The correlation between the $\alpha$-cluster separation and the neutron S-factor in $^{12}$Be

TL;DR

This study investigates how the separation of alpha clusters in $^{12}$Be correlates with the neutron S-factor, revealing a positive relationship between cluster separation and neutron orbital occupation.

Contribution

It introduces a theoretical analysis linking alpha-cluster separation with neutron orbital occupation using the generator coordinates method in $^{12}$Be.

Findings

Positive correlation between alpha-cluster separation and $\sigma$ orbital occupation.

Theoretical insight into the structure of $^{12}$Be.

Use of the generator coordinates method for cluster analysis.

Abstract

The reduced width amplitudes (RWA) and the spectroscopic factor (S-factor) of $\alpha$-cluster and valence neutron in $^{12}$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 $^{12}$Be. The analysis of the results shows that the percentage of the $\sigma$ orbital occupation in $^{12}$Be is positively related to the clustering separation.