The ${}^{17}\mathrm{O}(p,\alpha ){}^{14}\mathrm{N}$ reaction plays a key role in various astrophysical scenarios, from asymptotic giant branch stars to classical novae. It affects the synthesis of rare isotopes such as ${}^{17}\mathrm{O}$ and ${}^{18}\mathrm{F}$, which can provide constraints on astrophysical models. A new direct determination of the $E_R=64.5\mathrm{keV}$ resonance strength performed at the Laboratory for Underground Nuclear Astrophysics (LUNA) accelerator has led to the most accurate value to date $\omega \gamma =10.0\pm 1.4_{\mathrm{stat}}\pm 0.7_{\mathrm{syst}}\mathrm{neV}$, thanks to a significant background reduction underground and generally improved experimental conditions. The (bare) proton partial width of the corresponding state at $E_x=5672\mathrm{keV}$ in ${}^{18}\mathrm{F}$ is ${\mathrm{\Gamma }}_p=35\pm 5_{\mathrm{stat}}\pm 3_{\mathrm{syst}}\mathrm{neV}$. This width is about a factor of 2 higher than previously estimated, thus leading to a factor of 2 increase in the ${}^{17}\mathrm{O}(p,\alpha ){}^{14}\mathrm{N}$ reaction rate at astrophysical temperatures relevant to shell hydrogen burning in red giant and asymptotic giant branch stars. The new rate implies lower ${}^{17}\mathrm{O}/{}^{16}\mathrm{O}$ ratios, with important implications on the interpretation of astrophysical observables from these stars.

Background: The ${}^{22}\mathrm{Ne}(p,\gamma ){}^{23}\mathrm{Na}$ reaction is the most uncertain process in the neon-sodium cycle of hydrogen burning. At temperatures relevant for nucleosynthesis in asymptotic giant branch stars and classical novae, its uncertainty is mainly due to a large number of predicted but hitherto unobserved resonances at low energy.

We investigate the impact of the new LUNA rate for the nuclear reaction ²²Ne(p, γ)²³Na on the chemical ejecta of intermediate-mass stars, with particular focus on the thermally pulsing asymptotic giant branch (TP-AGB) stars that experience hot-bottom burning. To this aim, we use the PARSEC and COLIBRI codes to compute the complete evolution, from the pre-main sequence up to the termination of the TP-AGB phase, of a set of stellar models with initial masses in the range 3.0–6.0 M_⊙ and metallicities Z_i = 0.0005, 0.006 and 0.014. We find that the new LUNA measures have much reduced the nuclear uncertainties of the ²²Ne and ²³Na AGB ejecta that drop from factors of ≃10 to only a factor of few for the lowest metallicity models. Relying on the most recent estimations for the destruction rate of ²³Na, the uncertainties that still affect the ²²Ne and ²³Na AGB ejecta are mainly dominated by the evolutionary aspects (efficiency of mass-loss, third dredge-up, convection). Finally, we discuss how the LUNA results impact on the hypothesis that invokes massive AGB stars as the main agents of the observed O–Na anticorrelation in Galactic globular clusters. We derive quantitative indications on the efficiencies of key physical processes (mass-loss, third dredge-up, sodium destruction) in order to simultaneously reproduce both the Na-rich, O-poor extreme of the anticorrelation and the observational constraints on the CNO abundance. Results for the corresponding chemical ejecta are made publicly available.