  We present nucleosynthesis calculations and the resulting 19F stellar yields
for a large set of models with different masses and metallicity. We find that
the production of fluorine depends on the temperature of the convective pulses,
the amount of primary 12C mixed into the envelope by third dredge up and the
extent of the partial mixing zone. Then we perform a detailed analysis of the
reaction rates involved in the production of 19F and the effects of their
uncertainties. We find that the major uncertainties are associated with the
14C(alpha,gamma)18O and the 19F(alpha,p)22Ne reaction rates. For these two
reactions we present new estimates of the rates and their uncertainties. The
importance of the partial mixing zone is reduced when using our estimate for
the 14C(alpha,gamma)18O rate. Taking into account both the uncertainties
related to the partial mixing zone and those related to nuclear reactions, the
highest values of 19F enhancements observed in AGB stars are not matched by the
models. This is a problem that will have to be revised by providing a better
understanding of the formation and nucleosynthesis in the partial mixing zone,
also in relation to reducing the uncertainties of the 14C(alpha,gamma)18O
reaction rate. At the same time the possible effect of Cool Bottom Processing
at the base of the convective envelope should be included in the computation of
AGB nucleosynthesis. This process could in principle help matching the highest
19F abundances observed by decreasing the C/O ratio at the surface of the star,
while leaving the 19F abundance unchanged.
