Coherency and Ant-Crossing Low-lying Levels in 12C Nucleus*

The 3-alpha phenomenological model describes the structure of the carbon-12 nucleus as a cluster of three alpha particles. This model incorporates both alpha-alpha interactions and a three-body force. To determine the parameters of the three-body potential, we utilize data from ¹²C, while ensuring that the pair potential accurately reproduces alpha-alpha scattering data.

 Alternatively, the mass-energy compensation (MEC) effect can be employed to approximate the influence of the three-body potential by adjusting the effective mass of the alpha particle. We demonstrate the MEC effect for the 3-alpha ground state by numerically solving the differential Faddeev equation, in which the alpha-alpha interaction is described using the Ali-Bodmer potential. We assess the effective masses of alpha particles for the ground state, as well as the excited 0⁺ and bound 2⁺ states. We observe a coupling (coherency) between the ground and first excited 0⁺ states, as indicated by an anti-crossing of their energy levels in the energy-mass coordinates.