Using the Beyond-Skyrme-Hartree-Fock approach with various Skyrme-type $NN$ effective interactions, we explore the large spectroscopic quadrupole moment $Q_s$ of the first excited $2_{ 1}^{ +}$ state in $^{ 20}$Ne. Our calculated $Q_s(2_{ 1}^{ +}) \approx -0.20~e\textrm{ b}$ aligns closely with the experimental value of $-0.22(2)~e\textrm{ b}$. Consistent with other theoretical methods, our results confirm the presence of an $\alpha$ cluster structure in this state. We also investigate the robustness of the $\alpha$ cluster against tensor-force, demonstrating that incorporating tensor components significantly enhances $Q_s(2_{ 1}^{ +})$ and strengthens the cluster structure along the symmetrical axis.
Categories: nucl-th