A large sample of carbon enhanced metal-poor stars enriched in s-process elements (CEMP-s) have been observed in the Galactic halo. These stars of low mass (M ~ 0.9 Msun) are located on the main-sequence or the red giant phase, and do not undergo third dredge-up (TDU) episodes. The s-process enhancement is most plausibly due to accretion in a binary system from a more massive companion when on the asymptotic giant branch (AGB) phase (now a white dwarf). In order to interpret the spectroscopic observations, updated AGB models are needed to follow in detail the s-process nucleosynthesis. We present nucleosynthesis calculations based on AGB stellar models obtained with FRANEC (Frascati Raphson-Newton Evolutionary Code) for low initial stellar masses and low metallicities. For a given metallicity, a wide spread in the abundances of the s-process elements is obtained by varying the amount of 13C and its profile in the pocket, where the 13C(a, n)16O reaction is the major neutron source, releasing neutrons in radiative conditions during the interpulse phase. We account also for the second neutron source 22Ne(a, n)25Mg, partially activated during convective thermal pulses. We discuss the surface abundance of elements from carbon to bismuth, for AGB models of initial masses M = 1.3 -- 2 Msun, low metallicities ([Fe/H] from -1 down to -3.6) and for different 13C-pockets efficiencies. In particular we analyse the relative behaviour of the three s-process peaks: light-s (ls at magic neutron number N = 50), heavy-s (hs at N = 82) and lead (N = 126). Two s-process indicators, [hs/ls] and [Pb/hs], are needed in order to characterise the s-process distribution. In the online material, we provide a set of data tables with surface predictions. ...
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