Confirmation of Precise Branching Ratio Measurement in the $\beta $ Decay of $^{34}$Ar

Precise \textit{ft}-values for superallowed $0^+\to 0^+ \quad \beta ^{+}$-decays yield a demanding test of the Standard Model via the unitarity of the Cabibbo-Kobayashi-Maskawa matrix. One of the ingredients of an \textit{ft}-value is the transition branching ratio which, to be relevant for the unitarity test, must be measured with a precision of $\sim $0.1{\%} or better. After a preliminary report of such a measurement for $^{34}$Ar [1], we have verified our methods and tested for any possible systematic effects by measuring the decay of $^{10}$C under similar conditions. This nucleus is very well suited for a test of the data reduction method: it has a simple decay scheme without a ground-state branch, and all decay branches generate a 718 keV gamma ray. As with the $^{34}$Ar measurement, an implanted $^{10}$C source was placed between a plastic scintillator for $\beta $ particles and a HPGe detector that is efficiency calibrated with high precision (0.2{\%} between 50 and 1400 keV). Both $\beta $ singles and $\beta -\gamma $ coincidences were then recorded, and the collect/move/detect cycle was repeated until the desired statistical accuracy was obtained. We determined experimentally that the percentage of $^{10}$C decays leading to a 718 keV gamma ray is statistically consistent with the expected 100{\%}. This result validates our methods and reinforces the branching-ratio value previously obtained for the $^{34}$Ar decay. [1] V. Iacob \textit{et al.}, Bulletin APS 52, (37) Apr-Meeting 2007