Structure and rotations of the Hoyle state

The excited state of the 12C nucleus known as the "Hoyle state" constitutes one of the most interesting, difficult and timely challenges in nuclear physics, as it plays a key role in the production of carbon via fusion of three alpha particles in red giant stars. In this letter, we present ab initio lattice calculations which unravel the structure of the Hoyle state, along with evidence for a low-lying spin-2 rotational excitation. For the 12C ground state and the first excited spin-2 state, we find a compact triangular configuration of alpha clusters. For the Hoyle state and the second excited spin-2 state, we find a "bent-arm" or obtuse triangular configuration of alpha clusters. We also calculate the electromagnetic transition rates between the low-lying states of 12C.