The evolution of AGB stars with convective overshoot

The influence of extended convective mixing (overshoot) on asymptotic giant branch stellar evolution is investigated in detail. The extended mixing is treated timedependently, and the efficiency declines exponentially with the geometric distance from the convective boundary. It has been considered at all convective boundaries, including the He-flash convection zone in the intershell region which forms during the thermal pulses. Both the structural and the chemical evolution are affected by the inclusion of overshoot. The main results include a very efficient third dredge-up which leads to the formation of carbon stars of low mass and luminosity. A 13C pocket which may serve as a neutron source for the s-process can form after the third dredge-up has reached into the 12C rich intershell. Overshoot applied to the pulse-driven convective zone during the He-flash leads to a deeper penetration of the bottom of this convective zone into the C/O core below the He-burning shell. This in turn causes 4He to be less abundant in the intershell while 12C and 16O are more abundant compared to calculations without overshoot. We show that overshoot at the He-flash convection zone as well as at the base of the envelope convection enhance the efficiency of the third dredge-up. Characteristic properties of the structural and chemical evolution of AGB stars are presented.