12C within the Semimicroscopic Algebraic Cluster Model

Abstract

The Semimicroscopic Algebraic Cluster Model (SACM) is applied to 12C as a system of three alpha- clusters. The microscopic model space, which observes the Pauli-Exclusion-Principle (PEP), is constructed. It is shown that the 12C nucleus can effectively be treated as a two-cluster system 8Be+alpha. The experimental spectrum is well reproduced. The geometrical mapping is discussed and it is shown that the ground state must correspond to a triangular structure, which is in agreement with other microscopic calculations. The non-zero B(E2; 0_2+ --> 2_1+) 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 at low energy. This model does not observe the PEP and one objective of our contribution is to verify the extend of importance of the PEP.

8 pages, 3 figures, 8 tables

References in corpus (3)

• Evidence for Triangular D_3h Symmetry in 12C
• Hoyle band and $\alpha$ condensation in ${}^{12}\mathrm{C}$
• Monopole excitation of the Hoyle state and linear-chain state in 12C

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• Semi-microscopic construction of multi-$\alpha$ cluster spaces
• Symplectic symmetry approach to clustering in atomic nuclei: The case of ${}^{24}$Mg
• Quantum Phase Transitions within a nuclear cluster model and an effective model of QCD