The measurement of a permanent electric dipole moment (EDM) in atoms is crucial for understanding the origins of CP-violation. Quadrupole and octupole deformed nuclei significantly enhance atomic EDM. However, accurate interpretation of the EDM in such systems requires the characterization of their deformation. While nuclear deformation is indicated in various structure models, there is substantial mutual disagreement between the theoretical models or between theoretical models and experimental values. Experimental confirmation of the same, particularly in heavy isotopes essential for EDM measurements, is lacking.

Nuclear E$2$ transitions allow access to quantify quadrupole deformation, but these transitions are often mixed with M$1$ transitions. Both E$2$ and M$1$ transitions are well characterized by Weisskopf estimates, which rely on a single-particle approximation, but are affected by collective nuclear deformation. Previously, Weisskopf estimates were only available for the mass range $A<150$, and in this work we have extended the Weisskopf estimates of both E$2$ and M$1$ transition lifetimes to the mass range of $150\le A\le 250$.

This allowed us to comprehensively study $91$ candidate isotopes, by comparing their E$2$ and M$1+$E$2$ transition lifetimes to their nearest even-even counterparts, whose E$2$ transition strengths are very well understood. Estimates of collective nuclear quadrupole deformation in $67$ of these isotopes were obtained, either from E$2$ or M$1+$E$2$ transition lifetimes, and in $32$ cases they were obtained from both types of transitions independently. We find that the quadrupole deformation extracted from the two different types of transitions are mutually consistent, as well as that they follow the trends established in theory. We thereby identify the isotopes $^{223,225}$Fr, $^{221,223}$Ra, $^{223,225,227}$Ac and $^{229}$Pa, where EDM measurements are foreseen and information on nuclear deformation is needed, for which no measurement of nuclear quadrupole deformation has been made.