{
  "abstract": "We present a closed-form construction of the orbital coefficients of fractional parentage (CFP) of three identical particles in the translationally invariant harmonic oscillator (HO) Jacobi basis. These are usually obtained by numerically diagonalizing a permutation operator in every energy-angular-momentum block. We show this diagonalization is unnecessary. Dressing the class operator $P_{13} + P_{23}$ with the single unitary $W = H^1 Φ$ -- a fixed complexification followed by the HO bracket with mass parameter $d=1$ -- turns it into the label swap times an integer. Every CFP is then the single ket $|K_{i,s}\\rangle = 2Q^s W^\\dagger|i\\rangle$ -- a 2-scaled, sign-decorated column of the $d=1$ bracket restricted to one $e_2$-parity of the labels -- whose norm, $1 + s\\langle i | J | i \\rangle$, is itself a single matrix element. The same $W$ carries label parity into swap symmetry, $W Q^s W^\\dagger = R^s$, making the bookkeeping collapse. The eigenvalues are exact integers $\\pm 2$ and $\\pm 1$ labeling the $S(3)$ symmetry classes. The construction is uniform in $E$, $L$ and symmetry class, reducing CFP-specific work from $O(n^3)$ to $O(n^2)$ in block dimension. An eigensolver remains only inside the bracket engine supplying $H^1$, where all residual numerical error originates. We implement this on an SU(3)-basis bracket engine, checking all 1301 blocks up to $E=50$ (912 366 CFPs, largest block $2907 \\times 2907$): the $S(3)$ class assignment is exact everywhere. The residual numerical error (entirely the bracket engine's) stays below $10^{-8}$ for $E \\leq 35$, restoring to $\\leq 10^{-22}$ via a quadruple-precision build beyond that. We further validate against independently generated antisymmetrization data of a production three-nucleon code, including the $^3$He ground-state energy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Nuclear Physics A .Volume 1077, 2027, 123535, ISSN 0375-9474",
  "arxiv": "2610.21385",
  "author_total": 3,
  "authors": [
    {
      "name": "A. Stepšys"
    },
    {
      "name": "S. Mickevičius"
    },
    {
      "name": "D. Germanas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/78hka3qnyhrns.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21385",
  "fulltext_url": null,
  "id": "78hka3qnyhrns",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21385",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "nucl-th"
    ],
    [
      "arxiv",
      "physics.comp-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.21385",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/78hka3qnyhrns.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:50Z",
      "native_id": "2610.21385",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21385"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:nucl-th",
      "subfield": "nuclear"
    }
  ],
  "title": "Algebraic coefficients of fractional parentage for three particles in the oscillator Jacobi basis",
  "title_text": "Algebraic coefficients of fractional parentage for three particles in the oscillator Jacobi basis",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:50Z",
  "url": "https://research.draconitic.com/paper/78hka3qnyhrns",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1016/j.nuclphysa.2026.123535",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}