Tetrahedral Magic Numbers in Rare Earth and Actinide Nuclei

In principle, in the present article we focus our illustrations of the tetrahedral symmetry on the example of the Rare Earth nuclei, but as a 'by-product' the tetrahedral magic numbers in the Actinide nuclei are obtained as well. We begin by the illustration of the realistic single-particle spectra in function of the tetrahedral deformation as calculated for the Rare-Earth nuclei. This choice was dictated by the recent study[9] suggesting that the phenomenon of the tetrahedral symmetry may be present in the whole range of Rare Earth nuclei, in particular in the isotones of $N\sim90$. Moreover, it seems today[9] that the experimental evidence for the presence of such a symmetry has already been found⁴.

Figure 2: Single-particle energy levels in function of the tetrahedral deformation for protons. Observe the presence of the four-fold degenerate orbitals marked with full lines and the strong gaps at Z=56, 64, 70, and 90/94 referred to as tetrahedral-magic.