Local versus nonlocal αα interactions in a 3α description of 12C

Local αα potentials reproducing the αα phase shifts fail to describe 12C as a 3α system. Nonlocal αα potentials that renormalize the energy-dependent kernel of the resonating group method allow interpreting simultaneously the ground state and 02+ resonance of 12C as 3α states. A comparison with fully microscopic calculations provides a measure of the importance of three-cluster exchanges in those states.