Approximately half of the solar abundances of nuclei heavier than iron are created in the deep layers of asymptotic giant branch (AGB) stars via slow neutron captures (the s process). Freshly made heavy elements such as Zr, Ba and Pb are carried to the stellar surface by recurrent mixing episodes and shed into the interstellar medium via strong stellar winds, thus contributing to the chemical evolution of Galaxies. Neutron sources available for the s process in AGB stars are the 13C(α, n)16O and the 22Ne(α, n)25Mg reactions. The 13C(α, n)16O reaction is activated at temperatures from ≃90 million degrees and is believed to be the main neutron source in AGB stars of masses below ≃4 M⊙. However, it is still much debated by which mechanism enough 13C can be produced in these stars to match the observed s-process enhancements, and the amount of 13C is usually taken as a relatively free parameter in theoretical models. Recently, new constraints on the amount of this neutron source have been produced by two independent approaches: (i) high-precision measurements of the isotopic composition of heavy elements in single presolar silicon carbide (SiC) grains from AGB stars, and (ii) synthesis of stellar populations including the s process and comparison of the results to spectroscopic observations. Both these methods indicate that the range of 13C amount needed to explain the observations at solar metallicity is much smaller (a factor of ≃2) than that believed before (a factor of ≃50). On the other hand, a somewhat lower 13C amount appears to be needed to cover observations at lower metallicities. The 22Ne(α, n)25Mg reaction is instead activated at a temperature around 300 million degrees and is believed to be the main neutron source in stars of mass above ≃4 M⊙. This neutron source produces a high neutron density resulting in a relatively high production of neutron-rich isotopes. The first observations of Zr and Rb in massive AGB stars in our Galaxy are finally producing constraints also on the s process in these environments. We present and discuss the new data, together with related challenges and opportunities.
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