Article révisé par les pairs
Résumé : Asymptotic giant branch (AGB) stars can experience proton ingestion events (PIEs), leading to a rich nucleosynthesis. During a PIE, the intermediate neutron capture process (i-process) develops, leading to the production of trans-iron elements. It is also suggested that lithium is produced during these events. We investigate the production of lithium and trans-iron elements in AGB stars experiencing a PIE with (Formula presented.) and (Formula presented.). We find that lithium is produced in all PIE models with surface abundances (Formula presented.) A(Li) (Formula presented.). The surface enrichment and overall AGB lithium yield increases with decreasing stellar mass. The lithium enrichment is accompanied by a production of 13C with (Formula presented.) C/13C (Formula presented.) at the surface just after the PIE. AGB stars experiencing PIE may be related to J-type carbon stars whose main features are excesses of lithium and13C. In addition to Li and 13C, heavy elements (e.g., Sr, Ba, Eu, Pb) are significantly produced in low-metallicity stars up to [Fe/H] (Formula presented.). The yields of our models are publicly available. Additionally, of interest to the Li nucleosynthesis, we provide an updated fitting formula for the 7Be((Formula presented.))7Li electron capture rate.