{
  "abstract": "We study the asymptotic behavior of positive ground states of $N$-particle atomic Coulomb Hamiltonians in a two-cluster region. For the $N$-particle ground state $ψ$, its one-particle density $ρ$, and $(N-1)$-particle ground state $ϕ$, we show that for $0<α<1$, as $|x_N|\\to\\infty$, $ψ(x_1,\\dots,x_N)/\\sqrt{ρ(x_N)}= ϕ(x_1,\\dots,x_{N-1})+O(|x_N|^{-2+α} \\ln |x_N|)$ uniformly in the region $|x_i|\\le |x_N|^α$. In the region $|x_i|\\le R_0\\ln |x_N|$, the convergence rate is $O(|x_N|^{-2} (\\ln |x_N|)^2)$. We also establish an $O(|x_N|^{-2})$ bound on the squared $L^2$ error. These results hold both below the essential spectrum and at threshold.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08257",
  "author_total": 1,
  "authors": [
    {
      "name": "Yukimi Goto"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6kgp9d42v82rd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08257",
  "fulltext_url": null,
  "id": "6kgp9d42v82rd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08257",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7212012291",
  "pdf_url": "https://arxiv.org/pdf/2609.08257",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6kgp9d42v82rd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:49Z",
      "native_id": "2609.08257",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08257"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Asymptotics of Ground States for Helium-Like and Bosonic Atoms in a Two-Cluster Region",
  "title_text": "Asymptotics of Ground States for Helium-Like and Bosonic Atoms in a Two-Cluster Region",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/6kgp9d42v82rd",
  "venue": "arXiv",
  "versions": []
}