The knockout of protons from ${}^8\mathrm{B}$ and ${}^9\mathrm{C}$ on a carbon target has been studied at average energies of 76 and 78 MeV/nucleon, respectively, with beams from the A1900 fragment separator incident on a stack of silicon detectors. The following cross sections were obtained: ${\sigma }_{-1\mathrm{p}}{(}^8{\overrightarrow{\mathrm{B}}}^7\mathrm{Be})=130\mathrm{}(11)\mathrm{}\mathrm{mb},$ ${\sigma }_{-1\mathrm{p}}{(}^9{\overrightarrow{\mathrm{C}}}^8\mathrm{B})=54\mathrm{}(4)\mathrm{}\mathrm{mb},$ and ${\sigma }_{-2\mathrm{p}}{(}^9{\overrightarrow{\mathrm{C}}}^7\mathrm{Be})=98\mathrm{}(7)\mathrm{}\mathrm{mb}.$ The results are discussed within the framework of an eikonal approach and compared with measurements performed at higher energies. From this analysis, a consistent picture emerges that gives evidence for the validity of the eikonal approach at energies below 100 MeV/nucleon. Knockout reactions at intermediate energy can thus be used to deduce absolute shell occupancies. We find the spectroscopic factors to be reduced by $R_s$ of 0.86(7) and 0.82(6) for ${}^8\mathrm{B}$ and ${}^9\mathrm{C},$ respectively, relative to shell-model predictions. The ${}^9\mathrm{C}$ result provides an accurate measurement of the asymptotic normalization coefficient of $1.27\left(10\right)\mathrm{}{\mathrm{fm}}^{-1}.$ A new technique is reported for determining separately the contributions from stripping and diffractive breakup.

• Received 12 December 2002

DOI:https://doi.org/10.1103/PhysRevC.67.064301