We have used existing data on the one-proton-removal cross section of ${}^9\mathrm{C}$ at 285 MeV/nucleon and Glauber model calculations to extract the asymptotic normalization coefficient for the wave function of the last proton in the ground state of ${}^9\mathrm{C}.$ The calculations are done first using folded potentials starting from two different effective nucleon-nucleon interactions and second in the optical limit using three nucleon-nucleon interactions, and the results are found to be consistent, with no new parameters adjusted. We find $C^2{(p}_{3/2}{)+C}^2{(p}_{1/2})=1.22\mathrm{}\pm 0.13{\mathrm{fm}}^{-1}.$ From this result we obtain the astrophysical factor for the proton radiative capture reaction ${}^8\mathrm{B}(p,\gamma {)}^9\mathrm{C}$ as $S_{18}\mathrm{}\left(0\right)=46\mathrm{}\pm 6\mathrm{eV}\mathrm{b}.$ The calculated energy dependence of the astrophysical S factor for the energy region $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=0\mathrm{}-0.8\mathrm{MeV}$ and the reaction rates for $T_9=0\mathrm{}-1$ are included.

• Received 13 June 2002

DOI:https://doi.org/10.1103/PhysRevC.66.035801