dorsal/arxiv
View SchemaPotential Harmonic Calculations of Helium Triplet States
| Authors | Anthony D. Klemm, Michel Fabre de la Ripelle, Sigurd Yves Larsen |
|---|---|
| Categories | |
| ArXiv ID | physics/0105076 |
| URL | https://arxiv.org/abs/physics/0105076 |
Abstract
The hyperspherical harmonics (HH) provide a complete basis for the expansion of atomic wave functions, but even for two particles the number of harmonics for a given order is not trivial and, as the number of electrons increases, this degeneracy becomes absolutely prohibitive. We modify the method by selecting a subset of the basis that, we feel, will yield the physically most important part of the wave function, and test the idea on simple systems. In a previous work (with M. Haftel) of the singlet ground and first excited states of the helium atom we found that the error in the binding energy of the ground state was of the order of 1 part in 10,000 and that it decreased for the first excited state. We now have applied our method to the equivalent triplet states. We report on this work, and our results, and hope to draw attention to the interesting accuracy that we obtain with the relatively simple wave functions of our formulation.
{
"annotation_id": "953efbe4-8993-4574-8265-98de415d4db4",
"date_created": "2026-03-02T18:00:36.165000Z",
"date_modified": "2026-03-02T18:00:36.165000Z",
"file_hash": "b04bf0161193b50ff951733b93436e2d085c2d9923ce8aea7f32f9566b23dc6c",
"private": false,
"record": {
"abstract": "The hyperspherical harmonics (HH) provide a complete basis for the expansion\nof atomic wave functions, but even for two particles the number of harmonics\nfor a given order is not trivial and, as the number of electrons increases,\nthis degeneracy becomes absolutely prohibitive. We modify the method by\nselecting a subset of the basis that, we feel, will yield the physically most\nimportant part of the wave function, and test the idea on simple systems.\n In a previous work (with M. Haftel) of the singlet ground and first excited\nstates of the helium atom we found that the error in the binding energy of the\nground state was of the order of 1 part in 10,000 and that it decreased for the\nfirst excited state.\n We now have applied our method to the equivalent triplet states. We report on\nthis work, and our results, and hope to draw attention to the interesting\naccuracy that we obtain with the relatively simple wave functions of our\nformulation.",
"arxiv_id": "physics/0105076",
"authors": [
"Anthony D. Klemm",
"Michel Fabre de la Ripelle",
"Sigurd Yves Larsen"
],
"categories": [
"physics.atom-ph"
],
"title": "Potential Harmonic Calculations of Helium Triplet States",
"url": "https://arxiv.org/abs/physics/0105076"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "0f929210-c4d8-45eb-94bd-8a8b6f48d694",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}