The second J ^ { \pi } = 2 ^ { + } state of ^ { 12 } C , predicted over fifty years ago as an excitation of the Hoyle state , has been unambiguously identified using the ^ { 12 } C ( \gamma, \alpha _ { 0 } ) ^ { 8 } Be reaction .
The alpha particles produced by the photodisintegration of ^ { 12 } C were detected using an Optical Time Projection Chamber ( O-TPC ) .
Data were collected at beam energies between 9.1 and 10.7 MeV using the intense nearly mono-energetic gamma-ray beams at the HI \gamma S 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 ^ { 12 } C 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 } \rightarrow 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 ^ { 12 } C presents a challenge and constraints for models attempting to reveal the nature of three alpha particle states in ^ { 12 } C .
Specifically it challenges the ab-initio Lattice Effective Field Theory ( L-EFT ) calculations that predict similar r.m.s .
radii for the ground state and the Hoyle state .