Tune-out and Magic Wavelengths for Helium Atom with Exponential-Cosine-Screened Coulomb Potentials

Yi-Han Wang, Zishi Jiang, Sabyasachi Kar
2026 · doi:10.21203/rs.3.rs-8770762/v1
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This study reports tune-out and magic wavelengths for helium atom states and transitions under exponential-cosine-screened Coulomb potentials, showing unique features as functions of the screening parameter.

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The paper investigates how exponential-cosine-screened Coulomb potentials (ECSCP) affect tune-out wavelengths and magic wavelengths for a helium atom, using correlated exponential wavefunctions and a pseudostate summation approach. It reports first tune-out wavelengths for specific 1S and 3S states, magic wavelengths for the 2 3S→3 3S transition, and dynamic dipole polarizabilities for selected singlet and triplet S states, all as functions of the ECSCP screening parameter, with results in free-atom cases agreeing with available theoretical and experimental data. A key limitation is that the study focuses on these model potentials and helium’s atomic structure calculations rather than any directly experimental or many-body condensed-phase context. The paper does not explicitly discuss endometriosis or adenomyosis; it was included in the corpus via a keyword match in the upstream search index.

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Abstract

Abstract We investigate the effects of exponential-cosine-screened Coulomb potentials (ECSCP) on the tune-out and magic wavelengths (TMW) of helium atom using correlated exponential wavefunctions based on the pseudostate summation approach. The first tune-out wavelengths (TWs) for the \(\:{\text{}\text{n}}^{\text{}\text{1}}\text{S\:(}\text{n}\text{}\text{=}\text{}\text{1,}\text{}\text{2,}\text{}\text{3)\:}\)and \(\:{\text{n}\text{}}^{\text{3}}\text{S}\text{\:(}\text{n}\text{}\text{=}\text{}\text{2,}\text{}\text{3}\text{)\:}\)states, and the magic wavelengths (MWs) for the \(\:{\text{2}}^{\text{3}}\text{S}\text{}\text{→}{\text{}\text{3}}^{\text{3}}\text{S}\) transition along with the dynamic dipole polarizabities (DDP) for the \(\:{\text{}\text{n}}^{\text{}\text{1}}\text{S\:(}\text{n}\text{}\text{=}\text{}\text{1,}\text{}\text{2,}\text{}\text{3)\:}\) and \(\:{\text{n}\text{}}^{\text{3}}\text{S}\text{\:(}\text{n}\text{}\text{=}\text{}\text{2,}\text{}\text{3}\text{)\:}\)states of helium atom are reported as functions of screening parameter. Our results in the free-atom cases are in good accord with the available theoretical and experimental data. Moreover, the TMW exhibit interesting features as functions of screening parameters, reflecting the unique characteristics of ECSCP.
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Tune-out and Magic Wavelengths for Helium Atom with Exponential-Cosine-Screened Coulomb Potentials | 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 Tune-out and Magic Wavelengths for Helium Atom with Exponential-Cosine-Screened Coulomb Potentials Yi-Han Wang, Zishi Jiang, Sabyasachi Kar This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8770762/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 investigate the effects of exponential-cosine-screened Coulomb potentials (ECSCP) on the tune-out and magic wavelengths (TMW) of helium atom using correlated exponential wavefunctions based on the pseudostate summation approach. The first tune-out wavelengths (TWs) for the \(\:{\text{}\text{n}}^{\text{}\text{1}}\text{S\:(}\text{n}\text{}\text{=}\text{}\text{1,}\text{}\text{2,}\text{}\text{3)\:}\) and \(\:{\text{n}\text{}}^{\text{3}}\text{S}\text{\:(}\text{n}\text{}\text{=}\text{}\text{2,}\text{}\text{3}\text{)\:}\) states, and the magic wavelengths (MWs) for the \(\:{\text{2}}^{\text{3}}\text{S}\text{}\text{→}{\text{}\text{3}}^{\text{3}}\text{S}\) transition along with the dynamic dipole polarizabities (DDP) for the \(\:{\text{}\text{n}}^{\text{}\text{1}}\text{S\:(}\text{n}\text{}\text{=}\text{}\text{1,}\text{}\text{2,}\text{}\text{3)\:}\) and \(\:{\text{n}\text{}}^{\text{3}}\text{S}\text{\:(}\text{n}\text{}\text{=}\text{}\text{2,}\text{}\text{3}\text{)\:}\) states of helium