A Si detector telescope, in which alternating thick and thin Si elements served as both targets and detectors, was used to measure the energy dependence of the inclusive one-proton-removal cross sections ${\sigma }_{1p}$ of ${}^8\mathrm{B}$, ${}^9\mathrm{C}$, and ${}^{12}\mathrm{C}$ on a Si target. A similar detector telescope was used to measure both ${\sigma }_{1p}$ and ${\sigma }_{2p}$ for ${}^9\mathrm{C}$; ${\sigma }_{2p}$ of ${}^9\mathrm{C}$ is more than twice as large as ${\sigma }_{1p}$ of ${}^9\mathrm{C}$ and almost as large as ${\sigma }_{1p}$ of ${}^8\mathrm{B}$. The measurements were compared with shell model calculations using eikonal reaction theory. The quenching factors $R_s$ (the ratio of the measurement to the theoretical prediction) for ${}^8\mathrm{B}$ and ${}^9\mathrm{C}$ were near unity, as at higher energies. They also agreed with those measured recently for those nuclei on a C target at $75\text{MeV}∕\text{nucleon}$. For ${}^{12}\mathrm{C}$ the quenching is greater with $R_s=0.44\pm 0.03$. This is comparable to the value $0.53\pm 0.02$ deduced at energies above $1\text{GeV}∕\text{nucleon}$.

• Received 22 May 2003

DOI:https://doi.org/10.1103/PhysRevC.69.024612