Abstract
We have studied gas-like states of $\alpha$ clusters around an $^{16}$O core in $^{24}$Mg based on a microscopic $\alpha$-cluster model. This study was performed by introducing a Monte Carlo technique for the description of the THSR (Tohsaki Horiuchi Schuck R\"{o}pke) wave function, and the coupling effect to other low-lying cluster states was taken into account. A large isoscalar monopole ($E0$) transition strength from the ground to the gas-like state is discussed. The gas-like state of two $\alpha$ clusters in $^{24}$Mg around the $^{16}$O core appears slightly below the 2$\alpha$-threshold e
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