Precision half-life measurement of P 29

A new precision half-life measurement of $^{29}\mathrm{P}$ was conducted using the TwinSol $\ensuremath{\beta}$-counting station at the University of Notre Dame Nuclear Science Laboratory. The resulting value of ${t}_{1/2}^{\mathrm{new}}=4.1055(44)\phantom{\rule{0.28em}{0ex}}\mathrm{s}$ is the most precise $^{29}\mathrm{P}$ half-life measurement to date. Utilizing this measurement and reevaluating the world data leads to a new world average of ${t}_{1/2}^{\mathrm{world}}=4.1031(58)\phantom{\rule{0.28em}{0ex}}\mathrm{s}$, which improves the Birge ratio from 3.11 to 1.45 and is 2.3 times more precise than the previous world value. The new Cabibbo-Kobayashi-Maskawa matrix element ${V}_{\mathrm{ud}}$ for $^{29}\mathrm{P}$ shifts closer into agreement with the superallowed pure Fermi value. The uncertainty in the mixed transition value of ${V}_{\mathrm{ud}}$, however, is still dominated by the Fermi to Gamow-Teller mixing ratio $\ensuremath{\rho}$. Using the new world half-life and assuming the validity of the standard model, a new predicted value for $\ensuremath{\rho}$ and its associated correlation parameters have been evaluated in order to guide future determination of $\ensuremath{\rho}$.