dorsal/arxiv
View SchemaCore-valence correlations for atoms with open shells
| Authors | V. A. Dzuba, V. V. Flambaum |
|---|---|
| Categories | |
| ArXiv ID | physics/0703121 |
| URL | https://arxiv.org/abs/physics/0703121 |
| DOI | 10.1103/PhysRevA.75.052504 |
| Journal | Phys. Rev. A 75, 052504 (2007) |
Abstract
We present an efficient method of inclusion of the core-valence correlations into the configuration interaction (CI) calculations. These correlations take place in the core area where the potential of external electrons is approximately constant. A constant potential does not change the core electron wave functions and Green's functions. Therefore, all operators describing interaction of $M$ valence electrons and $N-M$ core electrons (the core part of the Hartree-Fock Hamiltonian $V^{N-M}$, the correlation potential $\hat\Sigma_1({\bf r},{\bf r'},E)$ and the screening of interaction between valence electrons by the core electrons $\hat\Sigma_2$) may be calculated with all $M$ valence electrons removed. This allows one to avoid subtraction diagrams which make accurate inclusion of the core-valence correlations for $M>2$ prohibitively complicated. Then the CI Hamiltonian for $M$ valence electrons is calculated using orbitals in complete $V^{N}$ potential (the mean field produced by all electrons); $\hat\Sigma_1$ + $\hat\Sigma_2$ are added to the CI Hamiltonian to account for the core-valence correlations. We calculate $\hat\Sigma_1$ and $\hat\Sigma_2$ using many-body perturbation theory in which dominating classes of diagrams are included in all orders. We use neutral Xe I and all positive ions up to Xe VIII as a testing ground. We found that the core electron density for all these systems is practically the same. Therefore, we use the same $\hat\Sigma_1$ and $\hat\Sigma_2$ to build the CI Hamiltonian in all these systems ($M=1,2,3,4,5,6,7,8$). Good agreement with experiment for energy levels and Land\'{e} factors is demonstrated for all cases from Xe I to Xe VIII.
{
"annotation_id": "4a73502b-a994-4f8a-ba39-82b575104da1",
"date_created": "2026-03-02T18:01:18.142000Z",
"date_modified": "2026-03-02T18:01:18.142000Z",
"file_hash": "54a3dca4cc8db02800f87c06b609289bad967b98e13d5b4a84a15b904a23875e",
"private": false,
"record": {
"abstract": "We present an efficient method of inclusion of the core-valence correlations\ninto the configuration interaction (CI) calculations. These correlations take\nplace in the core area where the potential of external electrons is\napproximately constant. A constant potential does not change the core electron\nwave functions and Green\u0027s functions. Therefore, all operators describing\ninteraction of $M$ valence electrons and $N-M$ core electrons (the core part of\nthe Hartree-Fock Hamiltonian\n $V^{N-M}$, the correlation potential $\\hat\\Sigma_1({\\bf r},{\\bf r\u0027},E)$ and\nthe screening of interaction between valence electrons by the core electrons\n$\\hat\\Sigma_2$) may be calculated with all\n $M$ valence electrons removed. This allows one to avoid subtraction diagrams\nwhich make accurate inclusion of the core-valence correlations for $M\u003e2$\nprohibitively complicated. Then the CI Hamiltonian for $M$ valence electrons is\ncalculated using orbitals in complete $V^{N}$ potential (the mean field\nproduced by all electrons); $\\hat\\Sigma_1$ + $\\hat\\Sigma_2$ are added to the CI\nHamiltonian to account for the core-valence correlations. We calculate\n$\\hat\\Sigma_1$ and $\\hat\\Sigma_2$ using many-body perturbation theory in which\ndominating classes of diagrams are included in all orders.\n We use neutral Xe I and all positive ions up to Xe VIII as a testing ground.\nWe found that the core electron density for all these systems is practically\nthe same. Therefore, we use the same $\\hat\\Sigma_1$ and $\\hat\\Sigma_2$ to build\nthe CI Hamiltonian in all these systems ($M=1,2,3,4,5,6,7,8$). Good agreement\nwith experiment for energy levels and Land\\\u0027{e} factors is demonstrated for all\ncases from Xe I to Xe VIII.",
"arxiv_id": "physics/0703121",
"authors": [
"V. A. Dzuba",
"V. V. Flambaum"
],
"categories": [
"physics.atom-ph"
],
"doi": "10.1103/PhysRevA.75.052504",
"journal_ref": "Phys. Rev. A 75, 052504 (2007)",
"title": "Core-valence correlations for atoms with open shells",
"url": "https://arxiv.org/abs/physics/0703121"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "78605060-086c-4d37-8789-e25c7621a207",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}