The10B(7Be,8B)9BeReaction and the7Be(p,γ)8BSFactor

The ${}^{10}\mathrm{B}{(}^7\mathrm{Be}{,}^8\mathrm{B}{)}^9\mathrm{Be}$ reaction has been studied with an 84 MeV ${}^7\mathrm{Be}$ radioactive beam. The measured cross section determines the asymptotic normalization coefficients for the virtual transitions ${}^7\mathrm{Be}+p\leftrightarrow {}^8\mathrm{B}$. These coefficients specify the amplitude of the tail of the ${}^8\mathrm{B}$ wave function in the two-body channel ${}^7\mathrm{Be}+p$, and may be used to calculate the $S$ factor for the direct capture reaction ${}^7\mathrm{Be}(p,\gamma {)}^8\mathrm{B}$ at solar energies, $S_{17}\left(0\right)$. We find that $S_{17}\left(0\right)=17.8\mathrm{}\pm 2.8\mathrm{eV}\mathrm{b}$.