dorsal/arxiv
View SchemaHow to derive and compute 1,648 diagrams
| Authors | Caleb C. Cannon, Andrei Derevianko |
|---|---|
| Categories | |
| ArXiv ID | physics/0306099 |
| URL | https://arxiv.org/abs/physics/0306099 |
Abstract
We present the first calculation for many-electron atoms complete through fourth order of many-body perturbation theory. Owing to an overwhelmingly large number of underlying diagrams, we developed a suite of symbolic algebra tools to automate derivation and coding. We augment all-order single-double excitation method with 1,648 omitted fourth-order diagrams and compute amplitudes of principal transitions in Na. The resulting ab initio relativistic electric-dipole amplitudes are in an excellent agreement with 0.05%-accurate experimental values. Analysis of previously unmanageable classes of diagrams provides a useful guide to a design of even more accurate, yet practical many-body methods.
{
"annotation_id": "4476e269-8d67-4ea4-835f-17ab4dcaf4f1",
"date_created": "2026-03-02T18:00:43.297000Z",
"date_modified": "2026-03-02T18:00:43.297000Z",
"file_hash": "22088c001936ed06c50d497f7fd8849100cc0a687de68436a7ac2422db99ea3a",
"private": false,
"record": {
"abstract": "We present the first calculation for many-electron atoms complete through\nfourth order of many-body perturbation theory. Owing to an overwhelmingly large\nnumber of underlying diagrams, we developed a suite of symbolic algebra tools\nto automate derivation and coding. We augment all-order single-double\nexcitation method with 1,648 omitted fourth-order diagrams and compute\namplitudes of principal transitions in Na. The resulting ab initio relativistic\nelectric-dipole amplitudes are in an excellent agreement with 0.05%-accurate\nexperimental values. Analysis of previously unmanageable classes of diagrams\nprovides a useful guide to a design of even more accurate, yet practical\nmany-body methods.",
"arxiv_id": "physics/0306099",
"authors": [
"Caleb C. Cannon",
"Andrei Derevianko"
],
"categories": [
"physics.atom-ph",
"physics.comp-ph"
],
"title": "How to derive and compute 1,648 diagrams",
"url": "https://arxiv.org/abs/physics/0306099"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "796d3a1f-2165-440c-a1ae-bbde1fa0e99a",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}