Low mass AGB Stars are the main contributors to the Galactic s-process enrichment. We present new theoretical results obtained by adopting a full network from H to Bi coupled with the physical evolution of the stellar structure. We describe the formation of a 13C pocket as a consequence of H diffusion from the envelope into the He-rich intershell. Such 13C is burnt during the interpulse phase and provides the main neutron source in these stars. We computed two models with the same total mass (that is 2 M[odot ]) but two different initial chemical composition, namely (Y=0.269 – Z=0.015) and (Y=0.245 – Z=0.0001), representative of disk and halo stars respectively. We evaluate the differences in the final s-process surface composition and compare the results with the available observational data.