The Right Angled Scattering Triangle Pre-Existing as the Scattering Vector Geometry in Partial Wave Analysis

The Right Angled Scattering Triangle Pre-Existing as the Scattering Vector Geometry in Partial Wave Analysis | 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 Right Angled Scattering Triangle Pre-Existing as the Scattering Vector Geometry in Partial Wave Analysis P Bhanumoorthy This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2853859/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 Bragg reflection necessitates an isosceles diffraction triangle. Absence of Bragg reflection contradicts presence of isosceles diffraction triangle. So must be the case with scattering triangle also. Scattering involves no reflection. When incident vector is doubled, reflection is removed and isosceles becomes right angled. And thus the scattering triangle becomes right angled. Partial wave analysis is in spherical coordinates and determines the correct substitute for the polar angle. As the substitute, Bragg angle implies isosceles scattering triangle and scattering angle implies right angled scattering triangle. As a standard, partial wave analysis is formulated with scattering angle as the substitute for polar angle. Hence, partial wave analysis becomes the already existing application for the right angled scattering triangle. Invariance of physical system in partial wave analysis validates the right angled scattering triangle. Standing wave description readily explains the wavelength invariance in elastic scattering with unequal magnitudes of incident and scattered vectors in the right angled. The existing scattering vector geometry as given in textbooks involves isosceles scattering triangle and hence needs to be modified. 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. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-2853859","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":194576831,"identity":"0557090d-2933-454c-8442-cfa5653f9c9a","order_by":0,"name":"P Bhanumoorthy","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA60lEQVRIiWNgGAWjYBACAwk4kwdE2DAwSOBUjK6FDawljXQthwlrMZdufvaYN8dGznx+7zEJxh3nE/tnNx98wFBjE41Li+WcY+bGvNvSjGWO8aVJMJ65nTjjzrFkA4ZjabkNuBx2I8FMmnfb4cQZbDxmEoxttxMbbuQAGQ2H8WhJ/4as5VzifMJaclBsOZC4gZAWyxk5ZZJzgX6RYMsxtmA8k2y88UZaskECHr+YS6Rvk3i7zUZOgvmM4Q3GHXay824kH3zwocYGpxZkwCL9t4HBEawygQjlIMD8gbGBwZ5IxaNgFIyCUTCCAACRlVdTuKRnOAAAAABJRU5ErkJggg==","orcid":"","institution":"Indian Institute of Science","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"P","middleName":"","lastName":"Bhanumoorthy","suffix":""}],"badges":[],"createdAt":"2023-04-24 09:14:33","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2853859/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2853859/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":36411199,"identity":"ad5e94a8-cf70-4ba8-b1d5-72e5b6efe1be","added_by":"auto","created_at":"2023-04-28 06:44:50","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":171937,"visible":true,"origin":"","legend":"","description":"","filename":"20230424Therightangledscatteringtriangle.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2853859/v1_covered_3483cee8-4ed1-4881-84e7-4ba6bb860f90.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"The Right Angled Scattering Triangle Pre-Existing as the Scattering Vector Geometry in Partial Wave Analysis","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"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-2853859/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2853859/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Bragg reflection necessitates an isosceles diffraction triangle.\nAbsence of Bragg reflection contradicts presence of isosceles diffraction triangle.\nSo must be the case with scattering triangle also.\nScattering involves no reflection.\nWhen incident vector is doubled, reflection is removed and isosceles becomes right angled.\nAnd thus the scattering triangle becomes right angled.\nPartial wave analysis is in spherical coordinates and determines the correct substitute for the polar angle.\nAs the substitute, Bragg angle implies isosceles scattering triangle and scattering angle implies right angled scattering triangle.\nAs a standard, partial wave analysis is formulated with scattering angle as the substitute for polar angle.\nHence, partial wave analysis becomes the already existing application for the right angled scattering triangle.\nInvariance of physical system in partial wave analysis validates the right angled scattering triangle.\nStanding wave description readily explains the wavelength invariance in elastic scattering with unequal magnitudes of incident and scattered vectors in the right angled.\nThe existing scattering vector geometry as given in textbooks involves isosceles scattering triangle and hence needs to be modified.\n\n","manuscriptTitle":"The Right Angled Scattering Triangle Pre-Existing as the Scattering Vector Geometry in Partial Wave Analysis","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2023-04-27 02:31:39","doi":"10.21203/rs.3.rs-2853859/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"928af3cd-5e9a-488f-b7ea-d328397b1730","owner":[],"postedDate":"April 27th, 2023","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2023-04-29T01:44:17+00:00","versionOfRecord":[],"versionCreatedAt":"2023-04-27 02:31:39","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-2853859","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-2853859","identity":"rs-2853859","version":["v1"]},"buildId":"WrCJVZZCHTDjtuVLN7oU0","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}