Unambiguous identification of the second 2+ state in 12C and the structure of the Hoyle state.

The second J(π)=2+ state of 12C, predicted over 50 years ago as an excitation of the Hoyle state, has been unambiguously identified using the 12C(γ,α0)(8)Be reaction. The alpha particles produced by the photodisintegration of 12C were detected using an optical time projection chamber. Data were collected at beam energies between 9.1 and 10.7 MeV using the intense nearly monoenergetic gamma-ray beams at the HIγS facility. The measured angular distributions determine the cross section and the E1-E2 relative phases as a function of energy leading to an unambiguous identification of the second 2+ state in 12C at 10.03(11) MeV, with a total width of 800(130) keV and a ground state gamma-decay width of 60(10) meV; B(E2:2(2)+→0(1)+)=0.73(13)e(2)  fm(4) [or 0.45(8) W.u.]. The Hoyle state and its rotational 2+ state that are more extended than the ground state of 12C presents a challenge and constraints for models attempting to reveal the nature of three alpha-particle states in 12C. Specifically, it challenges the ab initio lattice effective field theory calculations that predict similar rms radii for the ground state and the Hoyle state.