The Hoyle state plays a crucial role in the hydrogen burning of stars heavier than our sun and in the production of carbon and other elements necessary for life. This excited state of the carbon-12 nucleus was postulated by Hoyle [1] as a necessary ingredient for the fusion of three alpha particles to produce carbon at stellar temperatures. Although the Hoyle state was seen experimentally more than a half century ago [2, 3] nuclear theorists have not yet uncovered the nature of this state from first principles. In this letter we report the first ab initio calculation of the low-lying states of carbon-12 using supercomputer lattice simulations and a theoretical framework known as effective field theory. In addition to the ground state and excited spin-2 state, we find a resonance at −85(3) MeV with all of the properties of the Hoyle state and in agreement with the experimentally observed energy. These lattice simulations provide insight into the structure of this unique state and new clues as to the amount of fine-tuning needed in nature for the production of carbon in stars.

The excited state of the 12 C 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 lowlying spin-2 rotational excitation. For the 12 C 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 12 C.PACS numbers: 21.10. Dr, 21.60.De, 26.20.Fj The carbon nucleus 12 C is produced by fusion of three alpha particles in red giant stars. However, without resonant enhancement the triple alpha reaction is too slow to account for the observed abundance of carbon in the Universe. In the early 1950's,Öpik and Salpeter noted independently that the first step of merging two alpha particles is enhanced by the formation of [6], which would imply low-lying rotational excitations of even parity. Other ideas also exist for the structure of the Hoyle state, such as a diffuse trimer of alpha particles [7]. Recently, the spin-2 excitation of the Hoyle state has attracted considerable interest from several experimental groups [8][9][10][11][12].We have recently presented an ab initio lattice calculation of the Hoyle state [13] where the low-lying spectrum of 12 C was explored using the framework of chiral effective field theory and Monte Carlo lattice calculations. However the central question regarding the alpha cluster structure of the Hoyle state remained unsolved, perhaps the greatest remaining challenge in ab initio nuclear theory. In this letter, we announce a major innovation of the lattice method that constructs and tests a wide class of nuclear wave functions explicitly. We present ab initio lattice results that resolve questions about the structure of the Hoyle state and the existence of rotational excitations. We also find evidence for a low-lying spin-2 rotational excitation of the Hoyle state. For the Hoyle state and its spin-2 excitation, we find strong overlap with a "bent-arm" or obtuse triangular configuration of alpha clusters. This is in contrast with the 12 C ground state and the first spin-2 state, where we note strong overlap with a compact triangular configuration of alpha clusters. We also calculate the electromagnetic transition rates among the low-lying even-parity states of 12 C. Our lattice results can be compared with other recent theoretical calculations for the low-lying spectrum of 12 C using the no-core shell model [14,15] and variational calculations using Fermionic Molecular Dynamics [16,17].Chiral effective field theory treats the interactions of protons and neutrons as a systematic expansion in powers of nucleon momenta...

We review recent experimental and theoretical progress in understanding the microscopic details of clustering in light nuclei. We discuss recent experimental results on α-conjugate systems, molecular structures in neutron-rich nuclei, and constraints for ab initio theory. We then examine nuclear clustering in a wide range of theoretical methods, including the resonating group and generator coordinate methods, antisymmetrized molecular dynamics, Tohsaki-Horiuchi-Schuck-Röpke wave function and container model, no-core shell model methods, continuum quantum Monte Carlo, and lattice effective field theory.

We extend Nuclear Lattice Effective Field Theory (NLEFT) to medium-mass nuclei, and present results for the ground states of alpha nuclei from 4 He to 28 Si, calculated up to next-to-next-to-leading order (NNLO) in the EFT expansion. This computational advance is made possible by extrapolations of lattice data using multiple initial and final states. For our soft two-nucleon interaction, we find that the overall contribution from multi-nucleon forces must change sign from attractive to repulsive with increasing nucleon number. This effect is not produced by three-nucleon forces at NNLO, but it can be approximated by an effective four-nucleon interaction. We discuss the convergence of the EFT expansion and the broad significance of our findings for future ab initio calculations.