{
  "annotation_id": "3f1745b5-be62-4c25-b3a3-b7afdfb99514",
  "date_created": "2026-03-02T18:00:00.892000Z",
  "date_modified": "2026-03-02T18:00:00.892000Z",
  "file_hash": "f9e0df3efe1e033cdc3cd6a84c3e67a95e6957bab07b33b85e717556090888c0",
  "private": false,
  "record": {
    "abstract": "In this paper we show that a system of three fermions is exactly solvable for\nthe case of a single-$j$ in the presence of an angular momentum-$J$ pairing\ninteraction. On the basis of the solutions for this system, we obtain new sum\nrules for six-$j$ symbols. It is also found that the \"non-integer\" eigenvalues\nof three fermions with angular momentum $I$ around the maximum appear as\n\"non-integer\" eigenvalues of four fermions when $I$ is around (or larger than)\n$J_{\\rm max}$ and the Hamiltonian contains only an interaction between pairs of\nfermions coupled to spin $J=J_{\\rm max}=2j-1$. This pattern is also found in\nfive and six fermion systems. A boson system with spin $l$ exhibits a similar\npattern.",
    "arxiv_id": "nucl-th/0404042",
    "authors": [
      "Y. M. Zhao",
      "A. Arima"
    ],
    "categories": [
      "nucl-th"
    ],
    "doi": "10.1103/PhysRevC.70.034306",
    "journal_ref": "Phys.Rev. C70 (2004) 034306",
    "title": "Classification of states of single-$j$ fermions with $J$-pairing   interaction",
    "url": "https://arxiv.org/abs/nucl-th/0404042"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "91cc8b3e-eff2-4d7f-880a-ab0c3b7f180c",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}