Indirect Measurement of the ²³Na(p, γ)²⁴Mg Direct Capture Reaction Rate via (³He,d) Spectroscopy

The origin of the Na-O anticorrelation in globular cluster stars is an active area of debate that required reliable nuclear physics input. At astrophysical temperatures below 50 MK, the key sodium destruction reaction during hydrogen burning, ²³Na(p, γ)²⁴Mg, is entirely determined by the direct capture cross section, and suffers from large uncertainties. In this work, a proton-stripping ²³Na(3He,d)²⁴Mg experiment was performed to constrain that direct capture cross section by determining the spectroscopic information of ²⁴Mg states below the proton separation energy. The experiment was performed in an angular range of 5°≤θlab≤21° at E(3He)=21MeV with the Enge Split-pole Spectrograph at Triangle Universities Nuclear Laboratory. Spectroscopic factors, C2S, were extracted for bound states from the angular cross sections with rigorous uncertainties determined using Bayesian techniques. The direct capture reaction rates were then calculated from the extracted C²S values and found to be smaller than previous studies by 55% in the T<50MK range.