Abstract
A theoretical analysis of available experimental data on elastic and inelastic $$\alpha+^{13}$$ C scattering in the energy region extending up to 90 MeV is performed. The parameters of a semimicroscopic potential are found on the basis of the dispersive optical model. The potentials found in this way are used in analyzing, by the distorted-wave Born approximation, data that the authors recently measured for inelastic scattering at energies of 65 and 90 MeV. Experimental data for the states at 3.68 and 7.55 MeV are presented for the first time. These states are considered under the assumption that, within the standard rotational model, they are members of the ground-state rotational band. A satisfactory description of angular distributions is obtained, and deformation lengths are determined. A model phenomenological form factor is used for the remaining excitations in the energy range extending up to 11 MeV. The present analysis confirms the presence of a neutron halo in the 3.09-MeV state. A similarity of form of the inelastic form factors obtained for the 8.86-, 10.996-, and 11.08 MeV states and the proximity of their radii gives grounds to assume that the $${}^{13}$$ C nucleus in these three states has an enhanced size and similar structures. A comparison of the radial dependences of the form factors for the 9.90- and 8.86-MeV states shows that the wave function for the 9.90-MeV state has a substantially smaller spatial extension. These results agree with the values obtained for the radii of the states under discussion on the basis of the modified diffraction model.