Cluster-shell competition in light nuclei

Abstract

We demonstrate whether the cluster structure dissolves or remains when the shell-model-like model space is introduced in addition to the cluster model space in light nuclei. Although the binding energies of $^{8}\mathrm{Be}$, $^{10}\mathrm{Be}$, and $^{10}\mathrm{B}$ become larger by about 1--2 MeV by adding shell-model-like basis states to the $\ensuremath{\alpha}+\ensuremath{\alpha}+N+N+\ensuremath{\cdots}$ basis states, the $\ensuremath{\alpha}\penalty1000-\hskip0pt\ensuremath{\alpha}$ structure is a dominant configuration of the ground states. However, $\ensuremath{\alpha}$-breaking wave functions strongly mix in $^{12}\mathrm{C}$, and the decrease of the energy from the $3\ensuremath{\alpha}$ configuration by about 6 MeV is a clue to resolving a long-standing problem of the binding energies of $^{12}\mathrm{C}$ and $^{16}\mathrm{O}$. The improved version of antisymmetrized molecular dynamics (AMD), AMD superposition of selected snapshots (AMD triple-S), is used to show the cluster-shell competition of these nuclei.