Reevaluation of the ${}_{22}\mathrm{Ne}(p,\gamma ){}_{23}\mathrm{Na}$ reaction rate

The ${}_{22}\mathrm{Ne}(p,\gamma ){}_{23}\mathrm{Na}$ capture reaction is a key step in the Ne-Na cycle of hydrogen burning. The rate of this reaction is critical in classical novae nucleosynthesis and hot bottom burning (HBB) processes in asymptotic giant branch (AGB) stars. Despite its astrophysical importance, significant uncertainty remains in the reaction rate due to several narrow low-energy resonances lying within and near the Gamow window. The present work revisits this reaction by examining the contribution of the 8664 keV subthreshold state and the 8945 keV doublet resonance state of $7/2^{-}$ configuration in ${}_{23}\mathrm{Na}$. Finite range distorted-wave Born approximation (FRDWBA) analysis of existing ${}_{22}\mathrm{Ne}({}_3\mathrm{He},d){}_{23}\mathrm{Na}$ transfer reaction data was carried out to extract the peripheral asymptotic normalization coefficients (ANCs) of the 8664 keV state. The ANC value obtained in the present work is $\approx 25\%$ higher compared to the previous work by Santra et al. [Phys. Rev. C 101, 025802 (2020)]. Systematic $R$-matrix calculations were performed to obtain the nonresonant astrophysical $S$ factor utilizing the enhanced ANC value. The resonance strengths of the 8945 keV doublets were deduced from shell model calculations. The rate calculations are performed by omitting the resonances at $E_x=8862$, 8894, and 9000 keV, which are unlikely to exist as reported by Carrasco-Rojas et al. [Phys. Rev. C 108, 045802 (2023)]. The total reaction rate is found to be $\approx 15–20\%$ higher at temperatures relevant for the HBB processes, compared to the recent rate measured by Williams et al. [Phys. Rev. C 102, 035801 (2020)], and matches their rate at temperatures of interest for classical novae nucleosynthesis.