Spectrum and electromagnetic properties of ${}^{24}\mathrm{M}\mathrm{g}$ in the Geometric $\alpha$-cluster Model with ${\mathcal{D}}_{4h}$ symmetry at leading order

The relevance of the point-symmetry group ${\mathcal{D}}_{4h}$ for the prediction of spectrum and electromagnetic properties of the ${}^{24}\mathrm{M}\mathrm{g}$ nucleus is discussed in the framework of the geometric $\alpha$-cluster model at leading order. The latter represents a macroscopic $\alpha$-cluster framework wherein nuclear excitations are described in terms of rotations and vibrations of ${}^4\mathrm{H}\mathrm{e}$ clusters about their equilibrium positions, at the vertices of a square bipyramid. The finite group associated with the latter regulates the composition of the rotational bands as well as the transitions between the energy levels, by means of additional selection rules, of molecular nature. A sample of reduced electric multipole transition probabilities of intraband nature is provided.