Indirect measurement of the Na 23 ( p , γ ) Mg 24 direct capture reaction rate via ( He 3 ,   d ) spectroscopy

The cross section of the ²³Na(p,γ)²⁴Mg reaction is dominated by direct capture at low energies relevant for stellar burning. Such cross sections can be constrained using spectroscopic factors (C²S) or asymptotic normalization coefficients from transfer reactions. In this work, the ²³Na(³He,d)²⁴Mg reaction was measured at Elab=21 MeV to extract spectroscopic factors for ²⁴Mg states with excitation energies in Eₓ=7--120.28em0exMeV 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 ²³Na(p,γ) 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.