{
  "annotation_id": "dd8525e5-56e0-4f61-9b19-593c293cd6f4",
  "date_created": "2026-03-02T18:00:04.610000Z",
  "date_modified": "2026-03-02T18:00:04.610000Z",
  "file_hash": "a607722aa9c2508a05ec010d1cc61c96df9346efc3219f360611ebd98c5ace14",
  "private": false,
  "record": {
    "abstract": "We consider the three-boson problem with $\\delta$-function interactions in\none spatial dimension. Three different approaches are used to calculate the\nphase shifts, which we interpret in the context of the effective range\nexpansion, for the scattering of one free particle a off of a bound pair. We\nfirst follow a procedure outlined by McGuire in order to obtain an analytic\nexpression for the desired S-matrix element. This result is then compared to a\nvariational calculation in the adiabatic hyperspherical representation, and to\na numerical solution to the momentum space Faddeev equations. We find excellent\nagreement with the exact phase shifts, and comment on some of the important\nfeatures in the scattering and bound-state sectors. In particular, we find that\nthe 1+2 scattering length is divergent, marking the presence of a zero-energy\nresonance which appears as a feature when the pair-wise interactions are\nshort-range. Finally, we consider the introduction of a three-body interaction,\nand comment on the cutoff dependence of the coupling.",
    "arxiv_id": "nucl-th/0504049",
    "authors": [
      "Nirav P. Mehta",
      "James R. Shepard"
    ],
    "categories": [
      "nucl-th"
    ],
    "doi": "10.1103/PhysRevA.72.032728",
    "title": "Three Bosons in One Dimension with Short Range Interactions I: Zero   Range Potentials",
    "url": "https://arxiv.org/abs/nucl-th/0504049"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "484c27b9-bc77-4fc4-8114-2ab014125898",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}