Tests of transfer reaction determinations of astrophysicalSfactors

The ${}^{16}\mathrm{O}{(}^3\mathrm{He}{,d)}^{17}\mathrm{F}$ reaction has been used to determine asymptotic normalization coefficients for transitions to the ground and first excited states of ${}^{17}\mathrm{F}.$ The coefficients provide the normalization for the tails of the overlap functions for ${}^{17}{\overrightarrow{\mathrm{F}}}^{16}\mathrm{O}+p$ and allow us to calculate the S factors for ${}^{16}\mathrm{O}(p,\gamma {)}^{17}\mathrm{F}$ at astrophysical energies. The calculated S factors are compared to measurements and found to be in very good agreement. This provides a test of this indirect method to determine astrophysical direct capture rates using transfer reactions. In addition, our results yield $S\left(0\right)\mathrm{}$ for capture to the ground and first excited states in ${}^{17}\mathrm{F},$ without the uncertainty associated with extrapolation from higher energies.