![]() ![]() We have calculated the 12C spectrum up to excitation energies of about 15 MeV. The second interaction is based on the framework of chiral effective field theory, carried out to next-to-next-to-leading order (N2LO). We call it an SU(4) interaction due to the symmetry with respect to the four nucleonic degrees of freedom. The first is an interaction that is independent of spin and isospin. We present results obtained from nuclear lattice simulations using two different interactions. Furthermore, we determine the full twelve-particle correlations and use a model-independent density projection to determine the intrinsic structure of each nuclear state. The lattice results are in good agreement with experimental data. ![]() We perform unconstrained lattice Monte Carlo simulations using the framework of NLEFT 35, 36, including all possible multi-particle quantum correlations. The second is the inability to measure the detailed spatial correlations required to determine the intrinsic structure of the twelve-particle wave function. The first is the inability to perform calculations that can handle strong multi-particle correlations. There are two main impediments to reaching definitive conclusions about the structure of the low-lying 12C states. Much progress has been made in understanding the spectrum of 12C including the Hoyle state, in theoretical studies using the no-core shell model 16, 17, symmetry-adapted no-core shell model 18, shell model 19, Monte Carlo shell model 20, quantum Monte Carlo simulations (QMC) 21, replica exchange MC (RXMC) 22, antisymmetrized molecular dynamics (AMD) 23, 24, 25, fermion molecular dynamics (FMD) 26, density functional theory 27, 28, 29, Bose-Einstein condensate (BEC) wave functions 30, 31, 32, alpha cluster models (ACM) 26, and nuclear lattice effective field theory (NLEFT) 33, 34. The Hoyle state is a narrow resonance, whose close proximity to the energy threshold for three alpha particles greatly enhances the reaction rate of the triple-alpha process, which is key to the production of carbon in evolved, helium-burning stars 14, 15. The most famous example is the case of the so-called Hoyle state, and its hypothetical rotational band partners. However, the underlying structures of several nuclear states of 12C remain without a consensus of agreement, and answers to such questions would provide deep insights into the emergent correlations relevant to nuclear binding and the panoply of possible structures that may appear in other nuclear systems. The physics of the 12C nucleus is a fascinating subject with a long and fabled history 1, 2, and recent groundbreaking experimental results have provided hints of new states with exotic structures 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13. ![]()
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