New measurement of the $E_{\mathrm{c.m.}}=323$ keV resonance in the $^{19}$F$($p,\gamma$)$^{20}$Ne reaction

At temperatures below 0.1 GK the $^{19}$F$(p,\gamma)^{20}$Ne reaction is the only breakout path out of the CNO cycle. Experimental studies of this reaction are challenging from a technical perspective due to copious $\gamma$-ray background from the far stronger $^{19}$F$(p,\alpha)^{16}$O reaction channel. Here we present the first inverse kinematics study of the $^{19}$F$(p,\gamma)^{20}$Ne reaction, in which we measure the strength of the 323-keV resonance. We find a strength value of $\omega\gamma = 3.3^{+1.1}_{-0.9}$ meV, which is a factor of two larger than the most recent previous study. The discrepancy is likely the result of a direct to ground state transition which previous studies were not sensitive to. We also observe the transition to the first $2^{-}$ state, which has not been observed for this resonance in previous studies. A new thermonuclear reaction rate is calculated and compared with the literature.