Asymptotic normalization coefficients (ANCs) for ${}^8{\overrightarrow{\mathrm{Li}}}^7\mathrm{Li}+n$ have been extracted from the neutron transfer reaction ${}^{13}\mathrm{C}{(}^7\mathrm{Li}{,}^8\mathrm{Li}{)}^{12}\mathrm{C}$ at 63 MeV. These are related to the ANCs in ${}^8{\overrightarrow{\mathrm{B}}}^7\mathrm{Be}+p$ using charge symmetry. We extract ANCs for ${}^8\mathrm{B}$ which are in very good agreement with those inferred from proton transfer and breakup experiments. We have also separated the contributions from the $p_{1/2}$ and $p_{3/2}$ components in the transfer. We find the astrophysical factor for the ${}^7\mathrm{Be}(p,\gamma {)}^8\mathrm{B}$ reaction to be $S_{17}\mathrm{}\left(0\right)=17.6\mathrm{}\pm 1.7\mathrm{eV}\mathrm{}\mathrm{b}.$ This is the first time that the rate of a direct capture reaction of astrophysical interest has been determined through a measurement of the ANCs in the mirror system.

• Received 24 January 2003

DOI:https://doi.org/10.1103/PhysRevC.67.062801