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Convective-reactive proton-C12 combustion in Sakurai's object (V4334 Sagittarii) and implications for the evolution and yields from the first generations of stars

Depending on mass and metallicity as well as evolutionary phase, stars occasionally experience convective-reactive nucleosynthesis episodes. We specifically investigate the situation when nucleosynthetically unprocessed, H-rich material is convectively mixed with a He-burning zone, for example in convectively unstable shell on top of electron-degenerate cores in AGB stars, young white dwarfs or X-ray bursting neutron stars. Such episodes are frequently encountered in stellar evolution models of stars of extremely low or zero metal content [...] We focus on the convective-reactive episode in the very-late thermal pulse star Sakurai's object (V4334 Sagittarii). Asplund etal. (1999) determined the abundances of 28 elements, many of which are highly non-solar, ranging from H, He and Li all the way to Ba and La, plus the C isotopic ratio. Our simulations show that the mixing evolution according to standard, one-dimensional stellar evolution models implies neutron densities in the He that are too low to obtain a significant neutron capture nucleosynthesis on the heavy elements. We have carried out 3D hydrodynamic He-shell flash convection [...] we assume that the ingestion process of H into the He-shell convection zone leads only after some delay time to a sufficient entropy barrier that splits the convection zone [...] we obtain significantly higher neutron densities (~few 10^15 1/cm^3) and reproduce the key observed abundance trends found in Sakurai's object. These include an overproduction of Rb, Sr and Y by about 2 orders of magnitude higher than the overproduction of Ba and La. Such a peculiar nucleosynthesis signature is impossible to obtain with the mixing predictions in our one-dimensional stellar evolution models. [...] We determine how our results depend on uncertainties of nuclear reaction rates, for example for the C13(α, n)O16 reaction.