To probe the ground state and transition densities, elastic and inelastic scattering on a proton target were measured in inverse kinematics for the unstable ${}^{10}\mathrm{C}$ and ${}^{11}\mathrm{C}$ nuclei at 45.3 and 40.6 MeV/nucleon, respectively. The detection of the recoil proton was performed by the MUST telescope array, in coincidence with a wall of scintillators for the quasiprojectile. The differential cross sections for elastic and inelastic scattering to the first excited states are compared to the optical model calculations performed within the framework of the microscopic nucleon-nucleus Jeukenne-Lejeune-Mahaux potential. Elastic scattering is sensitive to the matter-root-mean square radius found to be $2.42\pm 0.1$ and $2.33\pm 0.1$ fm, for ${}^{10,11}\mathrm{C}$, respectively. The transition densities from cluster and mean-field models are tested, and the cluster model predicts the correct order of magnitude of cross sections for the transitions of both isotopes. Using the Bohr-Mottelson prescription, a profile for the ${}^{10}\mathrm{C}$ transition density from the $0^{+}$ ground to the $2_1^{+}$ state is deduced from the data. The corresponding neutron transition matrix element is extracted: $M_n=5.51\pm 1.09$ fm${}^2$.

• Received 15 March 2005

DOI:https://doi.org/10.1103/PhysRevC.72.014308