Deformation and cluster structures in ${}^{12}$C studied with configuration mixing using Skyrme interactions

Abstract

We report an investigation of the structure of ${}^{12}$C nucleus employing a newly developed configuration-mixing method. In the three-dimensional coordinate-space representation, we generate a number of Slater determinants with various correlated structures using the imaginary-time algorithm. We then diagonalize a many-body Hamiltonian with the Skyrme interaction in the space spanned by the Slater determinants with parity and angular momentum projections. Our calculation reasonably describes the ground and excited states of ${}^{12}$C nucleus, both for shell-model-like and cluster-like states. The excitation energies and transition strengths of the ground-state rotational band are well reproduced. Negative parity excited states, $1_1^{-}$, $2_1^{-}$, and $3_1^{-}$, are also reasonably described. The second and third $0^{+}$ states, $0_2^{+}$ and $0_3^{+}$, appear at around 8.8 MeV and 15 MeV, respectively. The $0_2^{+}$ state shows a structure consistent with former results of the α-cluster models, however, the calculated radius of the $0_2^{+}$ state is smaller than those calculations. The three-α linear-chain configuration dominates in the $0_3^{+}$ state.

15 pages, 13 figures

References in corpus (4)

• Recent developments in no-core shell-model calculations
• Unambiguous Identification of the Second 2+ State in 12C and the Structure of the Hoyle State
• Benchmarks of the full configuration interaction, Monte Carlo shell model, and no-core full configuration methods
• Configuration mixing calculation for complete low-lying spectra with the mean-field Hamiltonian

Cited by in corpus (21)

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• Local alpha-removal strength in the mean-field approximation
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