Jost function for the description of resonance in finite quantum multichannel systems

Jost function for the description of resonance in finite quantum multichannel systems | 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 Jost function for the description of resonance in finite quantum multichannel systems Kazuhito Mizuyama This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8501414/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 10 Mar, 2026 Read the published version in Few-Body Systems → Version 1 posted 9 You are reading this latest preprint version Abstract The Jost function is defined as the coefficient function connecting the regular and irregular solutions of the fundamental differential equations. It is known that the zeros of the Jost function on the complex energy plane correspond to the poles of the S-matrix, which represent the complex eigenvalues of bound and resonant states. This paper reviews our recent extensions of the Jost function method to nuclear multichannel systems, specifically within the frameworks of the Hartree-Fock-Bogoliubov (HFB) theory and the Random Phase Approximation (RPA) theory (Jost-RPA method). A unitary S-matrix is derived using these extended Jost functions. By focusing on the poles of the S-matrix, we attempt to analyze and classify the resonances. We discuss three key applications: (1) the extraction of Fano parameters to analyze asymmetric line shapes in neutron scattering within the HFB framework, (2) the decomposition of the RPA strength function using eigenphase shifts, and (3) the application of the Mittag-Leffler theorem to decompose the RPA response into contributions from individual resonance poles. Jost function Resonance Hartree-Fock-Bogoliubov Random-phase approximation Fano effect Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 10 Mar, 2026 Read the published version in Few-Body Systems → Version 1 posted Editorial decision: Accepted 26 Feb, 2026 Reviews received at journal 12 Feb, 2026 Reviewers agreed at journal 28 Jan, 2026 Reviews received at journal 21 Jan, 2026 Reviewers agreed at journal 14 Jan, 2026 Reviewers invited by journal 09 Jan, 2026 Editor assigned by journal 08 Jan, 2026 Submission checks completed at journal 03 Jan, 2026 First submitted to journal 02 Jan, 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. 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Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Jost function, Resonance, Hartree-Fock-Bogoliubov, Random-phase approximation, Fano effect","lastPublishedDoi":"10.21203/rs.3.rs-8501414/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8501414/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":" The Jost function is defined as the coefficient function connecting the regular and irregular solutions\n of the fundamental differential equations. It is known that the zeros of the Jost function on the complex\n energy plane correspond to the poles of the S-matrix, which represent the complex eigenvalues of bound\n and resonant states. This paper reviews our recent extensions of the Jost function method to nuclear\n multichannel systems, specifically within the frameworks of the Hartree-Fock-Bogoliubov (HFB) theory and\n the Random Phase Approximation (RPA) theory (Jost-RPA method). A unitary S-matrix is derived using these extended Jost functions.\n By focusing on the poles of the S-matrix, we attempt to\n analyze and classify the resonances. 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