Large quadrupole deformation in $^{20}$Ne challenges rotor model and modern theory: urging for $\alpha$ clusters in nuclei

TL;DR

This study measures the quadrupole moment of $^{20}$Ne's first excited state, revealing significant deviations from rotor model predictions and highlighting the importance of $ ext{alpha}$ clustering in nuclear structure theories.

Contribution

It provides precise experimental data on $Q_{_S}(2^{+}_{1})$ in $^{20}$Ne and demonstrates the necessity of including $ ext{alpha}$ clustering in modern nuclear models.

Findings

Measured $Q_{_S}(2^{+}_{1})$ as -0.22(2) eb, confirming previous results.

Discrepancies with rotor model predictions are nearly 3$\sigma$, indicating model limitations.

$ ext{Alpha}$ clustering in $^{20}$Ne explains deviations from traditional models.

Abstract

The spectroscopic quadrupole moment of the first excited state, $Q_{_S}(2^{+}_{1})$, at 1.634 MeV in $^{20}$Ne was determined from sensitive reorientation-effect Coulomb-excitation measurements using a heavy target and safe energies well below the Coulomb barrier. Particle-$\gamma$ coincidence measurements were collected at iThemba LABS with a digital data-acquisition system using the {\sc AFRODITE} array coupled to an annular, doubled-sided silicon detector. A precise value of $Q_{_S}(2^{+}_{1})=-0.22(2)$ eb was determined at backward angles in agreement with the only safe-energy measurement prior to this work, $Q_{_S}(2^{+}_{1})=-0.23(8)$ eb. This result adopts 1$\hbar\omega$ shell-model calculations of the nuclear dipole polarizability of the 2$^+_1$ state that contributes to the effective quadrupole interaction and determination of $Q_{_S}(2^{+}_{1})$. It disagrees, however, with the ideal rotor model for axially-symmetric nuclei by almost $3\sigma$. Larger discrepancies are computed by modern state-of-the-art calculations performed in this and prior work, including {\it ab initio} shell model with chiral effective interactions and the multi-reference relativistic energy density functional ({\sc MR-EDF}) model. The intrinsic nucleon density of the 2$^+_1$ state in $^{20}$Ne calculated with the {\sc MR-EDF} model illustrates the presence of $\alpha$ clustering, which explains the largest discrepancy with the rotor model found in the nuclear chart and motivates the explicit inclusion of $\alpha$ clustering for full convergence of $E2$ collective properties.