Simultaneous impacts of nuclear shell structure and collectivity on $\beta$ decay: Evidence from $^{80}$Ga$_{49}$

The Gamow-Teller strength distribution covering the entire $\beta$-decay window, up to 10.312(4) MeV, of $^{80g+m}$Ga was measured for the first time in photo fission of UC$_x$ induced by a 50 MeV electron beam. The new data show significant enhancement in the high-energy region with a jump structure. Simultaneously, the $\gamma$ deexciting behavior of $\beta$-populated states presents a competition between deexcitation to 2$_1^+$ [$\beta_2$ = 0.155(9)] and to 2$_2^+$ [$\beta_2$ = 0.053$_{0.009}^{0.008}$)] in $^{80}$Ge. To understand these data, we performed a realistic shell-model calculation and systematic analysis of log $\it{ft}$ ratios between precursors' $\beta$ decay to 2$_2^+$ and to 2$_1^+$ of Ga isotopes. We conclude that these phenomena evidence simultaneous impacts of nuclear shell structure and collectivity on $\it{B}$(GT) distribution and therefore the half-life of the precursor.