We have performed a direct measurement of the ^{19}Ne(p,γ)^{20}Na reaction in inverse kinematics using a beam of radioactive ^{19}Ne. The key astrophysical resonance in the ^{19}Ne+p system has been definitely measured for the first time at E_{c.m.}=456_{-2}^{+5} keV with an associated strength of 17_{-5}^{+7} meV. The present results are in agreement with resonance strength upper limits set by previous direct measurements, as well as resonance energies inferred from precision (^{3}He, t) charge exchange reactions. However, both the energy and strength of the 456 keV resonance disagree with a recent indirect study of the ^{19}Ne(d, n)^{20}Na reaction. In particular, the new ^{19}Ne(p,γ)^{20}Na reaction rate is found to be factors of ∼8 and ∼5 lower than the most recent evaluation over the temperature range of oxygen-neon novae and astrophysical x-ray bursts, respectively. Nevertheless, we find that the ^{19}Ne(p,γ)^{20}Na reaction is likely to proceed fast enough to significantly reduce the flux of ^{19}F in nova ejecta and does not create a bottleneck in the breakout from the hot CNO cycles into the rp process.
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