Local versus nonlocal $\alpha \alpha$ interactions in $3\alpha$ description of ${}^{12}$C

Abstract

Local $\alpha \alpha$ potentials fail to describe ${}^{12}$C as a $3\alpha$ system. Nonlocal $\alpha \alpha$ potentials that renormalize the energy-dependent kernel of the resonating group method allow interpreting simultaneously the ground state and $0_2^{+}$ resonance of ${}^{12}$C as $3\alpha$ states. A comparison with fully microscopic calculations provides a measure of the importance of three-cluster exchanges in those states.

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