Constraining the $^{30}$P($p,γ)^{31}$S reaction rate in ONe novae via the weak, low-energy, $β$-delayed proton decay of $^{31}$Cl

The $^{30}$P$(p,γ)^{31}$S reaction plays an important role in understanding nucleosynthesis of $A\geq 30$ nuclides in oxygen-neon novae. The Gaseous Detector with Germanium Tagging was used to measure $^{31}$Cl $β$-delayed proton decay through the key $J^π=3/2^{+}$, 260-keV resonance. The intensity $I^{260}_{βp} = 8.3^{+1.2}_{-0.9} \times 10^{-6}$ represents the weakest $β$-delayed, charged-particle emission ever measured below 400 keV, resulting in a proton branching ratio of $Γ_p / Γ= 2.5^{+0.4}_{-0.3} \times 10^{-4}$. By combining this measurement with shell-model calculations for $Γ_γ$ and past work on other resonances, the total $^{30}$P$(p,γ)^{31}$S rate has been determined with reduced uncertainty. The new rate has been used in hydrodynamic simulations to model the composition of nova ejecta, leading to a concrete prediction of $^{30}$Si/$^{28}$Si excesses in presolar nova grains and the calibration of nuclear thermometers.