{
  "abstract": "In this paper, we show that the optical depths of any OH $Λ$-doublet quartet obey one exact linear relation in every velocity channel. No approximation is needed. The only exception is the $^{2}Π_{1/2}$ $J{=}1/2$ level, which has three transitions only, because its $F{=}0{\\leftrightarrow}0$ line is strictly forbidden. The relation is $τ_{S_1}(v)/μ_{S_1}^{2}+τ_{S_2}(v)/μ_{S_2}^{2}=τ_{M_1}(v)/(aμ_{M_1}^{2})+τ_{M_2}(v)/(bμ_{M_2}^{2})$, where $a=2J^{2}+J-1$, $b=2J^{2}+3J$, and the $μ_i^{2}$ are reduced transition dipole moments derived from the catalogued Einstein $A$ coefficients. It holds equally for gas in local thermodynamic equilibrium (LTE), for non-LTE gas, for masers and for conjugate gas. We suggest that it is a powerful tool for measuring the variation of fundamental physical constants.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36007",
  "author_total": 2,
  "authors": [
    {
      "name": "Renzhi Su"
    },
    {
      "name": "Minfeng Gu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0ry3c7bppczpv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36007",
  "fulltext_url": null,
  "id": "0ry3c7bppczpv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.36007",
  "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",
      "astro-ph.CO"
    ],
    [
      "arxiv",
      "physics.atom-ph"
    ],
    [
      "openalex",
      "3107|Atomic and Molecular Physics"
    ]
  ],
  "openalex": "W7224101056",
  "pdf_url": "https://arxiv.org/pdf/2610.36007",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0ry3c7bppczpv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:50Z",
      "native_id": "2610.36007",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36007"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.CO",
      "subfield": "cosmology"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.atom-ph",
      "subfield": "amo"
    }
  ],
  "title": "Derivation of OH sum rules without Rayleigh--Jeans approximation: a powerful tool for measuring the variation of fundamental physical constants",
  "title_text": "Derivation of OH sum rules without Rayleigh--Jeans approximation: a powerful tool for measuring the variation of fundamental physical constants",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:50Z",
  "url": "https://research.draconitic.com/paper/0ry3c7bppczpv",
  "venue": "arXiv",
  "versions": []
}