Breakout from the hot CNO cycle: The18F(p,γ)vs18F(p,α)branching ratio

We have studied the properties of low-lying ${}^{18}\mathrm{F}+p$ resonances as excited states in ${}^{19}\mathrm{Ne}.$ Three new levels have been found in the range $0l~{E}_{\mathrm{c}.\mathrm{m}.}l~1 \mathrm{MeV}$ just above the ${}^{18}\mathrm{F}+p$ threshold, and partial decay widths and isospin-mirror connections are suggested to known states in ${}^{19}\mathrm{F}$ for each of the nine states in this energy range. The properties of these resonances have been used to calculate the reaction rate ${N}_{A}〈\ensuremath{\sigma}v〉$ for the ${}^{18}\mathrm{F}(p,\ensuremath{\gamma}{)}^{19}\mathrm{Ne}$ and ${}^{18}\mathrm{F}(p,\ensuremath{\alpha}{)}^{15}\mathrm{O}$ reactions in the temperature range ${10}^{8}lTl{10}^{9}.$ A comparison of these rates indicates that in this temperature range, the ${}^{14}\mathrm{O}(\ensuremath{\alpha}{,p)}^{17}\mathrm{F}(p,\ensuremath{\gamma}{)}^{18}\mathrm{Ne}{(e}^{+}\ensuremath{\nu}{)}^{18}\mathrm{F}(p,\ensuremath{\gamma}{)}^{19}\mathrm{Ne}$ reaction sequence is not as fast as the ${}^{15}\mathrm{O}(\ensuremath{\alpha},\ensuremath{\gamma}{)}^{19}\mathrm{Ne}$ reaction.