The second $J^{\pi }=2^{+}$ state of ${}^{12}\mathrm{C}$, predicted over 50 years ago as an excitation of the Hoyle state, has been unambiguously identified using the ${}^{12}\mathrm{C}(\gamma ,{\alpha }_0){}^8\mathrm{Be}$ reaction. The alpha particles produced by the photodisintegration of ${}^{12}\mathrm{C}$ 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 $\mathrm{HI}\gamma \mathrm{S}$ facility. The measured angular distributions determine the cross section and the $E1\mathrm{\text{−}}E2$ relative phases as a function of energy leading to an unambiguous identification of the second $2^{+}$ state in ${}^{12}\mathrm{C}$ at 10.03(11) MeV, with a total width of 800(130) keV and a ground state gamma-decay width of 60(10) meV; $B(E2:2_2^{+}\to 0_1^{+})=0.73(13)e^2{\mathrm{fm}}^4$ [or 0.45(8) W.u.]. The Hoyle state and its rotational $2^{+}$ state that are more extended than the ground state of ${}^{12}\mathrm{C}$ presents a challenge and constraints for models attempting to reveal the nature of three alpha-particle states in ${}^{12}\mathrm{C}$. Specifically, it challenges the ab initio lattice effective field theory calculations that predict similar rms radii for the ground state and the Hoyle state.

• Received 25 January 2013

DOI:https://doi.org/10.1103/PhysRevLett.110.152502