Effect of cluster-shell competition of $^{12}$C on $E0$ transitions in $^{16}$O

TL;DR

This study explores how the competition between cluster and shell structures in $^{16}$O affects $E0$ transition strengths, revealing that spin-orbit interactions influence the cluster configurations and transition suppression.

Contribution

It introduces the antisymmetrized quasi cluster model (AQCM) to analyze the impact of spin-orbit force on cluster-shell competition and $E0$ transitions in $^{16}$O.

Findings

$E0$ transition is suppressed with increasing spin-orbit strength.

The $0_2^+$ state shifts from $^{12}$C$+alpha$ to shell-like structure.

$E0$ matrix elements are sensitive to intrinsic spin differences.

Abstract

In $^{16}$O, we investigate the relation between the $E0$ monopole transition matrix elements and cluster-shell competition using antisymmetrized quasi cluster model (AQCM), where the dissolution of $alpha$ clusters into quasi clusters due to the effect of the spin-orbit force is introduced. We focus on the structure change when the strength of the spin-orbit force is varied. The ground state dominantly has a compact four $alpha$ structure (doubly magic structure of the $p$ shell), which is rather independent of the strength. However the first excited state ($0_2^+$) has $^{12}$C$+alpha$ cluster structure and this state is largely affected by the increase of the strength; the subclosure configuration of the $p_{3/2}$ shell for the $^{12}$C cluster part becomes more important than three $alpha$ configuration. The $E0$ transition from the ground state with compact four $alpha$ configuration to the $0^+_2$ state with $^{12}$C$+alpha$ cluster configuration is suppressed when increasing the spin-orbit strength. Although the $E0$ operator itself does not have the spin dependence, the matrix element is sensitive to the difference of intrinsic spin structures of the two states. The $E0$ transition characterizes the persistence of four $alpha$ structure in the $0^+_2$ state.