3-body cluster gas structures in the excited $0^{+}$ states of $N=6$ nuclei

Abstract

We investigate the cluster structure of $\hat{I}\pm +{}^{2}n+{}^{2}n$ in ${}^8\mathrm{He}(0_2^{+})$ and compare it with those of $2\hat{I}\pm +{}^{2}n$ in ${}^{10}\mathrm{Be}(0_2^{+})$ and $3\hat{I}\pm$ in ${}^{12}\mathrm{C}(0_2^{+})$ to understand the emergence mechanism of the 3-body cluster gas states. We apply an extended cluster model combined with cluster breaking components in a microscopic framework using effective nuclear forces based on nucleon degrees of freedom including the antisymmetrization between nucleons. In detailed analysis of the 3-body cluster structures of excited $0^{+}$ states, it is shown that ${}^8\mathrm{He}(0_2^{+})$ exhibits 3-body cluster gas feature of $\hat{I}\pm +{}^{2}n+{}^{2}n$ similar to ${}^{12}\mathrm{C}$ but contains significant mixing of a 2-body-like $(\hat{I}\pm +{}^{2}n)+{}^{2}n$ component. We discuss cluster structures of ${}^8\mathrm{He}(0_2^{+})$ and ${}^{12}\mathrm{C}(0_2^{+})$ from the point of view of inter-cluster energies of ${}^{2}n\text{-}{}^{2}n$ and $\hat{I}\pm \text{-}{}^{2}n$ in comparison with the $\hat{I}\pm \text{-}\hat{I}\pm$ energies and find that the origin for the 2-body-like $(\hat{I}\pm +{}^{2}n)+{}^{2}n$ mixing is the unbalance of the $\hat{I}\pm \text{-}{}^{2}n$ and ${}^{2}n\text{-}{}^{2}n$ energies, in which Pauli effects play an essential role through the kinetic energy loss and internal potential energy loss of clusters. We clarify the emergence mechanism of the 3-body cluster gas state in excited $0^{+}$ states of ${}^8\mathrm{He}$ and ${}^{12}\mathrm{C}$ systems. The balance of inter-cluster interactions is essential for the appearance of 3-body cluster gas states. Microscopic effects, i.e., the Pauli effects of nucleons between clusters play a crucial role in cluster structures of excited $0^{+}$ states.

18 pages, 14 figures