Precise β branching-ratio measurement for the 0+→0+ superallowed decay of Ar34

We have measured the branching ratio for the superallowed ${0}^{+}\ensuremath{\rightarrow}$ ${0}^{+}\phantom{\rule{4pt}{0ex}}\ensuremath{\beta}$ transition from $^{34}\mathrm{Ar}$ to be 0.9448(8), and determined its $ft$ value to be 3058.1(28) s, a result with $\ifmmode\pm\else\textpm\fi{}0.09$% precision, which is a factor of 3 improvement over the previous result based on current world data. The $ft$-value ratio for the mirror pair of superallowed transitions $^{34}\mathrm{Ar}$ $\ensuremath{\rightarrow}^{34}\mathrm{Cl}$ and $^{34}\mathrm{Cl}$ $\ensuremath{\rightarrow}^{34}\mathrm{S}$ becomes the most precise yet measured and, in a sensitive test of the method used to calculate the isospin-symmetry-breaking correction, ${\ensuremath{\delta}}_{C}$, it agrees well with the ratio as calculated with Woods-Saxon radial wave functions. This confirms the method used in the most recent survey of superallowed decays to extract ${V}_{\text{ud}}$, the up-down quark-mixing element of the Cabibbo-Kobayashi-Maskawa matrix. In addition, our branching-ratio results for the four observed Gamow-Teller branches to ${1}^{+}$ states in $^{34}\mathrm{Cl}$ are shown to agree well with shell-model calculations based on the same effective interactions that were used in the determination of ${\ensuremath{\delta}}_{C}$.