Large quadrupole moment in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Ne</mml:mi><mml:mprescripts/><mml:none/><mml:mn>20</mml:mn></mml:mmultiscripts></mml:math>: 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 $^{20}\mathrm{Ne}$. Our calculated ${Q}_{s}({2}_{1}^{+})\ensuremath{\approx}\ensuremath{-}0.20\phantom{\rule{0.16em}{0ex}}e\text{b}$ aligns closely with the experimental value of $\ensuremath{-}0.22(2)\phantom{\rule{0.16em}{0ex}}e\text{b}$. Consistent with other theoretical methods, our results confirm the presence of an $\ensuremath{\alpha}$ cluster structure in this state. We also investigate the robustness of the $\ensuremath{\alpha}$ cluster against tensor force, demonstrating that incorporating tensor components significantly enhances ${Q}_{s}({2}_{1}^{+})$ and strengthens the cluster structure along the symmetrical axis.