Title: Structure and geometry of 12C from a Wigner SU(4) symmetric interaction
The carbon-12 nucleus, one of the most crucial elements for life, is full of interesting structures and multifaceted complexity. One famous example is the first excited 0+ state, the so called Hoyle state. It can not be described by most of the ab initio calculations. Moreover, a lack of model-independent description for the shape also hinders an understanding of its geometric properties. Here we present calculations of 12C by nuclear lattice effective field theory using a simple nucleon–nucleon interaction that is independent of spin and isospin and therefore invariant under Wigner’s SU(4) symmetry. Despite the simplicity of the interaction, the agreement with experiment is impressive, not only for all the low-lying levels including the Hoyle state, but also properties such as the charge radius, density profiles, and BE2 transitions. Furthermore, we provide the first model-independent tomographic scan of the three-dimensional geometry for those nuclear states, which show many interesting shapes and features.