Precise Branching Ratio Measurement for the $\beta$ Decay of $^{21}$\textbf{Na}

A recent paper [1] reports a measurement of the $\beta -\nu $ correlation coefficient for the ground-state mirror $\beta ^{+}$ transition $^{21}Na(3/2^+)\to ^{21}Ne(3/2^+)$ of $a_{\beta \nu } =\mbox{0.5243(91)}$, which is significantly different from the Standard Model prediction of 0.558. However, both these values depend on the transition branching ratio, the currently accepted value of which, 94.97(13) {\%}, is an average over mutually inconsistent measurements (25 to 45 years old!). We set out to improve this value. We used a 28$\cdot A$ MeV $^{22}$Ne beam from the Texas A{\&}M cyclotron to initiate the $^{1}$H($^{22}$Ne, 2n)$^{ 21}$Na reaction. The recoils passed through the MARS recoil separator and, after being degraded, the $^{21}$Na ions were implanted as a $>$99{\%} pure source in the tape of a fast transport system. After a few-second collection time, the beam was turned off and the implanted source moved in 175 ms to a shielded region where it stopped between a plastic scintillator and a HPGe detector that is efficiency calibrated with high precision (0.2{\%} between 50 and 1400 keV [2]). Both $\beta $ singles and $\beta -\gamma $ coincidences were then recorded for 60s, and the collect/move/detect cycle was repeated to achieve the desired statistical accuracy. Our result for the ground-state branching ratio is 95.27(5){\%} . [1] N.D. Scielzo \textit{et al.}, Phys. Rev. Lett. \textbf{93 }102501 (2004). [2] R.G. Helmer \textit{et al.}, Nucl. Instr. Meth. \textbf{A511}, 360 (2003).