Resonant Rate for15O(α,γ)19Ne

We have measured angular distributions for the ${}^{15}\mathrm{N}{(}^6\mathrm{Li},d{)}^{19}$F and ${}^{16}\mathrm{O}{(}^6\mathrm{Li},d{)}^{20}$Ne reactions at a bombarding energy of 22 MeV. Distorted-wave Born-approximation and Hauser-Feshbach calculations were used to analyze the data. Ratios of $\alpha$-transfer cross sections in ${}^{19}\mathrm{F}$ and ${}^{20}$Ne, plus isospin invariance, provide ratios of $\alpha$ widths in ${}^{19}$Ne and ${}^{20}$Ne. Using ${}^{20}$Ne ( $1^{-}$, 5.788 MeV) as a standard allows the determination of the $\alpha$-particle width for the state at 4.033 MeV in ${}^{19}$Ne, and hence the resonant rate for the ${}^{15}$O $(\alpha ,\gamma {)}^{19}$Ne reaction, contributed from the 504 keV, ${\frac{3}{2}}^{+}$ resonance, at temperatures of astrophysical interest.