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A high-precision branching ratio measurement for the superallowed Fermi$\beta^{+}$ emitter $^{62}$Ga was performed with the Gamma-Ray Infrastructurefor Fundamental Investigations of Nuclei (GRIFFIN) spectrometer at the IsotopeSeparator and Accelerator (ISAC) radioactive ion beam facility at TRIUMF. Thehigh efficiency of the GRIFFIN spectrometer allowed 63 $\gamma$-raytransitions, with intensities down to $\approx$1 part per million (ppm) per$^{62}$Ga $\beta^{+}$ decay, to be placed in the level scheme of the daughternucleus $^{62}$Zn, establishing the superallowed $\beta$ branching ratio for$^{62}$Ga decay to be 99.8577$^{+0.0023}_{-0.0029}\%$, a factor of 4 moreprecise than the previous world average. For several cascades, $\gamma-\gamma$angular correlation measurements were performed to assign spins and/ordetermine the mixing ratios of transitions. In particular, the spin of the2.342 MeV excited state in the daughter nucleus $^{62}$Zn was definitivelyassigned as $J = 0$. This assignment resolves a discrepancy between previousmeasurements and has important implications for the isospin symmetry breakingcorrection, $\delta_{C1}$, in $^{62}$Ga superallowed Fermi $\beta$ decay.

High-Precision Branching Ratio Measurement and Spin Assignment Implications for $^{62}$Ga Superallowed $\beta$ Decay