  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.
