Charge-changing cross sections ${\sigma }_{\mathrm{cc}}$ of stable and unstable nuclei (${}^{9–11}\mathrm{Be}$, ${}^{14–16}\mathrm{C}$, and ${}^{16–18}\mathrm{O}$) on a carbon target were investigated at $300\mathrm{MeV}/\mathrm{nucleon}$. A phenomenological analysis based on the Glauber theory indicates an approximate, but universal, scaling of ${\sigma }_{\mathrm{cc}}$ over a wide range of $A/Z$. This allows the determination of the density distributions of protons tightly bound in the nuclei. An application to ${}^{16}\mathrm{C}$, which is considered to be an anomalously deformed nucleus, indicates a systematic evolution of proton root-mean-square radii and has revealed for the first time a neutron skin effect in carbon isotopes. Being complementary to isotope-shift and electron-scattering experiments, the present method can open up a new approach to explore the structure of exotic nuclei.

• Received 5 April 2011

DOI:https://doi.org/10.1103/PhysRevLett.107.032502