$β$-delayed spectroscopy of $^{80}$Ge$_{48}$ and competition between Gamow-Teller and first-forbidden transitions in $^{80g+m}$Ga$_{49}$ $β$ decay
The $β$-delayed spectroscopy of $^{80}$Ge has been studied using sources of ground and low-lying isomeric states of $^{80}$Ga. A hybrid $γ$-ray spectrometer was used, composed of high-purity germanium (HPGe) detectors for low-energy $γ$-ray detection, phoswich detectors from the PARIS array for high-energy $γ$ rays and a plastic detector for $β$ tagging. The new decay level schemes are presented, with 13 and 14 states $β$ populated by $^{80g}$Ga and $^{80m}$Ga, respectively, being reported for the first time. We quantitatively compare summed intensities of first-forbidden and previously reported Gamow-Teller $β$ transitions [R. Li et al., \href{https://doi.org/10.1103/PhysRevC.111.034303}{Phys. Rev. C 111, 034303 (2025)}]. The upper-limit fractions of first-forbidden transitions contributing to the decays of $^{80g}$Ga and $^{80m}$Ga are (48.0 $\pm$ 2.7)$\%$ and (47.9 $\pm$ 3.3)$\%$ of the observed total $β$ transition intensities of (78.2 $\pm$ 2.5)$\%$ and (82.2 $\pm$ 3.7)$\%$, respectively. Notably, the half-lives decrease in accordance with the upper limits of (48.0 $\pm$ 6.0)$\%$ [3.67(20) s $\rightarrow$ 1.91(3) s] and (47.9 $\pm$ 7.2)$\%$ [3.01(19) s $\rightarrow$ 1.57(1) s] for $^{80g}$Ga and $^{80m}$Ga, respectively, when including first-forbidden transitions, in contrast to those by Gamow-Teller transitions only.