Tetrahedral $4\alpha$ and ${}^{12}\text{C}+\alpha$ cluster structures in ${}^{16}$O

Abstract

We have investigated structures of the ground and excited states of ${}^{16}\text{O}$ with the method of variation after spin-parity projection in the antisymmetrized molecular dynamics model combined with the generator coordinate method of ${}^{12}\text{C}+\alpha$ cluster. The calculation reasonably reproduces the experimental energy spectra, $E2$, $E3$, $E4$, $IS1$ transitions, and $\alpha$-decay properties. The formation of 4 $\alpha$ clusters has been confirmed from nucleon degrees of freedom in the AMD model without assuming existence of any clusters. They form "tetrahedral" $4\alpha$- and ${}^{12}\text{C}+\alpha$-cluster structures. The ${}^{12}\text{C}+\alpha$ structure constructs the $K^{\pi }=0^{+}$ band consisting of the $0_2^{+}$, $2_1^{+}$, and $4_1^{+}$ states and the $K^{\pi }=0^{-}$ band of the $1_2^{-}$, $3_2^{-}$, and $5_1^{-}$ states. The $0_1^{+}$, $3_1^{-}$, and $4_2^{+}$ states are assigned to the ground band constructed from the tetrahedral 4$\alpha$ structure. The $0_1^{+}$ and $3_1^{-}$ are approximately interpreted as $T_d$ band members with the ideal tetrahedral configuration. The ground state $4\alpha$ correlation plays an important role in enhancement of the $E3$ transition strength to the $3_1^{-}$. The $4_2^{+}$ state is not the ideal $T_d$ member but constructed from a distorted tetrahedral $4\alpha$ structure. Moreover, significant state mixing of the tetrahedral $4\alpha$ and ${}^{12}\text{C}+\alpha$ cluster structures occurs between $4_1^{+}$ and $4_2^{+}$ states, indicating that the $T_d$ configuration of $4\alpha$ is rather fragile at $J^{\pi }=4^{+}$.

arXiv comment12 pages, 7 figures

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• Direct and indirect $\alpha$ transfer in the elastic ${}^{16}$O+${}^{12}$C scattering
• Investigation of spatial manifestation of $\alpha$ clusters in ${}^{16}$O via $\alpha$-transfer reactions
• Properties of $K^{\pi }=0_1^{+}$, $K^{\pi }=2^{-}$, and $K^{\pi }=0_1^{-}$ bands of ${}^{20}$Ne probed via proton and alpha inelastic scattering
• Microscopic calculation of inelastic proton scattering off ${}^{18}$O, ${}^{10}$Be, ${}^{12}$Be, and ${}^{16}$C for study of neutron excitation in neutron-rich nuclei
• First microscopic coupled-channel calculation of $\alpha$ inelastic cross sections on ${}^{16}$O
• 16O within the Semimicroscopic Algebraic Cluster Model and the importance of the Pauli Exclusion Principle
• Low-energy dipole excitation mode in ${}^{18}$O with antisymmetrized molecular dynamics
• Low-energy dipole excitations in ${}^{20}$O with antisymmetrized molecular dynamics