dorsal/arxiv
View SchemaImplications of non-feasible transformations among icosahedral $h$ orbitals
| Authors | Edwin Lo, B. R. Judd |
|---|---|
| Categories | |
| ArXiv ID | physics/9903001 |
| URL | https://arxiv.org/abs/physics/9903001 |
| DOI | 10.1103/PhysRevLett.82.3224 |
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 $SO(5) \supset SO_L(3) \supset I$. Among the elements of $S_6$ is the kaleidoscope operator ${\cal K}$ 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.
{
"annotation_id": "66da05ce-5d35-4820-b4f2-7ffe2609fff1",
"date_created": "2026-03-02T18:01:24.029000Z",
"date_modified": "2026-03-02T18:01:24.029000Z",
"file_hash": "4f2290849ba8ef25450fced88f6ac40d06510784eb30eb28d5ce8452fd0ab3b3",
"private": false,
"record": {
"abstract": "The symmetric group $S_6$ that permutes the six five-fold axes of an\nicosahedron is introduced to go beyond the simple rotations that constitute the\nicosahedral group $I$. Owing to the correspondence $h\\leftrightarrow d$, the\ncalculation of the Coulomb energies for the icosahedral configurations $h^N$\nbased on the sequence $O(5) \\supset S_6 \\supset S_5 \\supset I$ can be brought\nto bear on Racah\u0027s classic theory for the atomic d shell based on $SO(5)\n\\supset SO_L(3) \\supset I$. Among the elements of $S_6$ is the kaleidoscope\noperator ${\\cal K}$ that rotates the weight space of SO(5) by $\\pi/2$. Its use\nexplains some puzzling degeneracies in d^3 involving the spectroscopic terms\n^2P, ^2F, ^2G and ^2H.",
"arxiv_id": "physics/9903001",
"authors": [
"Edwin Lo",
"B. R. Judd"
],
"categories": [
"physics.atom-ph",
"physics.atm-clus"
],
"doi": "10.1103/PhysRevLett.82.3224",
"title": "Implications of non-feasible transformations among icosahedral $h$ orbitals",
"url": "https://arxiv.org/abs/physics/9903001"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "fb3063e6-01ac-4d00-a896-d231e3e10dab",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}