(^{22}\)Ne and \(^{23}\)Na ejecta from intermediate-mass stars: The impact of the new LUNA rate for \(^{22}\)Ne(p,\(\gamma\))\(^{23}\)Na

We investigate the impact of the new LUNA rate for the nuclear reaction \(^{22}\)Ne\((p,\gamma)^{23}\)Na 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 \(3.0\,M_{\odot} - 6.0\,M_{\odot}\), and metallicities \(Z_{\rm i}=0.0005\), \(Z_{\rm i}=0.006\), and \(Z_{\rm i} = 0.014\). We find that the new LUNA measures have much reduced the nuclear uncertainties of the \(^{22}\)Ne and \(^{23}\)Na AGB ejecta, which drop from factors of \(\simeq 10\) to only a factor of few for the lowest metallicity models. Relying on the most recent estimations for the destruction rate of \(^{23}\)Na, the uncertainties that still affect the \(^{22}\)Ne and \(^{23}\)Na AGB ejecta are mainly dominated by 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 anti-correlation 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 anti-correlation, and the observational constraints on the CNO abundance. Results for the corresponding chemical ejecta are made publicly available.