{
  "abstract": "A particle launched normally into a half space, scattering by the Henyey-Greenstein (HG) phase function, exits after a first-return time whose count of flights n approaches the distribution-free Sparre Andersen exponent, f(n) ~ n^{-3/2}, with an amplitude fixed by the launch rather than by the theorem. Conditioned on n, and past a correlation-set transient, the lateral exit position is Gaussian with variance proportional to n, a scaling we test directly. Subordinating that Gaussian displacement to the one-sided 1/2-stable first-return time gives, in the diffusion limit, an isotropic 1-stable scaling limit: the far tail of the point-spread function (PSF) for a normally incident pencil beam is the two-dimensional Cauchy tail p(r) ~ r^{-3}, the large-radius limit of the half-space Poisson kernel. The index alpha = 1 is the product of the central limit theorem and the distribution-free first-return exponent, so no phase function admitting the same diffusion limit - finite step variance, short-range angular correlation - can move it. Absorption weights each path by exp(-mu_a L) in its total length L, truncating the subordinator and producing the screened radial structure (mu_eff + 1/r) exp(-mu_eff r)/r^2 carried by each source term of the Farrell-Patterson-Wilson (1992) diffusion dipole; the finite-depth two-source dipole is not derived here. Keeping the launch-depth factor that the tail calculation discards continues the same kernel into a finite core of radius 1.7 l*, with no additional fitted parameter. A scale-dependent index alpha_eff from the empirical characteristic function tracks the similarity parameter gamma, separating phase functions matched in g_1 by 0.15-0.22 near one transport mean free path. Results are Monte Carlo at g = 0 to 0.9 with up to 10^6 walkers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28940",
  "author_total": 2,
  "authors": [
    {
      "name": "Claude Zeller"
    },
    {
      "name": "Robert Cordery"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dhr9c9x1hkr8w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28940",
  "fulltext_url": null,
  "id": "dhr9c9x1hkr8w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28940",
  "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",
      "physics.optics"
    ],
    [
      "openalex",
      "2741|Optical Imaging and Spectroscopy Techniques"
    ]
  ],
  "openalex": "W7204883937",
  "pdf_url": "https://arxiv.org/pdf/2608.28940",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dhr9c9x1hkr8w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "2608.28940",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28940"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.optics",
      "subfield": "optics-photonics"
    }
  ],
  "title": "First-return statistics and the point-spread function of a Henyey-Greenstein random walk - a far-field stable law",
  "title_text": "First-return statistics and the point-spread function of a Henyey-Greenstein random walk - a far-field stable law",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:41Z",
  "url": "https://research.draconitic.com/paper/dhr9c9x1hkr8w",
  "venue": "arXiv",
  "versions": []
}