{
  "annotation_id": "333750b0-ff71-4dc1-a069-7195a1cc3f5a",
  "date_created": "2026-03-02T18:00:01.309000Z",
  "date_modified": "2026-03-02T18:00:01.309000Z",
  "file_hash": "ddb5c96c77d60d1a1fd44bdf4b91874645302d542044c44d240f532a6010d54b",
  "private": false,
  "record": {
    "abstract": "The many $2^k$-pole boson states, $|N_kv_k\\alpha_k I_kM_k\u003e$ with $k=2,3$,\nrealize the irreducible representation (IR) for the group reduction chains\n$SU(2k+1)\\supset R_{2k+1}\\supset R_3\\supset R_2$. They have been analytically\nstudied and widely used for the description of nuclear systems. However, no\nanalytical expression for the degeneracy $d_v(I)$ of the $R_{2k+1}$\u0027s IR,\ndetermined by the reduction $R_{2k+1}\\supset R_3$, is available. Thus, the\nnumber of distinct values taken by $\\alpha_k$ has been so far obtained by\nsolving some complex equations. Here we derive analytical expressions for the\ndegeneracy $d_v(I)$ characterizing the octupole and quadrupole boson states,\nrespectively. The merit of this work consists of the fact that it completes the\nanalytical expressions for the $2^k$-pole boson basis.",
    "arxiv_id": "nucl-th/0405065",
    "authors": [
      "A. Gheorghe",
      "A. A. Raduta"
    ],
    "categories": [
      "nucl-th"
    ],
    "doi": "10.1088/0305-4470/37/45/013",
    "journal_ref": "J.Phys. A37 (2004) 10951-10958",
    "title": "New results for the missing quantum numbers labeling the quadrupole and   octupole boson basis",
    "url": "https://arxiv.org/abs/nucl-th/0405065"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5aed281f-be25-43a7-b045-bdf70b60b689",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}