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Asymptotic giant branch (AGB) stars are a main site of production of nuclei heavier than iron via the s process. In massive (>4 M⊙) AGB stars the operation of the 22 Ne neutron source appears to be confirmed by observations of high Rb enhancements, while the lack of Tc in these stars rules out 13 C as a main source of neutrons. The problem is that the Rb enhancements are not accompanied by Zr enhancements, as expected by s-process models. This discrepancy may be solved via a better understanding of the complex atmospheres of AGB stars. Second- generation stars in globular clusters (GCs), on the other hand, do not show enhancements in any s-process elements, not even Rb. If massive AGB stars are responsible for the composition of these GC stars, they may have evolved differently in GCs than in the field. In AGB stars of lower masses, 13 C is the main source of neutrons and we can potentially constrain the effects of rotation and proton-ingestion episodes using the observed composition of post-AGB stars and of stardust SiC grains. Furthermore, independent asteroseismology observations of the rotational velocities of the cores of red giants and of white dwarves will play a fundamental role in helping us to better constrain the effect of rotation. Observations of carbon-enhanced metal-poor stars enriched in both Ba and Eu may require a neutron flux in-between the s and the r process, while the puzzling increase of Ba as function of the age in open clusters, not accompanied by increase in any other element heavier than iron, require further observational efforts. Finally, stardust SiC provides us high-precision constraints to test nuclear inputs such as neutron-capture cross sections of stable and unstable isotopes and the impact of excited nuclear states in stellar environments

Current hot questions on thesprocess in AGB stars