The overlap function and the spectroscopic factor (SF) of $\alpha$-cluster and valence neutron in ${}^{12}\mathrm{Be}$ are calculated by the generator coordinates method (GCM) with the cluster model. By fixing the distance between the $\alpha$-clusters' generated coordinates, we make a theoretical experiment to analyze the relationship between the $\alpha$-clustering separation and the orbital occupation of the valence neutron in ${}^{12}\mathrm{Be}$. The analysis of the results shows that the percentage of the $\sigma$-orbital occupation in ${}^{12}\mathrm{Be}$ is positively related to the clustering separation.

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• Cluster models
• Nuclear many-body theory
• Nuclear structure & decays
• S-factor