  Electromagnetic observables are able to give insight into collective and
emergent features in nuclei, including nuclear clustering. These observables
also provide strong constraints for ab initio theory, but comparison of these
observables between theory and experiment can be difficult due to the lack of
convergence for relevant calculated values, such as $E2$ transition strengths.
By comparing the ratios of $E2$ transition strengths for mirror transitions, we
find that a wide range of ab initio calculations give robust and consistent
predictions for this ratio. To experimentally test the validity of these ab
initio predictions, we performed a Coulomb excitation experiment to measure the
$B(E2; 3/2^- \rightarrow 1/2^-)$ transition strength in $^7$Be for the first
time. A $B(E2; 3/2^- \rightarrow 1/2^-)$ value of $26(6)(3) \, e^2
\mathrm{fm}^4$ was deduced from the measured Coulomb excitation cross section.
This result is used with the experimentally known $^7$Li $B(E2; 3/2^-
\rightarrow 1/2^-)$ value to provide an experimental ratio to compare with the
ab initio predictions. Our experimental value is consistent with the
theoretical ratios within $1 \sigma$ uncertainty, giving experimental support
for the value of these ratios. Further work in both theory and experiment can
give insight into the robustness of these ratios and their physical meaning.
