Spatial measure of reaction size in proton scattering

Abstract

The microscopic coupled-channel (MCC) calculations for proton + 12C inelastic scattering are performed in the energy range of Ep = 29.95 MeV to 65 MeV. The nuclear interactions for the proton −12C system are constructed from the folding model, which employs the internal wave function of 12C, obtained from the 3α resonating group method (3α RGM), and an effective nucleon-nucleon interaction of the density-dependent Michigan three-range Yukawa (DDM3Y). The MCC calculation with the 3α RGM + DDM3Y nicely reproduces all of the differential cross sections for elastic and inelastic scattering in the angular range of θc.m. = 30° to 120°. We introduce a scattering radius, which characterizes a spatial size of the scattering area, from partial wave decompositions of an angle-integrated cross section. 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. We found that the scattering radii for the inelastic channels with a well developed 3α structure are strongly enhanced in comparison to the scattering radii 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.