Evidence of enhanced nuclear radius of the <i>&alpha;</i> halo states via &alpha; + ¹²C inelastic scattering

In light nuclear systems, it is well known that cluster structures appear in excited states. One of characteristic properties in the cluster states is a prominent extension of the nuclear radius. Typical examples are the 0₂⁺ and 2₂⁺ states in ¹²C, which have the developed 3α cluster structure.  The radii of these states are expected to be more enhanced by about 60 % than the radius of the ground state but the direct measurement of their radius is completely impossible.

In the present study, we focus on the 2₂⁺ state and demonstrate that the evidence of the enhanced radius in the 2₂⁺ state can be clearly identified in the differential cross section of the α + ¹²C inelastic scattering. We have performed the microscopic coupled-channel (MCC) calculation for the α + ¹²C inelastic scattering at the incident energy of  E/A= 96.5 MeV.

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 nuclear radius in the 2₂⁺ state. In the present report, we will discuss the relation of the nuclear radius and the differential cross section in the 3α final channel.