The intermediate neutron capture process: IV. Impact of nuclear model and parameter uncertainties

We investigate both the systematic and statistical uncertainties associated with theoretical nuclear reaction rates of relevance during the i-process and explore their impact on the i-process elemental production, and subsequently on the surface enrichment, for a low-mass low-metallicity star during the early AGB phase. We use the TALYS reaction code (Koning et al. 2023) to estimate both the model and parameter uncertainties affecting the photon strength function and the nuclear level densities, hence the radiative neutron capture rates. The STAREVOL code (Siess et al. 2006) is used to determine the impact of nuclear uncertainties on the i-process nucleosynthesis in a 1 $M_{\odot}$ [Fe/H] = - 2.5 model star during the proton ingestion event in the early AGB phase. A large nuclear network of 1160 species coherently coupled to the transport processes is solved to follow the i-process nucleosynthesis. We find that the non-correlated parameter uncertainties lead the surface abundances uncertainties of element with $Z\geq 40$ to range between 0.5 and 1.0 dex, with odd-$Z$ elements displaying higher uncertainties. The correlated model uncertainties are of the same order of magnitude, and both model and parameter uncertainties have an important impact on potential observable tracers such as Eu and La. Both the correlated model and uncorrelated parameter uncertainties need to be estimated coherently before being propagated to astrophysical observables through multi-zone stellar evolution models. Many reactions are found to affect the i-process predictions and will require improved nuclear models guided by experimental constraints. Priority should be given to the reactions influencing the observable tracers.