{
  "abstract": "We develop a deterministic radial approximation to the static Bethe-Salpeter equation (BSE), designed for rapid preliminary screening of Wannier-Mott exciton binding across direct-gap bulk materials. The approximation replaces the electron-hole transition problem by small radial eigenvalue problems that require no stochastic sampling. Starting from the four-point BSE and its matrix representation in a Bloch electron-hole basis, we retain one valence and one conduction band in the effective-mass limit within the Tamm-Dancoff approximation. We introduce a central projection of the screened direct interaction and omit bare electron-hole exchange. The resulting model applies to spatially extended excitons whose envelopes vary slowly on the scale of the unit cell, provided that the effective-mass description and central screened interaction adequately represent the exciton of interest. A partial-wave decomposition separates the angular-momentum channels and expresses their interaction kernels as spherical-Bessel transforms of the real-space screened Coulomb interaction. Nyström discretization produces real symmetric radial matrices suitable for standard eigensolvers. Their dimension is set by the radial grid independently of the Brillouin-zone sampling used to calculate screening. We implement the formulation in the all-electron, full-potential code $\\texttt{exciting}$. For bulk GaAs, the compact radial problem reproduces the corresponding conventional matrix-BSE binding energy within $(1~\\mathrm{meV})$ at matched sampling. Further refinement achieves finite-mesh stability within the same tolerance on denser screening meshes without increasing the radial matrix size.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01570",
  "author_total": 3,
  "authors": [
    {
      "name": "Christian Tantardini"
    },
    {
      "name": "Benedikt Maurer"
    },
    {
      "name": "Claudia Draxl"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/09032m7002419.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01570",
  "fulltext_url": null,
  "id": "09032m7002419",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01570",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.mtrl-sci"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01570",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/09032m7002419.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:59Z",
      "native_id": "2611.01570",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01570"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mtrl-sci",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Fredholm approximations to the Bethe-Salpeter equation with spherical-Bessel kernels for Wannier-Mott excitons",
  "title_text": "Fredholm approximations to the Bethe-Salpeter equation with spherical-Bessel kernels for Wannier-Mott excitons",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:18Z",
  "url": "https://research.draconitic.com/paper/09032m7002419",
  "venue": "arXiv",
  "versions": []
}