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The radionuclide $^{22}$Na is a target of $\gamma$-ray astronomy searches,predicted to be produced during thermonuclear runaways driving classical novae.The $^{22}$Na(p,$\gamma$)$^{23}$Mg reaction is the main destruction channel of$^{22}$Na during a nova, hence, its rate is needed to accurately predict the$^{22}$Na yield. However, experimental determinations of the resonancestrengths have led to inconsistent results. In this work, we report ameasurement of the branching ratios of the $^{23}$Al $\beta$-delayed protons,as a probe of the key 204--keV (center-of-mass) $^{22}$Na(p,$\gamma$)$^{23}$Mgresonance strength. We report a factor of 5 lower branching ratio compared tothe most recent literature value. The variation in $^{22}$Na yield due tonuclear data inconsistencies was assessed using a series of hydrodynamic novaoutburst simulations and has increased to a factor of 3.8, corresponding to afactor of $\sim$2 uncertainty in the maximum detectability distance. This isthe first reported scientific measurement using the Gaseous Detector withGermanium Tagging (GADGET) system.

Low-energy $^{23}$Al $\beta$-delayed proton decay and $^{22}$Na destruction in novae