  Asymptotic normalization coefficients (ANCs) for 8Li->7Li+n have been
extracted from the neutron transfer reaction 13C(7Li,8Li)12C at 63 MeV. These
are related to the ANCs in 8B->7Be+p using charge symmetry. We extract ANCs for
8B that 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
7Be(p,gamma)8B reaction to be S_17(0)=17.6+/-1.7 eVb. 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.
