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Description
The spectroscopic quadrupole moment of the first excited 2$^{+}_{1}$ state, $Q_{_S}(2^{+}_{1})$, at 1.633 MeV in $^{20}$Ne has been determined from reorientation effect Coulomb-excitation measurements at safe energies using the {\small AFRODITE} array at iThemba LABS. A diagonal matrix element of $\langle 2^+_1\mid\mid \hat{E2} \mid\mid 2^+_1\rangle=-0.34(5)$ eb yields a large value
of $Q_{_S}(2^{+}_{1})=-0.26(4)$ eb, which presents strong discrepancies when compared with cluster-model and mean-field calculations, which underestimate it by at least 30$\%$, and is in disagreement by 3$\sigma$ with the collective model of Bohr and Mottelson. Nevertheless, a slightly larger nuclear polarizability than the one assumed in previous work resolves this 45-year old conundrum between Coulomb-excitation measurements versus nuclear theory and the collective model.