New energy for the 133-keV resonance in the ${}^{23}\mathrm{Na}(\mathrm{p},\gamma ){}^{24}\mathrm{Mg}$ reaction and its impact on nucleosynthesis in globular clusters

Globular cluster stars exhibit star-to-star anticorrelations between oxygen and sodium in their atmospheres. An improved description of the sodium-destroying ${}^{23}\mathrm{Na}+\mathrm{p}$ reaction rates is essential to understanding these observations. We present an energy analysis of ${}^{24}\mathrm{Mg}$ states based on a new measurement of the ${}^{23}\mathrm{Na}({}^3\mathrm{He},\mathrm{d}){}^{24}\mathrm{Mg}$ reaction. A key resonance in ${}^{23}\mathrm{Na}(\mathrm{p},\gamma ){}^{24}\mathrm{Mg}$ is found to be at $E_r^{\text{c.m.}}=133\left(3\right)$ keV, 5 keV lower than previously adopted. This finding has a dramatic effect on the ${}^{23}\mathrm{Na}(\mathrm{p},\gamma ){}^{24}\mathrm{Mg}$ reaction rate, increasing it by a factor of 2 for the recommended rate. The nucleosynthesis impact of this change is investigated.

Figure 1

Part of the calibrated deuteron focal plane spectra from the ${}^{23}\mathrm{Na}({}^3\mathrm{He},\mathrm{d}){}^{24}\mathrm{Mg}$ reaction collected at laboratory angles of ${11}^{\circ }$ and ${17}^{\circ }$. The binned counts are plotted as a function of excitation energy in ${}^{24}\mathrm{Mg}$ with the corresponding states labelled with their adopted energies in MeV. States with asterisks were used as calibration points (7 in total, some fall outside the plotted range). Highlighted states (red) correspond to background lines from target contaminants and are labeled with their corresponding excited state. For example, ${}^{17}\mathrm{F}_1$ labels the 1st excited state in ${}^{17}\mathrm{F}$, which is populated by ${}^{16}\mathrm{O}({}^3\mathrm{He},\mathrm{d}){}^{17}\mathrm{F}$ on oxygen contamination in the target. The insets provide the region around the important $E_x=11826$ keV state with fits to the peaks depicted in red.

Figure 2

Reaction rate ratio for the ${}^{23}\mathrm{Na}(\mathrm{p},\gamma ){}^{24}\mathrm{Mg}$ reaction: shown as a blue shaded region are the present temperature-dependent 1-sigma reaction rate uncertainties (“high” and “low” rates) normalized to the recommended rate. The solid-black line represents the recommended rate from Ref. [17], with grey shaded region corresponding to the associated 1-sigma uncertainty.