Effect of $^{12}\mathrm{C}+\alpha$ clustering on the $E0$ transition in $^{16}\mathrm{O}$

Abstract

We investigate cluster structures and $E0$ transitions of $0^+$ states in $^{16}$O. In particular, we discuss the mixing effect of $3\alpha$ and $\alpha$ breaking components in the $^{12}$C cluster on the $E0$ transitions. To this end, we perform a microscopic calculation including $\alpha$ cluster and cluster-breaking model spaces. By analyzing the obtained results, we confirm that the $0_2^+$ and $0_3^+$ states of $^{16}$O are indeed the weak-coupling $^{12}\mathrm{C}(0^+)+\alpha$ and $^{12}\mathrm{C}(2^+)+\alpha$ cluster states, respectively. We find mainly two important mechanisms for reducing the $E0$ transition: (i) the difference in intrinsic spin configurations between the initial and final states caused by the cluster breaking and (ii) the mixing of planar $4\alpha$ configurations in the excited states. We show that the $E0$ operator excites the initial (ground) state not to planar $4\alpha$ configurations but predominantly to triangular pyramid $4\alpha$ configurations. Thus, the mixture of the planar $4\alpha$ configurations in the $0_2^+$ state significantly reduces the $E0$ transition matrix elements to this state. We conclude that the $E0$ transitions tend to be enhanced by cluster states, but they are affected by various mechanisms originating in the detailed structures of the final states.