{
  "annotation_id": "04d5e988-8d10-4acd-8fde-d6de68498369",
  "date_created": "2026-03-02T18:00:11.715000Z",
  "date_modified": "2026-03-02T18:00:11.715000Z",
  "file_hash": "0b51abd879a65ebc39abbd55a33eb6730a34bd7816f92aa422d31e4d2e7bb394",
  "private": false,
  "record": {
    "abstract": "We report empirical findings that a simple formula in terms of the mass\nnumber $A$, the valence proton number $N_p$, and the valence neutron number\n$N_n$ can describe the essential trends of excitation energies $E_x$ of the\nfirst $2^+$ and $3^-$ states in even-even nuclei throughout the periodic table.\nThe formula reads as $E_x = \\alpha A^{-\\beta} + \\exp (- \\lambda N_p) + \\exp (-\n\\lambda N_n)$. The parameter $\\beta$ in the first term is determined by the\nmass number $A$ dependence of the bottom contour line of the excitation energy\nsystematics. The other two parameters $\\alpha$ and $\\lambda$ are fitted by\nminimizing the $\\chi^2$ value between the measured and calculated excitation\nenergies. Our results suggest that the single large-$j$ shell simulation can be\napplied to the excitation energies of the first $2^+$ and $3^-$ states in\neven-even nuclei.",
    "arxiv_id": "nucl-th/0612003",
    "authors": [
      "Eunja Ha",
      "Dongwoo Cha"
    ],
    "categories": [
      "nucl-th"
    ],
    "doi": "10.3938/jkps.50.1172",
    "journal_ref": "J. Korean Phys. Soc. 50 (2007) 1172-1175",
    "title": "Empirical formula for the excitation energies of the first $2^+$ and   $3^-$ states in even-even nuclei",
    "url": "https://arxiv.org/abs/nucl-th/0612003"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d4503da9-e062-45cb-8c95-2d6220748889",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}