{
  "annotation_id": "34ee1043-9772-48cb-a625-5b4a41475490",
  "date_created": "2026-03-02T18:02:03.648000Z",
  "date_modified": "2026-03-02T18:02:03.648000Z",
  "file_hash": "00f85f50adf3977a103678f286668d217749344d116ae175c20367c18aa742b4",
  "private": false,
  "record": {
    "abstract": "We show that a quantum system with nonlocal interaction can have bound states\nof unusual type -- Isolated States (IS). IS is a bound state that is not in\ncorrespondence with the $S$-matrix pole. IS can have a positive as well as a\nnegative energy and can be treated as a generalization of the bound states\nembedded in continuum on the case of discrete spectrum states. The formation of\nIS in the spectrum of a quantum system is studied using a simple rank--2\nseparable potential with harmonic oscillator form factors. Some physical\napplications are discussed, in particular, we propose a separable $NN$\npotential supporting IS that describes the deuteron binding energy and the\ns-wave triplet and singlet scattering phase shifts. We use this potential to\nexamine the so-called problem of the three-body bound state collapse discussed\nin literature. We show that the variation of the two-body IS energy causes\ndrastic changes of the binding energy and of the spectrum of excited states of\nthe three-nucleon system.",
    "arxiv_id": "quant-ph/0312065",
    "authors": [
      "A. M. Shirokov",
      "S. A. Zaytsev"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "$J$-matrix and Isolated States",
    "url": "https://arxiv.org/abs/quant-ph/0312065"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "21ba232f-cfe8-451f-8801-49bd48e9ad50",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}