¹²C within the Semimicroscopic Algebraic Cluster Model

The Semimicroscopic Algebraic Cluster Model (SACM) is applied to ¹²C as a system of three α clusters. A microscopic model space for the 3α cluster system is used, which observes the Pauli Exclusion Principle (PEP) and is symmetric under permutation of the 3α particles. A phenomenological Hamiltonian is used, justifying the name Semi. The experimental spectrum is well reproduced. The geometrical mapping is discussed and it is shown that the ground state corresponds approximately to a triangular structure, which is consistent with other microscopic calculations. The non-zero B(E2; 0₂⁺ → 2₁⁺) transition requires a mixing of SU(3) irreducible representations (irreps) whose consequences are discussed. The Hoyle state turns out to contain large shell excitations. The results are compared to another phenomenological model, which assumes a triangular structure and, using simple symmetry arguments, can reproduce the states observed up to now at low energy. This model does not observe the PEP and one objective of our contribution is to verify the extent of importance of the PEP. (orig.)