High precision measurements of ${}^{26}\mathrm{Na}{\beta }^{-}$ decay

High-precision measurements of the half-life and β-branching ratios for the ${\beta }^{-}$ decay of ${}^{26}\mathrm{Na}$ to ${}^{26}\mathrm{Mg}$ have been measured in β-counting and γ-decay experiments, respectively. A 4π proportional counter and fast tape transport system were employed for the half-life measurement, whereas the γ rays emitted by the daughter nucleus ${}^{26}\mathrm{Mg}$ were detected with the $8\pi$ γ-ray spectrometer, both located at TRIUMF's isotope separator and accelerator radioactive beam facility. The half-life of ${}^{26}\mathrm{Na}$ was determined to be $T_{1/2}=1.07128\pm 0.00013\pm 0.00021\text{s}$, where the first error is statistical and the second systematic. The logft values derived from these experiments are compared with theoretical values from a full sd-shell model calculation.

Figure 1

Schematic of the 4π continuous gas flow proportional counter and fast tape transport system used in the β-counting experiment.

Figure 2

Typical dead-time-corrected decay curve containing 156 cycles obtained from one MCS for a single run (run 10).

Figure 3

Half-life versus run number obtained with the 4π continuous gas flow proportional counter and fast tape transport system. The solid line represents the deduced half-life (1.07128 s) obtained from a weighted average of these 24 data sets, whereas the dotted lines indicate the 1σ uncertainties (±0.00013 s).

Figure 4

Effect of removing leading channels on the deduced ${}^{26}\mathrm{Na}$ half-life. Each data point presented here is obtained by removing the two leading channels from the previous data point. The half-life obtained in this work is overlayed for comparison as one cannot perform a linear regression to these highly correlated data.

Figure 5

Half-life measurements of ${}^{26}\mathrm{Na}$ sorted by adjustable electronic setting. Each data point corresponds to a different grouping as indicated in the legend. As an example, the first three data points correspond to the half-life obtained with the first MCS, the half-life obtained with the first MCS with a fixed dead time per event of 3.024 ± 0.012 μs, and the half-life obtained with the first MCS with a fixed dead time per event of 4.036 ± 0.012 μs, respectively.

Figure 6

γ-ray singles spectrum for the entire data set obtained from approximately 12 hours of beam at $~{10}^5$ s${}^{-1}$. A total of $(1.5419\pm 0.0002)\times {10}^8$ counts were observed in the 1808.7-keV photopeak. Several γ rays from the β decay of ${}^{156}\mathrm{Tm}$ (indicated by an asterisk) are visible at low energies.

Figure 7

Comparison of B(GT) values from experiment (top panel) to a full sd-shell-model calculation (bottom panel) for all $I^{\pi }=2{}^{+}$, $3{}^{+}$, $4{}^{+}$ states in ${}^{26}\mathrm{Mg}$. The experimental sensitivity curve (indicated by the dashed line) is the boundary below which the β-branching ratios are expected to be too weak $(<2\times \hspace{1em}{10}^{-5})$ to be measured experimentally.

Figure 8

(Color online) Comparison of the experimental logft values versus the theoretical logft values. Perfect agreement between experiment and theory in this figure would correspond to the $y=x$ diagonal.