Converged results for $E2$ observables are notoriously challenging to obtain in ab initio no-core configuration interaction approaches. Matrix elements of the $E2$ operator are sensitive to the large-distance tails of the nuclear wave function, which converge slowly in an oscillator basis expansion. Similar convergence challenges beset ab initio prediction of the nuclear charge radius. However, we exploit systematic correlations between the calculated $E2$ and radius observables to yield meaningful predictions for relations among these observables. In particular, we examine ab initio predictions for dimensionless ratios of the form $Q/r^2$ for nuclei throughout the $p$ shell. Meaningful predictions for electric quadrupole moments may then be made by calibrating to the ground-state charge radius, if experimentally known, or vice versa. Moreover, these dimensionless ratios provide ab initio insight into the nuclear quadrupole deformation.

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• Nuclear shapes and moments
• Nuclear structure & decays
• Spectroscopic factors & electromagnetic moments
• 6 ≤ A ≤ 19
• Ab initio calculations
• Shell model