We present computations of nucleosynthesis in low-mass red-giant-branch and asymptotic-giant-branch stars of Population I experiencing extended mixing. We adopt the updated version of the FRANEC evolutionary model, a new post-process code for non-convective mixing and the most recent revisions for solar abundances. In this framework, we discuss the effects of recent improvements in relevant reaction rates for proton captures on intermediate-mass nuclei (from carbon to aluminum). For each nucleus we briefly discuss the new choices and their motivations. The calculations are then performed on the basis of a parameterized circulation, where the effects of the new nuclear inputs are best compared to previous works. We find that the new rates (and notably the one for the 14N(p,g)15O reaction) imply considerable modifications in the composition of post-main sequence stars. In particular, the slight temperature changes due to the reduced efficiency of proton captures on 14N induce abundance variations at the first dredge up (especially for 17O, whose equilibrium ratio to 16O is very sensitive to the temperature). In this new scenario presolar oxide grains of AGB origin turn out to be produced almost exclusively by very-low mass stars (M<=1.5-1.7Msun), never becoming C-rich. The whole population of grains with 18O/16O below 0.0015 (the limit permitted by first dredge up) is now explained. Also, there is now no forbidden area for very low values of 17O/16O (below 0.0005), contrary to previous findings. A rather shallow type of transport seems to be sufficient for the CNO changes in RGB stages. Both thermohaline diffusion and magnetic-buoyancy-induced mixing might provide a suitable physical mechanism for this. Thermohaline mixing is in any case certainly inadequate to account for the production of 26Al on the AGB. Other transport mechanisms must therefore be at play.

The available information on isotopic abundances in the atmospheres of low-mass Red Giant Branch (RGB) and Asymptotic Giant Branch (AGB) stars requires that episodes of extensive mixing occur below the convective envelope, reaching down to layers close to the hydrogen burning shell (Cool Bottom Processing). Recently \cite{Busso:2007jw} suggested that dynamo-produced buoyant magnetic flux tubes could provide the necessary physical mechanisms and also supply sufficient transport rates. Here, we present an $\alpha-\Omega$ dynamo in the envelope of an RGB/AGB star in which shear and rotation drain via turbulent dissipation and Poynting flux. In this context, if the dynamo is to sustain throughout either phase, convection must resupply shear. Under this condition, volume-averaged, peak toroidal field strengths of $\simeq3\times10^3$ G (RGB) and $\simeq5\times10^3$ G (AGB) are possible at the base of the convection zone. If the magnetic fields are concentrated in flux tubes, the corresponding field strengths are comparable to those required by Cool Bottom Processing.Comment: Replaced to correct small error in published version: In \S 2.1, paragraphs 2 and 3 incorrectly refer to the poloidal field when qualitatively discussing magnetic diffusion in the shear zone. The correct physical interpretation is that the toroidal field diffuses through the shear zone consistent with the value of $\beta_\phi

Recent spectroscopic measurements in open clusters younger than the Sun with [Fe/H] 0 showed that the abundances of neutron-rich elements have continued to increase in the Galaxy after the formation of the Sun, roughly maintaining a solar-like distribution. This growth requires neutron fluences larger than those so far assumed, as these would have too few neutrons per iron seed. We suggest that the observed enhancements can be produced by nucleosynthesis in asymptotic giant branch (AGB) stars of low mass (M < 1.5 M _☉) if they release neutrons from the ¹³C(α,n)¹⁶O reaction in reservoirs larger by a factor of four than assumed in more massive AGB stars (M > 1.5 M _☉). Adopting such a stronger neutron source as a contributor to the abundances at the time of formation of the Sun, we show that this also affects the solar s-process distribution, so that its main component is well reproduced, without the need to assume ad hoc primary sources for the synthesis of s elements up to A ~ 130, contrary to suggestions from other works. The changes in the expected abundances that we find are primarily due to the following reasons. (1) Enhancing the neutron source increases the efficiency of the s process, so that the ensuing stellar yields now mimic the solar distribution at a metallicity higher than before ([Fe/H ] –0.1). (2) The age-metallicity relation is rather flat for several Gyr in that metallicity regime, so that those conditions remain stable and the enhanced nuclear yields, which are necessary to maintain a solar-like abundance pattern, can dominate the composition of the interstellar medium from which subsequent stars are formed.

Background: The competing ${}^{22}\mathrm{Ne}(\alpha ,\gamma ){}^{26}\mathrm{Mg}$ and ${}^{22}\mathrm{Ne}(\alpha ,n){}^{25}\mathrm{Mg}$ reactions control the production of neutrons for the weak $s$ process in massive and asymptotic giant branch (AGB) stars. In both systems, the ratio between the corresponding reaction rates strongly impacts the total neutron budget and strongly influences the final nucleosynthesis. A number of experimental studies have been performed over recent years which necessitate the reevaluation of the ${}^{22}\mathrm{Ne}(\alpha ,\gamma ){}^{26}\mathrm{Mg}$ and ${}^{22}\mathrm{Ne}(\alpha ,n){}^{25}\mathrm{Mg}$ reaction rates. Evaluations of the reaction rates following the collection of new nuclear data presently show differences of up to a factor of 500, resulting in considerable uncertainty in the resulting nucleosynthesis.