The cross section of the ${}^{23}\mathrm{Na}(p,\gamma ){}^{24}\mathrm{Mg}$ reaction is dominated by direct capture at low energies relevant for stellar burning. Such cross sections can be constrained using spectroscopic factors ($C^{2}S$) or asymptotic normalization coefficients from transfer reactions. In this work, the ${}^{23}\mathrm{Na}({}^3\mathrm{He},d){}^{24}\mathrm{Mg}$ reaction was measured at $E_{\text{lab}}=21$ MeV to extract spectroscopic factors for ${}^{24}\mathrm{Mg}$ states with excitation energies in $E_x=7–12\mathrm{MeV}$ using the Enge split-pole spectrograph at the Triangle Universities Nuclear Laboratory. A new nonresonant astrophysical $S$ factor and the direct capture reaction rate for the ${}^{23}\mathrm{Na}(p,\gamma )$ reaction are calculated and presented based on this measurement. The new rate at $T<0.04$ GK is $43\%$ smaller than in previous studies. Rigorous treatments of uncertainties are presented using a Bayesian Markov Chain Monte Carlo (MCMC) method. Sources of uncertainties for computing the direct capture cross section are also discussed in detail.

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• Nuclear astrophysics
• Nuclear reaction rates
• Radiative capture
• Spectroscopic factors & electromagnetic moments
• Transfer reactions
• 20 ≤ A ≤ 38
• Spectrometers & spectroscopic techniques