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

Abstract: We have investigated structures of the ground and excited states of $<sup>{16}\textrm{O}$ with the method of variation after spin-parity projection in the antisymmetrized molecular dynamics model combined with the generator coordinate method of $<sup>{12}\textrm{C}+\alpha$ 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 $<sup>{12}\textrm{C}+\alpha$-cluster structures. The $<sup>{12}\textrm{C}+\alpha$ structure constructs the $K<sup>\pi=0<sup>+$ band consisting of the $0<sup>+_2$, $2<sup>+_1$, and $4<sup>+_1$ states and the $K<sup>\pi=0<sup>-$ band of the $1<sup>-_2$, $3<sup>-_2$, and $5<sup>-_1$ states. The $0<sup>+_1$, $3<sup>-_1$, and $4<sup>+_2$ states are assigned to the ground band constructed from the tetrahedral 4$\alpha$ structure. The $0<sup>+_1$ and $3<sup>-_1$ 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 $3<sup>-_1$. The $4<sup>+_2$ 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 $<sup>{12}\textrm{C}+\alpha$ cluster structures occurs between $4<sup>+_1$ and $4<sup>+_2$ states, indicating that the $T_d$ configuration of $4\alpha$ is rather fragile at $J<sup>\pi=4<sup>+$.