Large quadrupole moment in $^{20}$Ne:Localization and tensor-force effects

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.