Spatial measure of reaction size in proton scattering

We introduce a scattering radius, which characterizes a spatial size of the scattering area, from partial wave decompositions of a cross section for a nucleon-nucleus scattering. The coupled-channel calculations of the p + ¹²C scattering are performed in the range of E_lab = 29.95 MeV to 65 MeV, and the scattering radii for the elastic scattering and the various inelastic channels, which involve the rotational or vibrational excitations and the 3α excitations in ¹²C, are derived from the partial wave decomposition. We found that the scattering radii for the inelastic channels with a well developed 3 a structure are strongly enhanced in comparison to the scattering radius for the elastic and collective channels. This enhancement of the scattering radius for the 3α channel strongly suggests that the scattering radius is sensitive to a size of the intrinsic structure of the finally excited state in the scattering process