Spectroscopic factors measured in inclusive proton-knockout reactions on8Band9Cat intermediate energies

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: ${\ensuremath{\sigma}}_{\ensuremath{-}1\mathrm{p}}{(}^{8}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{B}}}^{7}\mathrm{Be})=130(11)\mathrm{mb},$ ${\ensuremath{\sigma}}_{\ensuremath{-}1\mathrm{p}}{(}^{9}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{C}}}^{8}\mathrm{B})=54(4)\mathrm{mb},$ and ${\ensuremath{\sigma}}_{\ensuremath{-}2\mathrm{p}}{(}^{9}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{C}}}^{7}\mathrm{Be})=98(7)\mathrm{mb}.$ 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 $1.27(10){\mathrm{fm}}^{\ensuremath{-}1}.$ A new technique is reported for determining separately the contributions from stripping and diffractive breakup.