atom are reported as functions of screening parameter. Our results in the free-atom cases are in good accord with the available theoretical and experimental data. Moreover, the TMW exhibit interesting features as functions of screening parameters, reflecting the unique characteristics of ECSCP. tune-out wavelength magic wavelength dynamic dipole polarizability Exponential-cosine-screened Coulomb potentials correlated exponential wavefunctions Rayleigh-Ritz variation method Hylleraas-Undheim method 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-8770762","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":588787398,"identity":"a74b098b-4c24-4e44-acf2-92d897144f10","order_by":0,"name":"Yi-Han Wang","email":"","orcid":"","institution":"Heilongjiang University","correspondingAuthor":false,"prefix":"","firstName":"Yi-Han","middleName":"","lastName":"Wang","suffix":""},{"id":588787399,"identity":"008bfca6-9b57-42f6-9e57-34bf92108e1d","order_by":1,"name":"Zishi Jiang","email":"","orcid":"","institution":"Heilongjiang University","correspondingAuthor":false,"prefix":"","firstName":"Zishi","middleName":"","lastName":"Jiang","suffix":""},{"id":588787400,"identity":"05b00615-772d-49a9-a639-a0172e11d408","order_by":2,"name":"Sabyasachi Kar","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAtElEQVRIiWNgGAWjYBACCQYGxscMBWwgtgHRWpiNGQxI1MImDVVMpBbJ9rPPqgsM+BIb2Ju3STDU3CGsRZon3ez2DAO2xAaeY2USDMeeEdYix5DGdpsHpEUix0yCseEwEVr4n7EVg7XIvyFSi7REGhszxBYeIrVIznjGLA3UYtzGk1ZskXCMCC0S59MYP/NUHJPtZz+88caHGiK0QMExBnBkJhCtgYGhhgS1o2AUjIJRMOIAAFhFLdPnOoByAAAAAElFTkSuQmCC","orcid":"","institution":"Heilongjiang University","correspondingAuthor":true,"prefix":"","firstName":"Sabyasachi","middleName":"","lastName":"Kar","suffix":""}],"badges":[],"createdAt":"2026-02-03 04:23:21","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8770762/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8770762/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104705406,"identity":"6a80a11c-35fb-49fb-837d-625d45d3b4ed","added_by":"auto","created_at":"2026-03-16 09:14:23","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1183770,"visible":true,"origin":"","legend":"","description":"","filename":"WangJiangKarFBS2026version1.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8770762/v1_covered_20c10394-d097-4e2d-b556-2a114e48405f.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Tune-out and Magic Wavelengths for Helium Atom with Exponential-Cosine-Screened Coulomb Potentials","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":"tune-out wavelength, magic wavelength, dynamic dipole polarizability, Exponential-cosine-screened Coulomb potentials, correlated exponential wavefunctions, Rayleigh-Ritz variation method, Hylleraas-Undheim method","lastPublishedDoi":"10.21203/rs.3.rs-8770762/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8770762/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe investigate the effects of exponential-cosine-screened Coulomb potentials (ECSCP) on the tune-out and magic wavelengths (TMW) of helium atom using correlated exponential wavefunctions based on the pseudostate summation approach. 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Our results in the free-atom cases are in good accord with the available theoretical and experimental data. Moreover, the TMW exhibit interesting features as functions of screening parameters, reflecting the unique characteristics of ECSCP.\u003c/p\u003e","manuscriptTitle":"Tune-out and Magic Wavelengths for Helium Atom with Exponential-Cosine-Screened Coulomb Potentials","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-11 13:50:15","doi":"10.21203/rs.3.rs-8770762/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":"2ebb0d1b-f716-4ec6-abab-2f370aaf5af4","owner":[],"postedDate":"February 11th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-03-16T09:13:49+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-11 13:50:15","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8770762","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8770762","identity":"rs-8770762","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}

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