{
  "annotation_id": "043e2b93-a607-4e6f-a0f0-51e0819d6010",
  "date_created": "2026-03-02T18:01:14.860000Z",
  "date_modified": "2026-03-02T18:01:14.860000Z",
  "file_hash": "d9f9f7d2ca5dd7149a5a2f531a215968d5f23720fc3c80af65f84d3b9e47654d",
  "private": false,
  "record": {
    "abstract": "A new measure of the crystal-field strength, complementary to the\nconventional one, is defined. It is based on the rotational invariants\n|B_{k0}|_{av} or |\\sum_{k}B_{k0}|_{av}, k=2,4,6, of the crystal-(ligand)-field\n(CF) Hamiltonian H_{CF} parametrizations, i.e. on the axial CF parameters\nmodules averaged over all reference frame orientations. They turn out to be\nequal to |H_{CF}^{(k)}|_{av} and |H_{CF}|_{av}, respectively. While the\ntraditional measure is established on the parametrization modules or on the\nsecond moment of the CF energy levels, the introduced scale employs rather the\nfirst moment of the energy modules and has better resolving power. The new\nscale is able to differentiate the strength of various iso-modular\nparametrizations according to the classes of rotationally equivalent\nparametrizations. Using both the compatible CF strength measures one may draw\nmore accurate conclusions about the Stark levels arrays and particularly their\ntotal splitting magnitudes.",
    "arxiv_id": "physics/0610094",
    "authors": [
      "Jacek Mulak",
      "Maciej Mulak"
    ],
    "categories": [
      "physics.chem-ph"
    ],
    "doi": "10.1088/1751-8113/40/9/012",
    "title": "On a complementary scale of crystal-field strength",
    "url": "https://arxiv.org/abs/physics/0610094"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "af400bfe-ea8b-48a6-b571-f570780b9a30",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}