Astrophysical reaction rate for F17 ( p , γ ) Ne18 from the transfer reaction C13 ( O17 , O18 ) C12

The asymptotic normalization coefficients of the bound states ${J}^{\ensuremath{\pi}}=({0}_{1}^{+},{2}_{1}^{+},{4}_{1}^{+},{2}_{2}^{+})$ in $^{18}\text{O}$ are extracted from the peripheral neutron transfer reaction $^{13}\text{C}$$(^{17}\text{O}$$,^{18}\text{O}$$)^{12}\text{C}$. They are then converted to their mirror states in $^{18}\text{Ne}$, which are further used to evaluate the astrophysical $S$ factor for the proton capture reaction $^{17}\text{F}$($p$,$\ensuremath{\gamma}$)$^{18}\text{Ne}$. The elastic-scattering cross sections have been measured in both incoming and outgoing channels in order to extract the optical potentials needed for distorted-wave-Born-approximation calculations. The $S$ factor is found to be ${S}_{1\ensuremath{-}17}(0)=2.17\ifmmode\pm\else\textpm\fi{}0.37$ keV b. The contribution of the direct capture rate to this reaction is estimated, and its consequences on the production of $^{18}\text{F}$ at stellar energies in ONe novae are discussed.