Simplified modeling of cluster-shell competition in ${}^{20}$Ne and ${}^{24}$Mg

Abstract

We investigate properties of the Generator Coordinate Method (GCM) on a collective basis of Antisymmetrized Quasi-Cluster (AQC) states to describe the cluster-shell competition in ${}^{20}$Ne and ${}^{24}$Mg due to the spin-orbit interaction. By introducing a single additional parameter in the antisymmetrized-cluster basis function, a continuous transformation of the $\alpha$ cluster(s) into independent nucleons can be described. We apply this GCM trial wave function to study in details the transition from cluster states ${[}^{16}$O+$\alpha ]$ and ${[}^{16}$O+$\alpha +\alpha ]$ to shell model (SM) states ${[}^{16}$O+$4N]$ and ${[}^{16}$O+$8N]$, respectively. An optimal value of the strength of the spin-orbit interaction is deduced by reproducing level spacing in ${}^{20}$Ne. A possible connection to the group theoretical understanding of the cluster-shell configuration transition is also discussed.

Comments: Phys. Rev. C in press