**4. Summary and Outlook**

In parallel to recent advances in accelerator and ion-source technologies, and the construction of new-generation high-resolution *γ*-ray tracking arrays as AGATA [19] and GRETINA [82], noteworthy developments have taken place in nuclear-structure theory. The state-of-the-art calculations, some of which were discussed in the preceding sections, are now able to predict the properties of nuclei with an unprecedented level of detail, particularly concerning the nuclear shape. Within the Shell Model, quadrupole shapes of ground and excited states can be inferred using T-plots [40] and the quadrupole sum rules approach [38]. Due to the large model spaces involved, Shell-Model studies of octupole collectivity are more rare, and one may hope that the availability of precise experimental data on *E*3 strengths will trigger further efforts in this direction.

The ongoing experimental and theoretical developments will bring forward our understanding of nuclear structure, while also being relevant for cross-disciplinary fields, such as astrophysics, neutrino physics, and physics of (and beyond) the Standard Model [4,33,83]. In this context, a precise understanding of the nuclear shape can bring us closer to answering long-standing questions in physics, such as how heavy elements originate in cataclysmic stellar events and the reason for the matter-antimatter asymmetry in the universe.

Thanks to the constant development of powerful computational resources, and refinements of Shell-Model codes and methods, this theoretical approach can now be extended to vast regions of the nuclear chart. It can be anticipated that this progress will be complemented and inspired by the availability of high-precision spectroscopic data and that low-energy Coulomb excitation will continue to play an important role in future studies throughout the nuclear chart. Let us emphasize, however, as in the cases of 98,100Mo and 130Xe, that the combination of data from a variety of techniques that probe both collective

and single-particle degrees of freedom will provide perhaps the most demanding tests of Shell-Model calculations, and studies in that direction should be pursued.

**Author Contributions:** The authors contributed equally to all aspects of this work. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded in part through the Natural Sciences and Engineering Research Council (NSERC) Canada.

**Data Availability Statement:** Data sharing not applicable.

**Acknowledgments:** We thankfully acknowledge P.E. Garrett for fruitful discussions and for the careful reading of the manuscript, and M. Siciliano for his contribution to Section 3.4 and Figure 4.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **Abbreviations**

The following abbreviations are used in this manuscript:

