{
  "annotation_id": "e3c20d98-68fb-4fe1-9b83-36ae5acd6824",
  "date_created": "2026-03-02T18:02:48.408000Z",
  "date_modified": "2026-03-02T18:02:48.408000Z",
  "file_hash": "67aa8b7521f2ec6aca42eefca75a65fe33b87269e67da6691387484c333d95eb",
  "private": false,
  "record": {
    "abstract": "The explicit semiclassical treatment of logarithmic perturbation theory for\nthe bound-state problem within the framework of the Dirac equation is\ndeveloped. Avoiding disadvantages of the standard approach in the description\nof exited states, new handy recursion formulae with the same simple form both\nfor ground and exited states have been obtained. As an example, the\nperturbation expansions for the energy eigenvalues for the Yukawa potential\ncontaining the vector part as well as the scalar component are considered.",
    "arxiv_id": "quant-ph/9911006",
    "authors": [
      "I. V. Dobrovolska",
      "R. S. Tutik"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1016/S0375-9601(99)00459-4",
    "journal_ref": "Physics Letters A 260 (1999) 10-16",
    "title": "A new approach to perturbation theory for a Dirac particle in a central   field",
    "url": "https://arxiv.org/abs/quant-ph/9911006"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "fffe50fb-a0b7-4dba-a39d-d18a3b1e86f0",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}