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

Context. The observed surface abundance distributions of carbon-enhanced metal-poor (CEMP) r/s stars suggest that these stars could have been polluted by an intermediate neutron capture process (the so-called i-process) occurring at intermediate neutron densities between the r- and s-processes. Triggered by the ingestion of protons inside a convective He-burning zone, the i-process could be hosted in several sites, a promising one being the early AGB phase of low-mass, low-metallicity stars. The i-process remains affected however by many uncertainties, including those of nuclear origin, since it involves hundreds of nuclei for which reaction rates have not yet been determined experimentally. Aims. 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, of a low-mass, low-metallicity star during the early AGB phase. Methods. We used the TALYS reaction code to estimate both the model and parameter uncertainties affecting the photon strength function and the nuclear level densities, and hence the radiative neutron capture rates. The impact of correlated systematic uncertainties was estimated by considering different nuclear models, as was detailed in Paper II. In contrast, the uncorrelated uncertainties associated with local variation in model parameters were estimated using a variant of the backward-forward Monte Carlo method to constrain the parameter changes to experimentally known cross sections before propagating them consistently to the neutron capture rates. The STAREVOL code (Siess 2006, A&A, 448, 717) was used to determine the impact of nuclear uncertainties on the i-process nucleosynthesis in a 1 M-Theta [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 was solved to follow the i-process nucleosynthesis. Results. We find that the uncorrelated parameter uncertainties lead the surface abundance uncertainties of elements with Z >= 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. We find around 125 important (n, gamma) reactions impacting the surface abundances, including 28 reactions that have a medium to high impact on the surface abundance of elements that are taken as observable tracers of i-process nucleosynthesis in CEMP stars. Conclusions. 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.