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The origin of fluorine is a longstanding problem in nuclear astrophysics. Itis widely recognized that Asymptotic Giant Branch (AGB) stars are among themost important contributors to the Galactic fluorine production. In general,extant nucleosynthesis models overestimate the fluorine production by AGB starswith respect to observations. In this paper we review the relevant nuclearreaction rates involved in the fluorine production/destruction. We perform thisanalysis on a model with initial mass M=2 M$_\odot$ and Z=0.001. We found thatthe major uncertainties are due to the $^{13}$C($\alpha$,n)$^{16}$O, the$^{19}$F($\alpha$,p)$^{22}$Ne and the $^{14}$N(p,$\gamma$)$^{15}$O reactions. Achange of the corresponding reaction rates within the present experimentaluncertainties implies surface $^{19}$F variations at the AGB tip lower than10\%. For some $\alpha$ capture reactions, however, larger variations in therates of those processes cannot be excluded. Thus, we explore the effects ofthe variation of some $\alpha$ capture rates well beyond the current publisheduncertainties. The largest $^{19}$F variations are obtained by varying the$^{15}$N($\alpha$,$\gamma$)$^{19}$F and the $^{19}$F($\alpha$,p)$^{22}$Nereactions. The analysis of some $\alpha$ capture processes assuming a wideruncertainty range determines $^{19}$F abundances in better agreement withrecent spectroscopic fluorine measurements at low metallicity. In the frameworkof the latter scenario the $^{15}$N($\alpha$,$\gamma$)$^{19}$F and the$^{19}$F($\alpha$,p)$^{22}$Ne reactions show the largest effects on fluorinenucleosynthesis. The presence of poorly known low energy resonances make such ascenario, even if unlikely, possible. We plan to directly measure theseresonances.

Effects of nuclear cross sections on $^{19}$F nucleosynthesis at low metallicities