Robust ab initio prediction of nuclear electric quadrupole observables by scaling to the charge radius

Meaningful predictions for electric quadrupole ($E2$) observables from ab initio nuclear theory are necessary, if the ab initio description of collective correlations is to be confronted with experiment, as well as to provide predictive power for unknown $E2$ observables. However, 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. We demonstrate that the convergence patterns of the $E2$ and radius observables are strongly correlated, and that meaningful predictions for the absolute scale of $E2$ observables may be made by calibrating to the experimentally known ground-state charge radius. We illustrate by providing robust ab initio predictions for several $E2$ transition strengths and quadrupole moments in p-shell nuclei, in cases where experimental results are available for comparison.