Search for the $^{73}\mathrm{Ga}$ ground-state doublet splitting in the $\beta$ decay of $^{73}\mathrm{Zn}$

The existence of two close-lying nuclear states in $^{73}$Ga has recently been experimentally determined: a 1/2$^−$ spin-parity for the ground state was measured in a laser spectroscopy experiment, while a J$^{\pi} = 3/2^−$ level was observed in transfer reactions. This scenario is supported by Coulomb excitation studies, which set a limit for the energy splitting of 0.8 keV. In this work, we report on the study of the excited structure of $^{73}$Ga populated in the $\beta$ decay of $^{73}$Zn produced at ISOLDE, CERN. Using $\beta$-gated, $\gamma$-ray singles, and $\gamma - \gamma$ coincidences, we have searched for energy differences to try to delimit the ground-state energy splitting, providing a more stringent energy difference limit. Three new half-lives of excited states in $^{73}$Ga have been measured using the fast-timing method with LaBr$_3$(Ce) detectors. From our study, we help clarify the excited structure of $^{73}$Ga and we extend the existing $^{73}$Zn decay to $^{73}$Ga with 8 new energy levels and 35 $\gamma$ transitions. We observe a 195-keV transition consistent with a $\gamma$ ray de-exciting a short-lived state in the $\beta$-decay parent $^{73}$Zn