Impact of the Confinement Strength on the Energy Spectra of Two Atoms Interacting via Zero-Range or Realistic Potentials

Impact of the Confinement Strength on the Energy Spectra of Two Atoms Interacting via Zero-Range or Realistic 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 Impact of the Confinement Strength on the Energy Spectra of Two Atoms Interacting via Zero-Range or Realistic Potentials Jakob Wulff, Matee ur Rehman, Alejandro Saenz This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9425981/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 5 You are reading this latest preprint version Abstract This work analyzes the influence of an external confinement on the energy spectrum of two interacting ultracold atoms, considering either a regularized contact or a more realistic Born-Oppenheimer potential. For two harmonically confined particles with contact interaction, the known analytical solution exhibits universality in the sense that the energy spectra solely depend on the ratio of the confinement length to the scattering length. In this work it is shown that this type of universality breaks down for realistic interatomic interactions, leading to an explicit trap-size dependence of the energy spectrum. This effect is especially pronounced for very tight confinement. Using first-order perturbation theory it is shown analytically that the here discussed universality persists for the contact interaction even in the case of anharmonic confinement, this result being also verified numerically beyond perturbation theory for a sextic trap potential. These findings demonstrate limitations of the popular contact-interaction model and highlight the necessity of considering more realistic finite-range interactions under tight trapping conditions. Full Text Additional Declarations Competing interest reported. One of the authors, A.S., is on the board of editors of Few-Body Systems and receives no compensation as member of the board of editors. Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 28 Apr, 2026 Reviewers invited by journal 23 Apr, 2026 Editor assigned by journal 17 Apr, 2026 Submission checks completed at journal 17 Apr, 2026 First submitted to journal 15 Apr, 2026 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. 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