Cluster states and monopole transitions in $^{16}$O

Cluster structures and monopole transitions in positive parity states of $^{16}$O were investigated based on the generator coordinate method calculation of an extended $^{12}$C+$\alpha$ cluster model. The ground and excited states of a $^{12}$C cluster are taken into account by using $^{12}$C wave functions obtained with the method of antisymmetrized molecular dynamics. The $0^+_2$ state of $^{16}$O and its rotational members, the $2^+_1$ and $4^+_1$ states are described well by the cluster states dominated by the $^{12}$C($0^+_1$)+$\alpha$ structure. Above the $^{12}$C($0^+_2$)+$\alpha$ threshold energy, we obtained a $0^+$ state having the $^{12}$C($0^+_2$)+$\alpha$ cluster structure, which is considered to be a candidate for the $4\alpha$ cluster gas state. The band structures were discussed based on the calculated $E2$ transition strength. Isoscalar Monopole excitations from the ground state were also discussed.