  Detection of nuclear-decay $\gamma$ rays provides a sensitive thermometer of
nova nucleosynthesis. The most intense $\gamma$-ray flux is thought to be
annihilation radiation from the $\beta^+$ decay of $^{18}$F, which is destroyed
prior to decay by the $^{18}$F($p$,$\alpha$)$^{15}$O reaction. Estimates of
$^{18}$F production had been uncertain, however, because key near-threshold
levels in the compound nucleus, $^{19}$Ne, had yet to be identified. This
Letter reports the first measurement of the
$^{19}$F($^{3}$He,$t\gamma$)$^{19}$Ne reaction, in which the placement of two
long-sought 3/2$^+$ levels is suggested via triton-$\gamma$-$\gamma$
coincidences. The precise determination of their resonance energies reduces the
upper limit of the rate by a factor of $1.5-17$ at nova temperatures and
reduces the average uncertainty on the nova detection probability by a factor
of 2.1.
