The asymptotic normalization coefficients of the bound states $J^{\pi }=(0_1^{+},2_1^{+},4_1^{+},2_2^{+})$ 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 ${}^{17}\text{F}$($p$,$\gamma$)${}^{18}\text{Ne}$. 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 $S_{1-17}\left(0\right)=2.17\pm 0.37$ 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.

• Received 23 August 2013
• Revised 27 January 2014

DOI:https://doi.org/10.1103/PhysRevC.89.025809