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$^{20}$Ne has been known as a typical example of a nucleus with $\alpha$cluster structure ($^{16}$O+$\alpha$ structure). However according to thespherical shell model, the spin-orbit interaction acts attractively for fournucleons outside of the $^{16}$O core, and this spin-orbit effect cannot betaken into account in the simple $\alpha$ cluster models. We investigate howthe $\alpha$ cluster structure competes with independent particle motions ofthese four nucleons. The antisymmetrized quasi-cluster model (AQCM) is a methodto describe a transition from the $\alpha$ cluster wave function to the$jj$-coupling shell model wave function. In this model, the cluster-shelltransition is characterized by only two parameters; $R$ representing thedistance between clusters and $\Lambda$ describing the breaking of $\alpha$clusters, and the contribution of the spin-orbit interaction, very important inthe $jj$-coupling shell model, can be taken into account by changing $\alpha$clusters to quasi clusters. In this article, based on AQCM, we apply $^{16}$Oplus one quasi cluster model for $^{20}$Ne. Here we focus on the $E0$transition matrix element, which has been known as the quantity characterizingthe cluster structure. The $E0$ transition matrix elements are sensitive to thechange of the wave functions from $\alpha$ cluster to $jj$-coupling shellmodel.

Cluster-shell competition and its effect on the $E0$ transition probability in $^{20}$Ne