dorsal/arxiv
View SchemaAn efficient approach for spin-angular integrations in atomic structure calculations
| Authors | G. Gaigalas, Z. Rudzikas, C. Froese Fischer |
|---|---|
| Categories | |
| ArXiv ID | physics/0405101 |
| URL | https://arxiv.org/abs/physics/0405101 |
| DOI | 10.1088/0953-4075/30/17/006 |
| Journal | J. Phys. B: At. Mol. Opt. Phys. 30 (1997) 3747-3771 |
Abstract
A general method is described for finding algebraic expressions for matrix elements of any one- and two-particle operator for an arbitrary number of subshells in an atomic configuration, requiring neither coefficients of fractional parentage nor unit tensors. It is based on the combination of second quantization in the coupled tensorial form, angular momentum theory in three spaces (orbital, spin and quasispin), and a generalized graphical technique. The latter allows us to calculate graphically the irreducible tensorial products of the second quantization operators and their commutators, and to formulate additional rules for operations with diagrams. The additional rules allow us to find graphically the normal form of the complicated tensorial products of the operators. All matrix elements (diagonal and non-diagonal with respect to configurations) differ only by the values of the projections of the quasispin momenta of separate shells and are expressed in terms of completely reduced matrix elements (in all three spaces) of the second quantization operators. As a result, it allows us to use standard quantities uniformly for both diagona and off-diagonal matrix elements.
{
"annotation_id": "b24ec2ad-f811-4d23-b6c5-f60c08158f01",
"date_created": "2026-03-02T18:00:49.940000Z",
"date_modified": "2026-03-02T18:00:49.940000Z",
"file_hash": "43e3af0894642bf3193e7785f7acd733c46c1e52082038e01c70de6c7c2e78ad",
"private": false,
"record": {
"abstract": "A general method is described for finding algebraic expressions for matrix\nelements of any one- and two-particle operator for an arbitrary number of\nsubshells in an atomic configuration, requiring neither coefficients of\nfractional parentage nor unit tensors. It is based on the combination of second\nquantization in the coupled tensorial form, angular momentum theory in three\nspaces (orbital, spin and quasispin), and a generalized graphical technique.\nThe latter allows us to calculate graphically the irreducible tensorial\nproducts of the second quantization operators and their commutators, and to\nformulate additional rules for operations with diagrams. The additional rules\nallow us to find graphically the normal form of the complicated tensorial\nproducts of the operators. All matrix elements (diagonal and non-diagonal with\nrespect to configurations) differ only by the values of the projections of the\nquasispin momenta of separate shells and are expressed in terms of completely\nreduced matrix elements (in all three spaces) of the second quantization\noperators. As a result, it allows us to use standard quantities uniformly for\nboth diagona and off-diagonal matrix elements.",
"arxiv_id": "physics/0405101",
"authors": [
"G. Gaigalas",
"Z. Rudzikas",
"C. Froese Fischer"
],
"categories": [
"physics.atom-ph"
],
"doi": "10.1088/0953-4075/30/17/006",
"journal_ref": "J. Phys. B: At. Mol. Opt. Phys. 30 (1997) 3747-3771",
"title": "An efficient approach for spin-angular integrations in atomic structure calculations",
"url": "https://arxiv.org/abs/physics/0405101"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "08d7e72b-7006-4201-ae19-828fc879014e",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}