The differential cross sections of the inelastic scattering leading to the excitation of short-lived states in the stable ${}^{13}$C and ${}^9$Be nuclei as well as the radioactive ${}^{11}$Be nucleus have been analyzed. Signatures of neutron halos in the excited states located close to the neutron emission thresholds have been investigated by applying a recently developed modified diffraction model. The abnormally large rms radius was identified for the 3.089-MeV $1/2^{+}$ state of ${}^{13}$C. Significantly enlarged diffraction radii were found for the 1.68-MeV $1/2^{+}$ and the 3.05-MeV $5/2^{+}$ states of ${}^9$Be. The analysis of the diffraction radii of the weakly bound radioactive ${}^{11}$Be nuclei have shown that the 1.78-MeV $5/2^{+}$ and 3.41-MeV $3/2^{+}$ states in ${}^{11}$Be have the same diffraction radii as the $1/2^{+}$ ground state, which is known as the best example of a state with one-neutron halo.

• Received 9 May 2010

DOI:https://doi.org/10.1103/PhysRevC.84.054601