{
  "annotation_id": "753d38c3-c9da-4cbc-be58-2d5272488b70",
  "date_created": "2026-03-02T17:59:57.639000Z",
  "date_modified": "2026-03-02T17:59:57.639000Z",
  "file_hash": "94deb7a70fd50a58d5a820c5afb8daba4babd74b6ccb54aa383d25befac90ce0",
  "private": false,
  "record": {
    "abstract": "We present in this paper empirical formulas for the number of angular\nmomentum I states for three and four identical fermions or bosons. In the cases\nwith large I we prove that the number of states with the same ${\\cal M}$ and n\nbut different J is identical if $I \\ge (n-2)J - {1/2} (n-1)(n-2)$ for fermions\nand $I \\ge (n-2)J$ for bosons, and that the number of states is also identical\nfor the same ${\\cal M}$ but different n and J if ${\\cal M} \\le $min(n, 2J+1 -\nn) for fermions and for ${\\cal M} \\le $min(n, 2J) for bosons. Here ${\\cal M}\n=I_{max}-I$, n is the particle number, and J refers to the angular momentum of\na single-particle orbit for fermions, or the spin L carried by bosons.",
    "arxiv_id": "nucl-th/0304038",
    "authors": [
      "Y. M. Zhao",
      "A. Arima"
    ],
    "categories": [
      "nucl-th"
    ],
    "doi": "10.1103/PhysRevC.68.044310",
    "journal_ref": "Phys.Rev. C68 (2003) 044310",
    "title": "Number of states with fixed angular momentum for identical fermions and   bosons",
    "url": "https://arxiv.org/abs/nucl-th/0304038"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0d48fc4c-8a26-454c-9b4d-a29a1caf5340",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}