Direct measurement of the ${}^{23}\mathrm{Mg}(p, γ){}^{24}\mathrm{Al}$ reaction using the DRAGON recoil separator and a hybrid array of $γ$-ray detectors

Background: The $^{23}$Mg$(p,γ)^{24}$Al reaction plays a key role in nova nucleosynthesis, serving as a bridge between the Ne-Na and Mg-Al cycles and impacting synthesis of a wide variety of nuclides. It is crucial that the rate of this reaction be well constrained by experimental data, in particular the properties of the key resonance at $E_{\mathrm{cm}}\approx480$ keV, which dominates the rate at nova temperatures. Purpose: Our study aims to improve experimental constraints on the energy and strength of the key $E_{\mathrm{cm}}\approx480$ keV $^{23}$Mg$(p,γ)^{24}$Al resonance through a new direct measurement of its strength and energy. Methods: We used a $^{23}\mathrm{Mg}$ radioactive beam to directly observe capture into the $E_{\mathrm{cm}}\approx480$ keV resonance in inverse kinematics. The $^{24}\mathrm{Al}$ recoils were selected by the DRAGON recoil separator, and coincident $γ$ rays were measured in a hybrid $\mathrm{LaBr}_3/\mathrm{CeBr}_3/\mathrm{BGO}$ scintillator array. The $^{24}\mathrm{Al}$ singles yield was used to determine the resonance strength, while the time difference between the coincident $γ$ rays and the incident beam was used to determine the resonance energy. Results: We obtained a strength of $ωγ=38(7)$ meV and an energy of $E_{\mathrm{cm}}=478.8(26)$ keV for the key astrophysical $^{23}\mathrm{Mg}(p,γ)^{24}\mathrm{Al}$ resonance. Conclusions: Our reported strength is in excellent agreement with the previously reported direct measurement, as well as shell model calculations. Our energy is in good agreement with earlier indirect measurements. Reaction rate calculations incorporating our results indicate that the $^{23}\mathrm{Mg}(p,γ)^{24}\mathrm{Al}$ rate is constrained to a $1σ$ up/down factor of 1.5 or smaller in the nova temperature range of 0.2--0.4 GK.