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We present post process neutron capture computations for Asymptotic Giant Branch stars of 1.5 to 3 Mo and metallicities -1.3 to 0.1. The reference stellar models are computed with the FRANEC code, using the Schwarzschild's criterion for convection. Motivations for this choice are outlined. We assume that MHD processes induce the penetration of protons below the convective boundary, when the third dredge up occurs. There, the 13C(alpha,n)16O neutron source can subsequently operate, merging its effects with those of the 22Ne(alpha,n)25Mg reaction, activated at the temperature peaks characterizing AGB stages. This work has three main scopes. i) We provide a grid of abundance yields, as produced through our MHD mixing scheme, uniformly sampled in mass and metallicity. From it, we deduce that the solar s process distribution, as well as the abundances in recent stellar populations, can be accounted for, without the need of the extra primary like contributions suggested in the past. ii) We formulate analytical expressions for the mass of the 13C pockets generated, in order to allow easy verification of our findings. iii) We compare our results with observations of evolved stars and with isotopic ratios in presolar SiC grains, also noticing how some flux tubes should survive turbulent disruption, carrying C rich materials into the winds even when the envelope is O rich. This wind phase is approximated through the G component of AGB s processing. We conclude that MHD induced mixing is adequate to drive slow neutron capture phenomena accounting for observations. Our prescriptions should permit its inclusion into current stellar evolutionary codes.