The intermediate neutron capture process. I. Development of the i-process in low-metallicity low-mass AGB stars

Results from observations report a growing number of metal-poor stars showing an abundance pattern midway between the s- and r-processes. These so-called r/s-stars raise the need for an intermediate neutron capture process (i-process), which is thought to result from the ingestion of protons in a convective helium-burning region, but whose astrophysical site is still largely debated. We investigate whether an i-process during the asymptotic giant branch (AGB) phase of low-metallicity low-mass stars can develop and whether it can explain the abundances of observed r/s-stars. At the beginning of the AGB phase, during the third thermal pulse, the helium driven convection zone is able to penetrate the hydrogen-rich layers. The subsequent proton ingestion leads to a strong neutron burst with neutron densities of $\approx 4.3 \times 10^{14}$ cm$^{-3}$ at the origin of the synthesis of i-process elements. The nuclear energy released by proton burning in the helium-burning convective shell strongly affects the internal structure: the thermal pulse splits and after approximately ten years the upper part of the convection zone merges with the convective envelope. The surface carbon abundance is enhanced by more than 3 dex. This leads to an increase in the opacity, which triggers a strong mass loss and prevents any further thermal pulse. We show that specific isotopic ratios of Ba, Nd, Sm, and Eu can represent good tracers of i-process nucleosynthesis. Finally, an extended comparison with 14 selected r/s-stars show that the observed composition patterns can be well reproduced by our i-process AGB model.