Implications of non-feasible transformations among icosahedral $h$ orbitals

Abstract

The symmetric group $S_6$ that permutes the six five-fold axes of an icosahedron is introduced to go beyond the simple rotations that constitute the icosahedral group $I$. Owing to the correspondence $h\leftrightarrow d$, the calculation of the Coulomb energies for the icosahedral configurations $h^N$ based on the sequence $O(5)\supset S_6\supset S_5\supset I$ can be brought to bear on Racah's classic theory for the atomic d shell based on $SO(5)\supset S{O}_L(3)\supset I$. Among the elements of $S_6$ is the kaleidoscope operator $\mathcal{K}$ that rotates the weight space of SO(5) by $\pi /2$. Its use explains some puzzling degeneracies in d^3 involving the spectroscopic terms ^2P, ^2F, ^2G and ^2H.

Tentatively scheduled to appear in Physical Preview Letters Apr 5, 99. Revtex, 1 ps figure

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