{"title":"厄林电势微分方程","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":1.7000,"publicationDate":"2024-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":1.7000,\"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}","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}
引用次数: 0
摘要
摘要 明确推导出了上林势的二阶微分方程。这个微分方程的右边是两个麦克唐纳函数\(K_{0}(b r)\)和\(K_{1}(b r)\)的线性组合。这个中心势在许多 QED 问题中都具有重大意义，因为它描述了少电子和多电子原子、离子、μ介子和双μ介子原子/离子以及其他类似系统中真空极化的最低阶修正。
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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