{
  "annotation_id": "fd29b6db-94a1-42b6-b108-b2ae40e2479d",
  "date_created": "2026-03-02T18:02:41.308000Z",
  "date_modified": "2026-03-02T18:02:41.308000Z",
  "file_hash": "98015076c98c105e5f04b046241720baa749639030f77f469d988f25accd78ed",
  "private": false,
  "record": {
    "abstract": "We study the critical behaviour near the threshold where a first bound state\nappears at some value of coupling constant in an attractive short-range\npotential in $2+\\epsilon $ dimensions. We obtain general expression for the\nbinding energy near the threshold and also demonstrate that the critical region\nis correctly described by an effective separable potential. The critical\nexponent of the radius of weakly bound state is shown to coincide with the\ncorrelation length exponent for the spin model in the large-N limit. In two\ndimensions, where the binding energy is exponentially small in coupling\nconstant, we obtain a general analytic expression for the prefactor.",
    "arxiv_id": "quant-ph/9803010",
    "authors": [
      "S. M. Apenko"
    ],
    "categories": [
      "quant-ph",
      "nucl-th"
    ],
    "doi": "10.1088/0305-4470/31/6/007",
    "journal_ref": "J.Phys.A31:1553-1562,1998",
    "title": "Weakly bound states in 2+\\epsilon dimensions",
    "url": "https://arxiv.org/abs/quant-ph/9803010"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "78d23547-693e-44b8-8744-52c645bf6c91",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}