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 13 C(α,n) 16 O 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 13 C were so far mimicked mainly parametrically. We discuss both problems and, in particular, we adopt one of the recent model proposed for producing 13 C 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 13 C 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.