{
  "annotation_id": "67f90e7e-0617-49f3-875f-28669dbf3ccb",
  "date_created": "2026-03-02T18:00:04.868000Z",
  "date_modified": "2026-03-02T18:00:04.868000Z",
  "file_hash": "2aa9d292b3f11a9da6a9d93dac778f0e79094f3bd613af70f79ea985abe94bb4",
  "private": false,
  "record": {
    "abstract": "In this paper we study $J$-pairing Hamiltonian and find that the sum of\neigenvalues of spin $I$ states equals sum of norm matrix elements within the\npair basis for four identical particles such as four fermions in a single-$j$\nshell or four bosons with spin $l$. We relate number of states to sum rules of\nnine-$j$ coefficients. We obtained sum rules for nine-$j$ coefficients\n$\u003c(jj)J,(jj)K:I| (jj)J, (jj)K:I\u003e$ and $\u003c(ll)J,(ll)K:I| (ll)J, (ll)K:I\u003e$ summing\nover (1) even $J$ and $K$, (2) even $J$ and odd $K$, (3) odd $J$ and odd $K$,\nand (4) both even and odd $J,K$, where $j$ is a half integer and $l$ is an\ninteger.",
    "arxiv_id": "nucl-th/0508018",
    "authors": [
      "Y. M. Zhao",
      "A. Arima"
    ],
    "categories": [
      "nucl-th"
    ],
    "doi": "10.1103/PhysRevC.72.054307",
    "journal_ref": "Phys.Rev. C72 (2005) 054307",
    "title": "$J$-pairing interaction, number of states, and nine-$j$ sum rules of   four identical particles",
    "url": "https://arxiv.org/abs/nucl-th/0508018"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b8685c19-6eed-49b3-ae49-794842667ad3",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}