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For electric quadrupole ($E2$) observables, which depend on thelarge-distance tails of the nuclear wave function, ab initio no-coreconfiguration interaction (NCCI) calculations converge slowly, makingmeaningful predictions challenging to obtain. Nonetheless, the calculatedvalues for different $E2$ matrix elements, particularly those involving levelswith closely-related structure (e.g., within the same rotational band) arefound to be robustly proportional. This observation suggests that a known valuefor one observable may be used to determine the overall scale of $E2$strengths, and thereby provide predictions for others. In particular, wedemonstrate that meaningful predictions for $E2$ transitions may be obtained bycalibration to the ground-state quadrupole moment. We test this approach forwell-measured low-lying $E2$ transitions in $^7$Li and $^9$Be, then providepredictions for transitions in $^8$Li and $^9$Li. In particular, we address the$2^+\rightarrow1^+$ transition in $^8$Li, for which the reported measuredstrength exceeds ab initio Green's function Monte Carlo (GFMC) predictions byover an order of magnitude.

Ab initio estimation of $E2$ strengths in $^8$Li and its neighbors by normalization to the measured quadrupole moment