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.

Figure 1

Energy level diagram of ${}^{23}\mathrm{Na}$ depicting resonances in the ${}^{22}\mathrm{Ne}+p$ system relevant for different astrophysical scenarios. The three tentative resonances at $E_x=8862$, 8894, and 9000 keV that are unlikely to exist [9] are shown in red.

Figure 2

Angular distributions of the 8664 keV state from the ${}^{22}\mathrm{Ne}({}^3\mathrm{He},d){}^{23}\mathrm{Na}$ reaction at 15 MeV [24]. The FRDWBA calculations are shown by the solid and dotted lines.

Figure 3

(a) Variation of spectroscopic factor ($S$) with single particle ANC ($b$) for the 8664 keV state. (b) Variation of ANC ($C$) with single particle ANC ($b$) for the 8664 keV state.

Figure 4

Variation of ANC ($C$) with binding energy for the 8664 keV state.

Figure 5

(a) Astrophysical $S$ factor and (b) differential $S$ factor at $\theta ={90}^{\circ }$, obtained from the $R$-matrix calculations for the DC $\to$ 8664 keV transition. The red dotted line corresponds to the $S$ factor using the mean ANC of $179.5{\mathrm{fm}}^{-1/2}$ for the 8664 keV state (b.g. represents background poles). The black dashed lines represent the external capture contribution. The bands correspond to the uncertainty in the $S$ factor (see text for details).

Figure 6

Astrophysical $S$ factor of the nonresonant capture in ${}^{22}\mathrm{Ne}(p,\gamma ){}^{23}\mathrm{Na}$ from previous direct measurements [2, 18, 19, 20, 21] and present $R$-matrix calculations. (a) Capture to the ground state in ${}^{23}\mathrm{Na}$. (b) Total $S$ factor (b.g. represents background poles). The black dashed lines represent the external capture contribution. The bands correspond to the uncertainty in the $S$ factor (see text for details).

Figure 7

Reaction rate for the ${}^{22}\mathrm{Ne}(p,\gamma ){}^{23}\mathrm{Na}$ reaction as a function of temperature in GK. (a) Comparison of the individual resonant and nonresonant capture contributions relative to the STARLIB-2013 rate. (b) The total rate from the present work (red) and the measurement by Williams et al. [20] (blue) normalized to the STARLIB-2013 rate. The bands correspond to the uncertainties in the rates and the dotted lines represent the mean rates.