{
  "abstract": "Proton and neutron densities can have similar multipole moments while differing locally. We use differential forms to measure and locate such differences between nuclear mean fields. A pair invariant measures the angle between two density gradients, weighted by their magnitudes, and the coarea formula resolves its contribution over level surfaces. A triple invariant factorizes exactly into a weighted pair term and a directional term that measures the variation of a third field along the level-surface intersections. We test these quantities in 98 magnetized Wigner-Seitz solutions, five static Hartree-Fock configurations, an illustrative $^{16}$O + $^{34}$Mg collision, and periodic nuclear pasta (a slab and a connected network). The pair invariant distinguishes cell solutions with comparable proton quadrupole moments and is 253 times larger in $^{34}$Mg than in $^{24}$Mg; refinement to 0.6 fm changes it by at most 1.3% in the four configurations recomputed. The directional factor separates the sampled triaxial configurations from the prolate ones. In the collision, it accounts for the 7.3-fold rise of the triple before the first recorded low-density connection, while the weighted pair term changes by at most 3%. In nuclear pasta, slab and network configurations have similar integrated proton-neutron misalignment but different distributions over density levels; their triple invariants differ by a factor of about 370 on the finer grid, mainly due to the variation of the Coulomb potential along joint density levels. These comparisons require no preferred origin or axis. A resolved nonzero triple excludes a common symmetry axis, but zero does not establish one. The pasta results require further convergence studies.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30046",
  "author_total": 1,
  "authors": [
    {
      "name": "Rafael C. R. de Lima"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dbc6ycf05cwg3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30046",
  "fulltext_url": null,
  "id": "dbc6ycf05cwg3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30046",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "nucl-th"
    ],
    [
      "openalex",
      "3106|Nuclear physics research studies"
    ]
  ],
  "openalex": "W7223203408",
  "pdf_url": "https://arxiv.org/pdf/2610.30046",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dbc6ycf05cwg3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:19Z",
      "native_id": "2610.30046",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30046"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:nucl-th",
      "subfield": "nuclear"
    }
  ],
  "title": "Relative geometry of nuclear mean fields through differential forms",
  "title_text": "Relative geometry of nuclear mean fields through differential forms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/dbc6ycf05cwg3",
  "venue": "arXiv",
  "versions": []
}