{
  "annotation_id": "265da2e7-882d-42ce-88a2-9c44806a440f",
  "date_created": "2026-03-02T18:02:47.313000Z",
  "date_modified": "2026-03-02T18:02:47.313000Z",
  "file_hash": "a05c9cd1cf3206d82f61c12f237ea7eac81097330c5e22faa44e9ec52f74f661",
  "private": false,
  "record": {
    "abstract": "The Dirac equation for the Coulomb problem is restated by incorporating a\nnonlinear effective interaction into the Dirac Hamiltonian: one keeps the $1/r$\ndependence for the Coulomb field, but the coupling constant is modified by a\nfactor depending on the n (principal quantum number) power of the mean value of\nthe Hamiltonian. In this simple context we study the Lamb shift and the\nhyperfine splitting of the s-levels of hydrogenic atoms. We discuss to what\nextent the corresponding calculations fit the energy splittings to the\nappropriate order in the fine structure constant.",
    "arxiv_id": "quant-ph/9905063",
    "authors": [
      "S. Bruce",
      "J. Diaz-Valdes"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "An approximation to the Lamb shift and hyperfine splitting as nonlinear   effective Coulomb-like interactions in the Dirac equation",
    "url": "https://arxiv.org/abs/quant-ph/9905063"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "44b86fab-a846-4f20-b313-0bb32e9f7952",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}