A high-precision branching ratio measurement for the superallowed Fermi $beta^{+}$ emitter $^{62}$Ga was performed with the Gamma-Ray Infrastructure for Fundamental Investigations of Nuclei (GRIFFIN) spectrometer at the Isotope Separator and Accelerator (ISAC) radioactive ion beam facility at TRIUMF. The high efficiency of the GRIFFIN spectrometer allowed 63 $gamma$-ray transitions, with intensities down to $approx$1 part per million (ppm) per $^{62}$Ga $beta^{+}$ decay, to be placed in the level scheme of the daughter nucleus $^{62}$Zn, establishing the superallowed $beta$ branching ratio for $^{62}$Ga decay to be 99.8577$^{+0.0023}_{-0.0029}%$, a factor of 4 more precise than the previous world average. For several cascades, $gamma-gamma$ angular correlation measurements were performed to assign spins and/or determine the mixing ratios of transitions. In particular, the spin of the 2.342 MeV excited state in the daughter nucleus $^{62}$Zn was definitively assigned as $J = 0$. This assignment resolves a discrepancy between previous measurements and has important implications for the isospin symmetry breaking correction, $delta_{C1}$, in $^{62}$Ga superallowed Fermi $beta$ decay.
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