The origin of fluorine is a widely debated issue. Nevertheless, the ^{15}N({alpha},{gamma})^{19}F reaction is a common feature among the various production channels so far proposed. Its reaction rate at relevant temperatures is determined by a number of narrow resonances together with the DC component and the tails of the two broad resonances at E_{c.m.} = 1323 and 1487 keV. Measurement through the direct detection of the 19F recoil ions with the European Recoil separator for Nuclear Astrophysics (ERNA) were performed. The reaction was initiated by a 15N beam impinging onto a 4He windowless gas target. The observed yield of the resonances at Ec.m. = 1323 and 1487 keV is used to determine their widths in the {alpha} and {gamma} channels. We show that a direct measurement of the cross section of the ^{15}N({alpha},{gamma})^{19}F reaction can be successfully obtained with the Recoil Separator ERNA, and the widths {Gamma}_{gamma} and {Gamma}_{alpha} of the two broad resonances have been determined. While a fair agreement is found with earlier determination of the widths of the 1487 keV resonance, a significant difference is found for the 1323 keV resonance {Gamma}_{alpha} . The revision of the widths of the two more relevant broad resonances in the 15N({alpha},{gamma})19F reaction presented in this work is the first step toward a more firm determination of the reaction rate. At present, the residual uncertainty at the temperatures of the ^{19}F stellar nucleosynthesis is dominated by the uncertainties affecting the Direct Capture component and the 364 keV narrow resonance, both so far investigated only through indirect experiments.
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