  We present new rates for the 22Ne(alpha, n)25Mg and 22Ne(alpha,gamma)26Mg
reactions, with uncertainties that have been considerably reduced compared to
previous estimates, and we study how these new rates affect the production of
the heavy magnesium isotopes in models of intermediate mass Asymptotic Giant
Branch (AGB) stars of different initial compositions. All the models have deep
third dredge-up, hot bottom burning and mass loss. Calculations have been
performed using the two most commonly used estimates of the 22Ne + alpha rates
as well as the new recommended rates, and with combinations of their upper and
lower limits. The main result of the present study is that with the new rates,
uncertainties on the production of isotopes from Mg to P coming from the 22Ne +
alpha-capture rates have been considerably reduced. We have therefore removed
one of the important sources of uncertainty to effect models of AGB stars. We
have studied the effects of varying the mass-loss rate on nucleosynthesis and
discuss other uncertainties related to the physics employed in the computation
of stellar structure, such as the modeling of convection, the inclusion of a
partial mixing zone and the definition of convective borders. These
uncertainties are found to be much larger than those coming from 22Ne +
alpha-capture rates, when using our new estimates. Much effort is needed to
improve the situation for AGB models.
