{
  "annotation_id": "b5a7dbd6-9e77-410e-bdfa-f37bfdac3b7f",
  "date_created": "2026-03-02T18:00:42.867000Z",
  "date_modified": "2026-03-02T18:00:42.867000Z",
  "file_hash": "3cdf78730b120385e6f47d92e4f21cc3dbf6f9932c2c2c92d4a994bd4c8571d6",
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  "record": {
    "abstract": "Virial relations for the Dirac equation in a central field and their\napplications to calculations of H-like atoms are considered. It is demonstrated\nthat using these relations allows one to evaluate various average values for a\nhydrogenlike atom. The corresponding relations for non-diagonal matrix elements\nprovide an effective method for analytical evaluations of infinite sums that\noccur in calculations based on using the reduced Coulomb-Green function. In\nparticular, this method can be used for calculations of higher-order\ncorrections to the hyperfine splitting and to the g factor in hydrogenlike\natoms.",
    "arxiv_id": "physics/0211087",
    "authors": [
      "V. M. Shabaev"
    ],
    "categories": [
      "physics.atom-ph"
    ],
    "doi": "10.1007/978-3-540-45059-7_6",
    "journal_ref": "In: \"Precision Physics of Simple Atomic Systems\", edited by S.G.\n  Karshenboim and V.B. Smirnov, (Berlin, Springer 2003) p. 97.",
    "title": "Virial relations for the Dirac equation and their applications to   calculations of H-like atoms",
    "url": "https://arxiv.org/abs/physics/0211087"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "7ca0dcd2-9eee-42b6-9c13-066adf22ed12",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}