Production of Lithium and Heavy Elements in AGB Stars Experiencing PIEs

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 $1<M_{\rm ini}/M_{\odot}< 3$ and $-3< \mathrm{[Fe/H]} <0$. We find that lithium is produced in all PIE models with surface abundances $3<$ A(Li) $<5$. The surface enrichment and overall AGB lithium yield increases with decreasing stellar mass. The lithium enrichment is accompanied by a production of $^{13}$C with $3<^{12}$C/$^{13}$C$<9$ 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 and $^{13}$C. In addition to Li and $^{13}$C, heavy elements (e.g., Sr, Ba, Eu, Pb) are significantly produced in low-metallicity stars up to [Fe/H]$\simeq-1$. The yields of our models are publicly available. Additionally, of interest to the Li nucleosynthesis, we provide an updated fitting formula for the $^{7}$Be($e^-,\nu_e$)$^{7}$Li electron capture rate.