{
  "abstract": "Within the Jost-random-phase approximation (Jost-RPA), the spurious center-of-mass mode is a zero of the Jost determinant and hence a pole of the $S$ matrix. A zero at zero excitation energy $E$, whether from self-consistency or from a calibration of the residual interaction, is a pole of exactly second order when it has a single independent solution, every unoccupied bound orbital lies above the holes, and each hole is paired with every allowed partial wave; the order follows from the position of the zero, not from self-consistency. The state of this double pole, given by the Autonne-Takagi factorization of its $E^{-2}$ coefficient, is the zero-energy solution normalized by its inertia. In a self-consistent model of one energy density of the neutron and proton densities, every physical $S$-matrix element continued to $E=0$ carries the $E^{-2}$ term, contrary to an earlier conclusion. Subtracting the mode's principal part from the response changes the strength at real $E\\neq0$ only through the smoothing and, in such a model, coincides with the projection of the ideal spurious state. In uncalibrated Woods-Saxon models of $^{16}$O and $^{208}$Pb the mode is a pair of poles on the imaginary axis.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05858",
  "author_total": 1,
  "authors": [
    {
      "name": "Kazuhito Mizuyama"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dr8xty7bgj4j2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05858",
  "fulltext_url": null,
  "id": "dr8xty7bgj4j2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05858",
  "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"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05858",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dr8xty7bgj4j2.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:20:56Z",
      "native_id": "2611.05858",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05858"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:nucl-th",
      "subfield": "nuclear"
    }
  ],
  "title": "Spurious center-of-mass mode as an $S$-matrix pole within the Jost-random-phase approximation",
  "title_text": "Spurious center-of-mass mode as an S-matrix pole within the Jost-random-phase approximation",
  "type": "preprint",
  "updated_at": "2026-11-07T18:20:05Z",
  "url": "https://research.draconitic.com/paper/dr8xty7bgj4j2",
  "venue": "arXiv",
  "versions": []
}