Interplay Between Tetrahedral and Octahedral Symmetries

The nuclear mean-field realization, using the parametrized potentials as presented in Sect. 3, is a perfect tool to study the point-group symmetries under the condition of using the multipole shape parametrization of Eq. (3). This will become evident from the following considerations.

Our method allows to find the representation of surfaces of a given predefined point-group symmetry through the exact diagonalisation of the Wigner $D$-functions as described in the preceding Section. Such diagonalizations have been performed using Mathematica for $\lambda\leq10$. The first three lowest-order solutions are as follows.