Breakout from the hot CNO cycle: The<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow/><mml:mrow><mml:mn>18</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mi mathvariant="normal">F</mml:mi><mml:mo>(</mml:mo><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi>γ</mml:mi><mml:mo>)</mml:mo></mml:math>vs<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow/><mml:mrow><mml:mn>18</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mi mathvariant="normal">F</mml:mi><mml:mo>(</mml:mo><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi>α</mml:mi><mml:mo>)</mml:mo></mml:math>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 $0&lt;~{E}_{\mathrm{c}.\mathrm{m}.}&lt;~1 \mathrm{MeV}$ 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 ${10}^{8}&lt;T&lt;{10}^{9}.$ 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.