Deformation and cluster structures in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mrow/><mml:mn>12</mml:mn></mml:msup></mml:math>C studied with configuration mixing using Skyrme interactions

Abstract

We report an investigation of the structure of the ${}^{12}$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 the ${}^{12}$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, ${1}_{1}^{\ensuremath{-}}$, ${2}_{1}^{\ensuremath{-}}$, and ${3}_{1}^{\ensuremath{-}}$, are also reasonably described. The second and third ${0}^{+}$ states, ${0}_{2}^{+}$ and ${0}_{3}^{+}$, appear at around 8.8 and 15 MeV, respectively. The ${0}_{2}^{+}$ state shows a structure consistent with former results of the $\ensuremath{\alpha}$-cluster models. However, the calculated radius of the ${0}_{2}^{+}$ state is smaller than in those calculations. The three-$\ensuremath{\alpha}$ linear-chain configuration dominates in the ${0}_{3}^{+}$ state.