Absence of Low-Energy Shape Coexistence in $^{80}$Ge: The Nonobservation of a Proposed Excited 0$_2^+$ Level at 639 keV

The $^{80}$Ge structure was investigated in a high-statistics $\beta$-decay experiment of $^{80}$Ga using the GRIFFIN spectrometer at TRIUMF-ISAC through $\gamma$, $\beta$-$e$, $e$-$\gamma$ and $\gamma$-$\gamma$ spectroscopy. No evidence was found for the recently reported 0$_2^{+}$ 639-keV level suggested as evidence for low-energy shape coexistence in $^{80}$Ge. Large-scale shell model calculations performed in $^{78,80,82}$Ge place the $0^{+}_{2}$ level in $^{80}$Ge at 2\,MeV. The new experimental evidence combined with shell model predictions indicate that low-energy shape coexistence is not present in $^{80}$Ge.