{"title":"类锗高电荷原子离子激发态的z相关三能级同时交叉","authors":"Fumihiro Koike , Chihiro Suzuki , Nobuyuki Nakamura , Izumi Murakami , Daiji Kato , Naoki Tamura","doi":"10.1016/j.physleta.2025.130795","DOIUrl":null,"url":null,"abstract":"<div><div>Simultaneous-crossing of three energy-levels has been found for the first time in the atomic number <em>Z</em>-dependent wavelength curves at <span><math><mi>Z</mi><mo>=</mo><mn>66</mn></math></span> of Ge-like highly charged atomic ions. Large Helical Device (LHD) and EBIT are used for obtaining the wavelength of EUV emissions from the transitions of 4<em>s</em> or 4<em>p</em> excited states into their ground state <span><math><msub><mrow><mo>(</mo><mo>[</mo><mrow><mi>Ni</mi></mrow><mo>]</mo><mn>4</mn><msup><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msup><mn>4</mn><msubsup><mrow><mi>p</mi></mrow><mrow><mo>−</mo></mrow><mrow><mn>2</mn></mrow></msubsup><mo>)</mo></mrow><mrow><mn>0</mn></mrow></msub></math></span>. Multi-Configuration Dirac-Fock calculation has been carried out for analysis. Interactions between the three excited-state configurations <span><math><msub><mrow><mo>(</mo><mo>[</mo><mrow><mi>Ni</mi></mrow><mo>]</mo><mn>4</mn><msup><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msup><mn>4</mn><msub><mrow><mi>p</mi></mrow><mrow><mo>−</mo></mrow></msub><mn>4</mn><msub><mrow><mi>d</mi></mrow><mrow><mo>−</mo></mrow></msub><mo>)</mo></mrow><mrow><mn>1</mn></mrow></msub></math></span>, <span><math><msub><mrow><mo>(</mo><mo>[</mo><mrow><mi>Ni</mi></mrow><mo>]</mo><mn>4</mn><mi>s</mi><mn>4</mn><msub><mrow><mi>p</mi></mrow><mrow><mo>−</mo></mrow></msub><msub><mrow><mo>(</mo><mn>4</mn><msubsup><mrow><mi>p</mi></mrow><mrow><mo>+</mo></mrow><mrow><mn>2</mn></mrow></msubsup><mo>)</mo></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></mrow><mrow><mn>1</mn></mrow></msub></math></span>, and <span><math><msub><mrow><mo>(</mo><mo>[</mo><mrow><mi>Ni</mi></mrow><mo>]</mo><mn>4</mn><mi>s</mi><mn>4</mn><msub><mrow><mi>p</mi></mrow><mrow><mo>−</mo></mrow></msub><msub><mrow><mo>(</mo><mn>4</mn><msubsup><mrow><mi>p</mi></mrow><mrow><mo>+</mo></mrow><mrow><mn>2</mn></mrow></msubsup><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></mrow><mrow><mn>1</mn></mrow></msub></math></span> lead to the three-dimensional rotation of atomic state-vectors in the configuration space on the way for <em>Z</em> to pass the crossing point. <em>Z</em>-evolution of the atomic states has been analyzed employing the quaternion algebra. The spectral anomalies near the level-crossing are simulated by the atomic state-vector rotation. The optically invisible states are thus become visible by sharing the intensities of optically allowed configuration <span><math><msub><mrow><mo>(</mo><mo>[</mo><mrow><mi>Ni</mi></mrow><mo>]</mo><mn>4</mn><msup><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msup><mn>4</mn><msub><mrow><mi>p</mi></mrow><mrow><mo>−</mo></mrow></msub><mn>4</mn><msub><mrow><mi>d</mi></mrow><mrow><mo>−</mo></mrow></msub><mo>)</mo></mrow><mrow><mn>1</mn></mrow></msub></math></span>.</div></div>","PeriodicalId":20172,"journal":{"name":"Physics Letters A","volume":"555 ","pages":"Article 130795"},"PeriodicalIF":2.6000,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Z-dependent three-level simultaneous-crossing of excited states in germanium-like highly charged atomic ions\",\"authors\":\"Fumihiro Koike , Chihiro Suzuki , Nobuyuki Nakamura , Izumi Murakami , Daiji Kato , Naoki Tamura\",\"doi\":\"10.1016/j.physleta.2025.130795\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Simultaneous-crossing of three energy-levels has been found for the first time in the atomic number <em>Z</em>-dependent wavelength curves at <span><math><mi>Z</mi><mo>=</mo><mn>66</mn></math></span> of Ge-like highly charged atomic ions. Large Helical Device (LHD) and EBIT are used for obtaining the wavelength of EUV emissions from the transitions of 4<em>s</em> or 4<em>p</em> excited states into their ground state <span><math><msub><mrow><mo>(</mo><mo>[</mo><mrow><mi>Ni</mi></mrow><mo>]</mo><mn>4</mn><msup><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msup><mn>4</mn><msubsup><mrow><mi>p</mi></mrow><mrow><mo>−</mo></mrow><mrow><mn>2</mn></mrow></msubsup><mo>)</mo></mrow><mrow><mn>0</mn></mrow></msub></math></span>. Multi-Configuration Dirac-Fock calculation has been carried out for analysis. Interactions between the three excited-state configurations <span><math><msub><mrow><mo>(</mo><mo>[</mo><mrow><mi>Ni</mi></mrow><mo>]</mo><mn>4</mn><msup><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msup><mn>4</mn><msub><mrow><mi>p</mi></mrow><mrow><mo>−</mo></mrow></msub><mn>4</mn><msub><mrow><mi>d</mi></mrow><mrow><mo>−</mo></mrow></msub><mo>)</mo></mrow><mrow><mn>1</mn></mrow></msub></math></span>, <span><math><msub><mrow><mo>(</mo><mo>[</mo><mrow><mi>Ni</mi></mrow><mo>]</mo><mn>4</mn><mi>s</mi><mn>4</mn><msub><mrow><mi>p</mi></mrow><mrow><mo>−</mo></mrow></msub><msub><mrow><mo>(</mo><mn>4</mn><msubsup><mrow><mi>p</mi></mrow><mrow><mo>+</mo></mrow><mrow><mn>2</mn></mrow></msubsup><mo>)</mo></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></mrow><mrow><mn>1</mn></mrow></msub></math></span>, and <span><math><msub><mrow><mo>(</mo><mo>[</mo><mrow><mi>Ni</mi></mrow><mo>]</mo><mn>4</mn><mi>s</mi><mn>4</mn><msub><mrow><mi>p</mi></mrow><mrow><mo>−</mo></mrow></msub><msub><mrow><mo>(</mo><mn>4</mn><msubsup><mrow><mi>p</mi></mrow><mrow><mo>+</mo></mrow><mrow><mn>2</mn></mrow></msubsup><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></mrow><mrow><mn>1</mn></mrow></msub></math></span> lead to the three-dimensional rotation of atomic state-vectors in the configuration space on the way for <em>Z</em> to pass the crossing point. <em>Z</em>-evolution of the atomic states has been analyzed employing the quaternion algebra. The spectral anomalies near the level-crossing are simulated by the atomic state-vector rotation. The optically invisible states are thus become visible by sharing the intensities of optically allowed configuration <span><math><msub><mrow><mo>(</mo><mo>[</mo><mrow><mi>Ni</mi></mrow><mo>]</mo><mn>4</mn><msup><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msup><mn>4</mn><msub><mrow><mi>p</mi></mrow><mrow><mo>−</mo></mrow></msub><mn>4</mn><msub><mrow><mi>d</mi></mrow><mrow><mo>−</mo></mrow></msub><mo>)</mo></mrow><mrow><mn>1</mn></mrow></msub></math></span>.</div></div>\",\"PeriodicalId\":20172,\"journal\":{\"name\":\"Physics Letters A\",\"volume\":\"555 \",\"pages\":\"Article 130795\"},\"PeriodicalIF\":2.6000,\"publicationDate\":\"2025-07-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physics Letters A\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0375960125005754\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physics Letters A","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0375960125005754","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
Z-dependent three-level simultaneous-crossing of excited states in germanium-like highly charged atomic ions
Simultaneous-crossing of three energy-levels has been found for the first time in the atomic number Z-dependent wavelength curves at of Ge-like highly charged atomic ions. Large Helical Device (LHD) and EBIT are used for obtaining the wavelength of EUV emissions from the transitions of 4s or 4p excited states into their ground state . Multi-Configuration Dirac-Fock calculation has been carried out for analysis. Interactions between the three excited-state configurations , , and lead to the three-dimensional rotation of atomic state-vectors in the configuration space on the way for Z to pass the crossing point. Z-evolution of the atomic states has been analyzed employing the quaternion algebra. The spectral anomalies near the level-crossing are simulated by the atomic state-vector rotation. The optically invisible states are thus become visible by sharing the intensities of optically allowed configuration .
期刊介绍:
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