Tetrahedral symmetry in nuclei: Search for its fingerprints in the Actinide and Rare-Earth regions

In series of recent theory articles, predictions have been formulated suggesting the existence of nuclear states whose mean-field Hamiltonians and thus the implied geometrical shapes, are characterized by tetrahedral symmetry. Following these publications, series of experiments for the Rare-Earth region have been proposed and performed. In this article, we shortly summarize the theory evolution developed in the original articles and discuss the status of the issue in light of the preliminary results of the ongoing experimental analyses. More recent theoretical results cross checked with extended literature investigations, suggest that the Actinide region might contain the best experimental candidates to investigate the fingerprints of the symmetry. A proposition is made to prove it via lifetime measurements with the so-called microwave method.