Fock Expansion for Two-Electron Atoms: High-Order Angular Coefficients
The Fock expansion, which describes the properties of two-electron atoms near the nucleus, is studied. The angular Fock coefficients <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ψ&...
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MDPI AG
2022-11-01
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| Online Access: | https://www.mdpi.com/2218-2004/10/4/135 |
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| author | Evgeny Z. Liverts Rajmund Krivec |
| author_facet | Evgeny Z. Liverts Rajmund Krivec |
| author_sort | Evgeny Z. Liverts |
| collection | DOAJ |
| description | The Fock expansion, which describes the properties of two-electron atoms near the nucleus, is studied. The angular Fock coefficients <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ψ</mi><mrow><mi>k</mi><mo>,</mo><mi>p</mi></mrow></msub><mrow><mo>(</mo><mi>α</mi><mo>,</mo><mi>θ</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> with the maximum possible value of subscript <i>p</i> are calculated on examples of the coefficients with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>5</mn><mo>≤</mo><mi>k</mi><mo>≤</mo><mn>10</mn></mrow></semantics></math></inline-formula>. The presented technique makes it possible to calculate such angular coefficients for any arbitrarily large <i>k</i>. The mentioned coefficients being leading in the logarithmic power series representing the Fock expansion, they may be indispensable for the development of simple methods for calculating the helium-like electronic structure. The theoretical results obtained are verified by other suitable methods. The Wolfram Mathematica is used extensively. |
| first_indexed | 2024-03-09T17:20:38Z |
| format | Article |
| id | doaj.art-effa6b73462146f99c63d3938862844d |
| institution | Directory Open Access Journal |
| issn | 2218-2004 |
| language | English |
| last_indexed | 2024-03-09T17:20:38Z |
| publishDate | 2022-11-01 |
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| spelling | doaj.art-effa6b73462146f99c63d3938862844d2023-11-24T13:14:15ZengMDPI AGAtoms2218-20042022-11-0110413510.3390/atoms10040135Fock Expansion for Two-Electron Atoms: High-Order Angular CoefficientsEvgeny Z. Liverts0Rajmund Krivec1Racah Institute of Physics, The Hebrew University, Jerusalem 91904, IsraelDepartment of Theoretical Physics, J. Stefan Institute, 1000 Ljubljana, SloveniaThe Fock expansion, which describes the properties of two-electron atoms near the nucleus, is studied. The angular Fock coefficients <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ψ</mi><mrow><mi>k</mi><mo>,</mo><mi>p</mi></mrow></msub><mrow><mo>(</mo><mi>α</mi><mo>,</mo><mi>θ</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> with the maximum possible value of subscript <i>p</i> are calculated on examples of the coefficients with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>5</mn><mo>≤</mo><mi>k</mi><mo>≤</mo><mn>10</mn></mrow></semantics></math></inline-formula>. The presented technique makes it possible to calculate such angular coefficients for any arbitrarily large <i>k</i>. The mentioned coefficients being leading in the logarithmic power series representing the Fock expansion, they may be indispensable for the development of simple methods for calculating the helium-like electronic structure. The theoretical results obtained are verified by other suitable methods. The Wolfram Mathematica is used extensively.https://www.mdpi.com/2218-2004/10/4/135two-electron atom/ionwave functionFock expansionangular coefficientsWolfram Mathematica |
| spellingShingle | Evgeny Z. Liverts Rajmund Krivec Fock Expansion for Two-Electron Atoms: High-Order Angular Coefficients Atoms two-electron atom/ion wave function Fock expansion angular coefficients Wolfram Mathematica |
| title | Fock Expansion for Two-Electron Atoms: High-Order Angular Coefficients |
| title_full | Fock Expansion for Two-Electron Atoms: High-Order Angular Coefficients |
| title_fullStr | Fock Expansion for Two-Electron Atoms: High-Order Angular Coefficients |
| title_full_unstemmed | Fock Expansion for Two-Electron Atoms: High-Order Angular Coefficients |
| title_short | Fock Expansion for Two-Electron Atoms: High-Order Angular Coefficients |
| title_sort | fock expansion for two electron atoms high order angular coefficients |
| topic | two-electron atom/ion wave function Fock expansion angular coefficients Wolfram Mathematica |
| url | https://www.mdpi.com/2218-2004/10/4/135 |
| work_keys_str_mv | AT evgenyzliverts fockexpansionfortwoelectronatomshighorderangularcoefficients AT rajmundkrivec fockexpansionfortwoelectronatomshighorderangularcoefficients |