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The $s$-process nucleosynthesis in Asymptotic Giant Branch (AGB) starsdepends on the modeling of convective boundaries. We present models ands-process simulations that adopt a treatment of convective boundaries based onthe results of hydrodynamic simulations and on the theory of mixing due togravity waves in the vicinity of convective boundaries. Hydrodynamicssimulations suggest the presence of convective boundary mixing (CBM) at thebottom of the thermal pulse-driven convective zone. Similarly,convection-induced mixing processes are proposed for the mixing below theconvective envelope during third dredge-up where the 13C pocket for the sprocess in AGB stars forms. In this work we apply a CBM model motivated bysimulations and theory to models with initial mass $M = 2$ and $M = 3M_\odot$,and with initial metal content Z = 0.01 and Z = 0.02. As reported previously,the He-intershell abundance of 12C and 16O are increased by CBM at the bottomof pulse-driven convection zone. This mixing is affecting the$^{22}Ne(\alpha,n)^{25}Mg$ activation and the s-process effciency in the13C-pocket. In our model CBM at the bottom of the convective envelope duringthe third dredgeup represents gravity wave mixing. We take further into accountthat hydrodynamic simulations indicate a declining mixing efficiency alreadyabout a pressure scale height from the convective boundaries, compared tomixing-length theory. We obtain the formation of the 13C-pocket with a mass of$\approx 10^{-4}M_\odot$. The final $s$-process abundances are characterized by0.36 < [s=Fe] < 0.78 and the heavy-to-light s-process ratio is 0.23 < [hs=ls] <0.45. Finally, we compare our results with stellar observations, pre-solargrain measurements and previous work.

Application of a Theory and Simulation based Convective Boundary Mixing model for AGB Star Evolution and Nucleosynthesis