We study the slow neutron capture process (s-process) in asymptotic giant branch (AGB) stars using three different stellar evolutionary models computed for a 3 M☉, solar metallicity star. First we investigate the formation and the efficiency of the main neutron source: the 13C(α, n)16O reaction that occurs in radiative conditions. A tiny region rich in 13C (the 13C pocket) is created by proton captures on the abundant 12C in the top layers of the He intershell, the zone between the H shell and the He shell. We parametrically vary the number of protons mixed from the envelope. For high local proton-to-12C number ratios, p/12C 0.3, most of the 13C nuclei produced are further converted by proton capture to 14N. Besides, 14N nuclei represent a major neutron poison. We find that a linear relationship exists between the amount of 12C in the He intershell and the maximum value of the time-integrated neutron flux. Then we generate detailed s-process calculations on the basis of stellar evolutionary models constructed with three different codes, all of them self-consistently finding the third dredge-up, although with different efficiency. One of the codes includes a mechanism at each convective boundary that simulates time-dependent hydrodynamic overshoot. This mechanism depends on a free parameter f and results in partial mixing beyond convective boundaries, the most efficient third dredge-up, and the formation of the 13C pocket. For the other two codes, an identical 13C pocket is introduced in the postprocessing nucleosynthesis calculations. The models typically produce enhancements of heavy elements of about 2 orders of magnitude in the He intershell and of up to 1 order of magnitude at the stellar surface, after dilution with the convective envelope, thus generally reproducing spectroscopic observations. The results of the cases without overshoot are remarkably similar, pointing out that the important uncertainty in s-process predictions is the 13C pocket and not the intrinsic differences among different codes when no overshoot mechanism is included. The code including hydrodynamic overshoot at each convective boundary finds that the He intershell convective zone driven by the recurrent thermal instabilities of the He shell (thermal pulses) penetrates the C-O core, producing a He intershell composition near that observed in H-deficient central stars of planetary nebulae. As a result of this intershell dredge-up, the neutron fluxes have a higher efficiency, both during the interpulse periods and within thermal pulses. The s-element distribution is pushed toward the heavier s-process elements, and large abundances of neutron-rich isotopes fed by branching points in the s-process path are produced. Several observational constraints are better matched by the models without overshoot. Our study needs to be extended to different masses and metallicities and in the space of the free overshoot parameter f.
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