measurement 2 and measurement 3 (see text).