The Toroidal Orbit Model: A Geometric Framework for Atomic,Molecular, and Nuclear Shell Structure

The Toroidal Orbit Model: A Geometric Framework for Atomic,Molecular, and Nuclear Shell Structure | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article The Toroidal Orbit Model: A Geometric Framework for Atomic,Molecular, and Nuclear Shell Structure James Bourassa This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7697813/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract We introduce the Toroidal Orbit Model (TOM), a geometric seat-filling framework forelectronic shells in atoms and molecules and for nucleonic shells in nuclei. TOM formalizes “tubeseats” around a central potential, derives the 2n2 electron-capacity rule via seat tiling, constructsthe nuclear magic-number sequence 2, 8, 20, 28, 50, 82, 126 without tunable parameters (3L+2Frule), and proposes compact templates for molecular angular distributions (ARPES/HHG). Wepair the framework with preregistered, equal-complexity head-to-head tests in atomic, molecular,and nuclear regimes and provide a reproducibility runbook. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7697813","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":519623481,"identity":"2013c024-7720-4e54-8c20-5e0a280672a3","order_by":0,"name":"James Bourassa","email":"data:image/png;base64,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","orcid":"","institution":"Quantum AetherDynamics Institute","correspondingAuthor":true,"prefix":"","firstName":"James","middleName":"","lastName":"Bourassa","suffix":""}],"badges":[],"createdAt":"2025-09-23 21:53:20","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7697813/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7697813/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":92459175,"identity":"646f0426-edb2-4479-837d-fa3829173d1a","added_by":"auto","created_at":"2025-09-30 03:12:49","extension":"json","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":2628,"visible":true,"origin":"","legend":"","description":"","filename":"3d5fe05989bb4f2fbe3d2ed49709f098.json","url":"https://assets-eu.researchsquare.com/files/rs-7697813/v1/162676261cfdaad2ce4f1cf4.json"},{"id":92970365,"identity":"9d8b0ee9-c71f-48a6-815f-07e740dc8612","added_by":"auto","created_at":"2025-10-07 16:39:37","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1231002,"visible":true,"origin":"","legend":"","description":"","filename":"TOMfoundationsofphysics2.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7697813/v1_covered_dc218e65-c4c4-4b41-8589-8ec5e14bb161.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"The Toroidal Orbit Model: A Geometric Framework for Atomic,Molecular, and Nuclear Shell Structure","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-7697813/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7697813/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"We introduce the Toroidal Orbit Model (TOM), a geometric seat-filling framework forelectronic shells in atoms and molecules and for nucleonic shells in nuclei. 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