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.
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