# 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+${\rm 4N} ]$ 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.
Document type :
Journal articles

http://hal.in2p3.fr/in2p3-00548569
Contributor : Michel Lion <>
Submitted on : Monday, December 20, 2010 - 9:46:43 AM
Last modification on : Thursday, February 1, 2018 - 1:26:23 AM

### Citation

N. Itagaki, J. Cseh, M. Ploszajczak. Simplified modeling of cluster-shell competition in $^{20}$Ne and $^{24}$Mg. Physical Review C, American Physical Society, 2011, 83, pp.014302. ⟨10.1103/PhysRevC.83.014302⟩. ⟨in2p3-00548569⟩

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