{"title":"氢原子O(α)阶引力张量-单极矩","authors":"Xiangdong Ji, Jinghong Yang, Yizhuang Liu","doi":"10.1103/physrevd.110.114045","DOIUrl":null,"url":null,"abstract":"We calculate the gravitational tensor-monopole moment of the momentum-current density T</a:mi>i</a:mi>j</a:mi></a:mrow></a:msup></a:math> in the ground state of the hydrogen atom to order <c:math xmlns:c=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><c:mi mathvariant=\"script\">O</c:mi><c:mo stretchy=\"false\">(</c:mo><c:mi>α</c:mi><c:mo stretchy=\"false\">)</c:mo></c:math> in quantum electrodynamics (QED). The result is <h:math xmlns:h=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><h:msub><h:mi>τ</h:mi><h:mi>H</h:mi></h:msub><h:mo>/</h:mo><h:msub><h:mi>τ</h:mi><h:mn>0</h:mn></h:msub><h:mo>−</h:mo><h:mn>1</h:mn><h:mo>=</h:mo><h:mfrac><h:mrow><h:mn>4</h:mn><h:mi>α</h:mi></h:mrow><h:mrow><h:mn>3</h:mn><h:mi>π</h:mi></h:mrow></h:mfrac><h:mrow><h:mo stretchy=\"false\">(</h:mo><h:mi>ln</h:mi><h:msup><h:mi>α</h:mi><h:mn>2</h:mn></h:msup><h:mo>−</h:mo><h:mn>0.028</h:mn><h:mo stretchy=\"false\">)</h:mo></h:mrow><h:mo>=</h:mo><h:mo>−</h:mo><h:mn>3.06</h:mn><h:mo>×</h:mo><h:msup><h:mn>10</h:mn><h:mrow><h:mo>−</h:mo><h:mn>2</h:mn></h:mrow></h:msup></h:math> where <l:math xmlns:l=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><l:msub><l:mi>τ</l:mi><l:mn>0</l:mn></l:msub><l:mo>=</l:mo><l:msup><l:mi>ℏ</l:mi><l:mn>2</l:mn></l:msup><l:mo>/</l:mo><l:mn>4</l:mn><l:msub><l:mi>m</l:mi><l:mi>e</l:mi></l:msub></l:math> is the leading-order moment. The physics of the next-to-leading-order correction is similar to that of the famous Lamb shift for energy levels. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2024</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20167,"journal":{"name":"Physical Review D","volume":"117 1","pages":""},"PeriodicalIF":5.3000,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Gravitational tensor-monopole moment of the hydrogen atom to order O(α)\",\"authors\":\"Xiangdong Ji, Jinghong Yang, Yizhuang Liu\",\"doi\":\"10.1103/physrevd.110.114045\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We calculate the gravitational tensor-monopole moment of the momentum-current density T</a:mi>i</a:mi>j</a:mi></a:mrow></a:msup></a:math> in the ground state of the hydrogen atom to order <c:math xmlns:c=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><c:mi mathvariant=\\\"script\\\">O</c:mi><c:mo stretchy=\\\"false\\\">(</c:mo><c:mi>α</c:mi><c:mo stretchy=\\\"false\\\">)</c:mo></c:math> in quantum electrodynamics (QED). The result is <h:math xmlns:h=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><h:msub><h:mi>τ</h:mi><h:mi>H</h:mi></h:msub><h:mo>/</h:mo><h:msub><h:mi>τ</h:mi><h:mn>0</h:mn></h:msub><h:mo>−</h:mo><h:mn>1</h:mn><h:mo>=</h:mo><h:mfrac><h:mrow><h:mn>4</h:mn><h:mi>α</h:mi></h:mrow><h:mrow><h:mn>3</h:mn><h:mi>π</h:mi></h:mrow></h:mfrac><h:mrow><h:mo stretchy=\\\"false\\\">(</h:mo><h:mi>ln</h:mi><h:msup><h:mi>α</h:mi><h:mn>2</h:mn></h:msup><h:mo>−</h:mo><h:mn>0.028</h:mn><h:mo stretchy=\\\"false\\\">)</h:mo></h:mrow><h:mo>=</h:mo><h:mo>−</h:mo><h:mn>3.06</h:mn><h:mo>×</h:mo><h:msup><h:mn>10</h:mn><h:mrow><h:mo>−</h:mo><h:mn>2</h:mn></h:mrow></h:msup></h:math> where <l:math xmlns:l=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><l:msub><l:mi>τ</l:mi><l:mn>0</l:mn></l:msub><l:mo>=</l:mo><l:msup><l:mi>ℏ</l:mi><l:mn>2</l:mn></l:msup><l:mo>/</l:mo><l:mn>4</l:mn><l:msub><l:mi>m</l:mi><l:mi>e</l:mi></l:msub></l:math> is the leading-order moment. The physics of the next-to-leading-order correction is similar to that of the famous Lamb shift for energy levels. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2024</jats:copyright-year> </jats:permissions> </jats:supplementary-material>\",\"PeriodicalId\":20167,\"journal\":{\"name\":\"Physical Review D\",\"volume\":\"117 1\",\"pages\":\"\"},\"PeriodicalIF\":5.3000,\"publicationDate\":\"2024-12-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physical Review D\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1103/physrevd.110.114045\",\"RegionNum\":2,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Physics and Astronomy\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review D","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physrevd.110.114045","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Physics and Astronomy","Score":null,"Total":0}
Gravitational tensor-monopole moment of the hydrogen atom to order O(α)
We calculate the gravitational tensor-monopole moment of the momentum-current density Tij in the ground state of the hydrogen atom to order O(α) in quantum electrodynamics (QED). The result is τH/τ0−1=4α3π(lnα2−0.028)=−3.06×10−2 where τ0=ℏ2/4me is the leading-order moment. The physics of the next-to-leading-order correction is similar to that of the famous Lamb shift for energy levels. Published by the American Physical Society2024
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Physical Review D (PRD) is a leading journal in elementary particle physics, field theory, gravitation, and cosmology and is one of the top-cited journals in high-energy physics.
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