Three-$\alpha$ configurations in the $0^{+}$ states of ${}^{12}\mathrm{C}$

Abstract

Geometric configurations of three-$\alpha$ particles in the ground- and first-excited $J^{\pi }=0^{+}$ states of ${}^{12}$C are discussed within two types of $\alpha$-cluster models which treat the Pauli principle differently. Though there are some quantitative differences especially in the internal region of the wave functions, equilateral triangle configurations are dominant in the ground state, while in the first excited $0^{+}$ state isosceles triangle configurations dominate, originating from ${}^8\mathrm{Be}+\alpha$ configurations.

arXiv comment7 pages, 4 figures, contribution to the 8th Asia-Pacific Conference on Few-Body Problems in Physics (APFB2020), 1-5 March 2021, Kanazawa, Japan

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Cited by in corpus (3)

• Angular momentum and parity projected multidimensionally constrained relativistic Hartree-Bogoliubov model
• Binding two and three $\alpha$ particles in cold neutron matter
• Three-$\alpha$ configurations of the second $J^{\pi }=2^{+}$ state in ${}^{12}$C