Precision Half-life Measurement of $^{17}$F

Precision measurements have led to considerable advances in understanding in several areas of physics, including fundamental symmetry. The precise determination of $ft$ values for superallowed mixed transitions between mirror nuclides could provide an avenue to test the theoretical corrections used to extract the V$_{ud}$ matrix element from superallowed pure Fermi transitions. The calculation of the $ft$ value requires knowledge of the half-life, branching ratio, and Q value. Thus the $^{17}$F decay is particularly interesting as it proceeds completely to the ground state of $^{17}$O, which removes the need for branching ratio measurements. In the addition the largest uncertainty on the relevant $ft$ value of the $^{17}$F mirror transition stems from the uncertainty in the half-life. An experiment to determine this life-time was conducted by the $\beta$ counting of implanted $^{17}$F on a Ta foil that was removed from the beam for counting. The $^{17}$F beam was produced by a transfer reaction and separated by the TwinSol facility of the Nuclear Science Laboratory of the University of Notre Dame. The results for $^{17}$F will be presented together with preliminary results of more recent half-life measurements. This work is supported in part by the National Science Foundation.