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 \alpha-cluster models, however, the calculated radius of the $0_2^{+}$ state is smaller than those calculations. The three-{\alpha} linear-chain configuration dominates in the $0_3^{+}$ state.

Comments: 15 pages, 13 figures