Spatial measure of reaction size in proton scattering

¹ Department of Pure and Applied Physics, Kansai University, Yamatecho, 3-3-35, Suita, Japan
² Research center for Nuclear Phtsics (RCNP), Osaka University, Mihogaoka 10-1, Suita 567-0047, Japan

^a e-mail: itomk@kansai-u.ac.jp

Published online: 21 June 2016

Abstract

The microscopic coupled-channel (MCC) calculations for proton + ¹²C inelastic scattering are performed in the energy range of E_p = 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 θ_c.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.