The main component of the s-process accounts for about 50% of elements heavier than Kr, through n-captures occurring in asymptotic giant branch (AGB) stars, where the 13C(α, n)16O reaction is the main neutron source. Its activation below the convective envelope at third dredge-up (TDU) and its efficiency are still matters of debate, as: (i) the astrophysical factor is affected by a broad resonance near the reaction threshold and (ii) mixing mechanisms to locally produce 13C were so far mimicked mainly parametrically. We discuss both problems and, in particular, we adopt one of the recent model proposed for producing 13C and based on an exact multi-D analytical solution of MHD equations, where magnetic buoyancy induces partial mixing at the envelope border. The resulting distribution of 13C is used, together with our upgraded prescription for the reaction rate, to reproduce solar abundances through AGB models. It can account for the chemical evolution of s-elements and for the s/(C/O) ratios in low-metallicity post-AGB stars....
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