Hindrance of the excitation of the Hoyle state and the ghost of the 22+ state in 12C

While the Hoyle state (the isoscalar 02+ excitation at 7.65 MeV in 12C) has been observed in almost all the electron and α inelastic scattering experiments, the second 2+ excited state of 12C at Ex≈10 MeV, believed to be an excitation of the Hoyle state, has not been clearly observed in these measurements excepting the high-precision (α,α′)C12 experiments at Eα=240 and 386 MeV. Given the (spin and isospin zero) α-particle as a good probe for the nuclear isoscalar excitations, it remains a puzzle why the peak of the 22+ state could not be clearly identified in the measured (α,α′)C12 spectra. To investigate this effect, we have performed a microscopic folding model analysis of the α+C12 scattering data at 240 and 386 MeV in both the Distorted Wave Born Approximation (DWBA) and coupled-channel (CC) formalism, using the nuclear transition densities given by the antisymmetrized molecular dynamics (AMD) approach and a complex CDM3Y6 density dependent interaction. Although AMD predicts a very weak transition strength for the direct (01+→22+) excitation, our detailed analysis has shown evidence that a weak ghost of the 22+ state could be identified in the 240 MeV (α,α′)C12 data for the 03+ state at 10.3 MeV, when the CC effects by the indirect excitation of the 22+ state are taken into account. Based on the same AMD structure input and preliminary (α,α′)C12 data at 386 MeV, we have estimated relative contributions from the 22+ and 03+ states to the excitation of 12C at Ex≈10 MeV as well as possible contamination by 31− state.