  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+${\rm 4N} ]$ and $[ ^{16}$O+${\rm 8N} ]$, 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.
