{"title":"Differential equation for the Uehling potential","authors":"Alexei M. Frolov","doi":"10.1140/epjb/s10051-024-00728-x","DOIUrl":null,"url":null,"abstract":"<p>The second-order differential equation for the Uehling potential is derived explicitly. The right side of this differential equation is a linear combination of the two Macdonald’s functions <span>\\(K_{0}(b r)\\)</span> and <span>\\(K_{1}(b r)\\)</span>. This central potential is of great interest in many QED problems, since it describes the lowest order correction for vacuum polarization in few- and many-electron atoms, ions, muonic and bi-muonic atoms/ions as well as in other similar systems.</p>","PeriodicalId":787,"journal":{"name":"The European Physical Journal B","volume":"97 6","pages":""},"PeriodicalIF":1.6000,"publicationDate":"2024-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"The European Physical Journal B","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1140/epjb/s10051-024-00728-x","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, CONDENSED MATTER","Score":null,"Total":0}
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Abstract
The second-order differential equation for the Uehling potential is derived explicitly. The right side of this differential equation is a linear combination of the two Macdonald’s functions \(K_{0}(b r)\) and \(K_{1}(b r)\). This central potential is of great interest in many QED problems, since it describes the lowest order correction for vacuum polarization in few- and many-electron atoms, ions, muonic and bi-muonic atoms/ions as well as in other similar systems.
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