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We investigate properties of the Generator Coordinate Method (GCM) on acollective basis of Antisymmetrized Quasi-Cluster (AQC) states to describe thecluster-shell competition in $^{20}$Ne and $^{24}$Mg due to the spin-orbitinteraction. By introducing a single additional parameter in theantisymmetrized-cluster basis function, a continuous transformation of the$\alpha$ cluster(s) into independent nucleons can be described. We apply thisGCM 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+${\rm 4N} ]$ and $[ ^{16}$O+${\rm 8N} ]$, respectively. Anoptimal value of the strength of the spin-orbit interaction is deduced byreproducing level spacing in $^{20}$Ne. A possible connection to the grouptheoretical understanding of the cluster-shell configuration transition is alsodiscussed.

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