The 2+ excitation of the Hoyle state

Abstract

To understand why the 2+ excitation of the Hoyle state was so difficult to observe in the direct reaction experiments with the 12C target, a detailed folding model + coupled-channel analysis of the inelastic α+12C scattering at Elab = 240 and 386 MeV has been done using the complex optical potential and inelastic scattering form factor obtained from the double-folding model using the nuclear transition densities predicted by the antisymmetrized molecular dynamics. With the complex strength of the density dependent nucleon-nucleon interaction fixed by the optical model description of the elastic α+12C scattering, the inelastic scattering form factor was fine tuned to the best coupled-channel description of the (α, α′) cross section measured for each excited state of 12C, and the corresponding isoscalar Eλ transition strength has been accurately determined. The present analysis of the (α, α′) data measured in the energy bins around Ex ≈ 10 MeV has unambiguously revealed the E2 transition strength that should be assigned to the 22+ state of 12C. A very weak transition strength B(E2; 01+ → 22+) ≈ 3 e2fm4 has been established, which is smaller than the E2 strength predicted for the transition from the Hoyle state to the 22+ state by at least two orders of magnitude. This is one of the main reasons why the direct excitation of the 22+ state of 12C has been difficult to observe in the experiments.