{"title":"Determination of Asymptotic Normalization Coefficients by Analytic Continuation of the \\({R}\\)-Matrix","authors":"L. D. Blokhintsev, D. A. Savin","doi":"10.1134/S1063778824700042","DOIUrl":null,"url":null,"abstract":"<p>The method of finding the values of asymptotic normalization coefficients (ANC) is proposed based on the analytic continuation of the <span>\\(R\\)</span>-matrix that describes the elastic nuclear scattering into the unphysical region of the negative energy of collision (<span>\\(E<0\\)</span>). The formula is derived, expressing the partial-wave scattering amplitude through the <span>\\(R\\)</span>-matrix and modified Coulomb functions. This formula allows, when continuing the amplitude to the region <span>\\(E<0\\)</span>, to overcome difficulties associated with irregular behavior of the scattering amplitude near <span>\\(E=0\\)</span> if the Coulomb interaction is present. The proposed method is used to determine the ANC for the channel <span>\\({}^{16}\\textrm{O}\\to\\alpha+{}^{12}\\)</span>C.</p>","PeriodicalId":728,"journal":{"name":"Physics of Atomic Nuclei","volume":"87 3","pages":"352 - 358"},"PeriodicalIF":0.3000,"publicationDate":"2024-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1134/S1063778824700042.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physics of Atomic Nuclei","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S1063778824700042","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"PHYSICS, NUCLEAR","Score":null,"Total":0}
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Abstract
The method of finding the values of asymptotic normalization coefficients (ANC) is proposed based on the analytic continuation of the \(R\)-matrix that describes the elastic nuclear scattering into the unphysical region of the negative energy of collision (\(E<0\)). The formula is derived, expressing the partial-wave scattering amplitude through the \(R\)-matrix and modified Coulomb functions. This formula allows, when continuing the amplitude to the region \(E<0\), to overcome difficulties associated with irregular behavior of the scattering amplitude near \(E=0\) if the Coulomb interaction is present. The proposed method is used to determine the ANC for the channel \({}^{16}\textrm{O}\to\alpha+{}^{12}\)C.
期刊介绍：
Physics of Atomic Nuclei is a journal that covers experimental and theoretical studies of nuclear physics: nuclear structure, spectra, and properties; radiation, fission, and nuclear reactions induced by photons, leptons, hadrons, and nuclei; fundamental interactions and symmetries; hadrons (with light, strange, charm, and bottom quarks); particle collisions at high and superhigh energies; gauge and unified quantum field theories, quark models, supersymmetry and supergravity, astrophysics and cosmology.
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