In light nuclear systems, it is well known that cluster structures appear in excited states. One of characteristic properties in the cluster structures is a prominent extension of the nuclear radius. Typical examples are the Hoyle 02+ state and its rotational excited state, 22+, in 12C, which are considered to have the developed 3alpha cluster structure. The matter radii of these 3alpha states are expected to be enhanced by about 60% in comparison to the radius of the ground state but the direct measurement of the radius of the 3alpha state is completely impossible.
In the present study, we focus on the 3alpha rotational state, 22+, and demonstrate that the evidence of the enhanced radius in the 22+ state can be clearly identified in the differential cross section of the alpha + 12C inelastic scattering. We perform the microscopic coupled-channel (MCC) calculation for the alpha + 12C inelastic scattering. The differential cross sections for the elastic and inelastic scattering are calculated at the incident energy of E/A= 96.5 MeV. The MCC calculations for the alpha scatterings nicely reproduce the differential cross sections of the various exit channels.
From the MCC calculation, we have found that the angular distribution of 22+ is prominently shrunk in comparison to the 21+ distribution. This shrinkage structure can be attributed to the enhanced matter radius in the 22+ state. In the present report, we will discuss the relation of the matter radius and the differential cross section in the 3alpha final channel. Furthermore, we will report the application of our analysis to the hyper nucleus production, such as 13C(K-,pi-)13LambdaC.