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Quadrupole Deformation $β$ and $γ$ Constraint in a Framework of Antisymmetrized Molecular Dynamics

We propose a new method of the $β$-$γ$ constraint for quadrupole deformation in antisymmetrized molecular dynamics (AMD) to describe various cluster and shell-model structures in the ground and excited states of light nuclei. We apply this method to N=6 isotones, $^{10}$Be, $^{12}$C, $^{9}$Li, and $^{11}$B, and find various structures as functions of the deformation parameters, $β$ and $γ$. In these nuclei, shell-model-like structures appear in the small $β$ region, while cluster structures develop well in the large $β$ region where various geometric configurations of clusters are obtained depending on the $γ$ parameter. For $^{10}$Be and $^{12}$C, we superpose the basis AMD wave functions obtained by the $β$-$γ$ constraint method to calculate energy spectra, and prove the advantages of the present method of the two-dimensional $β$-$γ$ constraint in the framework of AMD.