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Identification of the Lowest $T=2$, $J^{π=}0^+$ Isobaric Analog State in $^{52}$Co and Its Impact on the Understanding of $β$-Decay Properties of $^{52}$Ni

Masses of $^{52g,52m}$Co were measured for the first time with an accuracy of $\sim 10$ keV, an unprecedented precision reached for short-lived nuclei in the isochronous mass spectrometry. Combining our results with the previous $β$-$γ$ measurements of $^{52}$Ni, the $T=2$, $J^π=0^+$ isobaric analog state (IAS) in $^{52}$Co was newly assigned, questioning the conventional identification of IASs from the $β$-delayed proton emissions. Using our energy of the IAS in $^{52}$Co, the masses of the $T=2$ multiplet fit well into the Isobaric Multiplet Mass Equation. We find that the IAS in $^{52}$Co decays predominantly via $γ$ transitions while the proton emission is negligibly small. According to our large-scale shell model calculations, this phenomenon has been interpreted to be due to very low isospin mixing in the IAS.