High-precision half-life measurements of the T =1/2 mirror $\beta$ decays $^{17}$F and $^{33}$Cl

Measurements of the ft values for T=1/2 mirror $\beta$+ decays offer a method to test the conserved vector current hypothesis and to determine Vud, the up-down matrix element of the Cabibbo-Kobayashi-Maskawa matrix. In most mirror decays used for these tests, uncertainties on the ft values are dominated by the uncertainties in the half-lives. Two precision half-life measurements were performed for the T=1/2 $\beta$+ emitters, 17F and 33Cl, in order to eliminate the half-life as the leading source of uncertainty in their ft values. \item[Method] Half-lives of 17F and 33Cl were determined using $\beta$ counting of implanted radioactive ion beam samples on a moving tape transport system at the SPIRAL low energy identification station at GANIL. The 17F half-life result, 64.347~(35) s, precise to $\pm$0.05 %, is a factor of 5 times more precise than the previous world average. The half-life of 33Cl was determined to be 2.5038~(22) s. The current precision of $\pm$0.09 % is nearly 2 times more precise compared to the previous world average. The precision achieved during the present measurements implies that the half-life no longer dominates the uncertainty of the ft values for both T=1/2 mirror decays 17F and 33Cl.