Calculation of the atomic states energies in the Thomas - Fermi approximation
A method for calculating the energies of levels for many-electron neutral atoms is proposed. In this case, in addition to the Coulomb field of the nucleus, an important contribution to the energy is connected with the interaction between the electrons. This interaction is taken into account approxim...
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| Format: | Article |
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Institute for Nuclear Research, National Academy of Sciences of Ukraine
2017-12-01
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| Series: | Ядерна фізика та енергетика |
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| Online Access: | http://jnpae.kinr.kiev.ua/18.3/html/18.3.0215.html |
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| author | S. N. Fedotkin |
| author_facet | S. N. Fedotkin |
| author_sort | S. N. Fedotkin |
| collection | DOAJ |
| description | A method for calculating the energies of levels for many-electron neutral atoms is proposed. In this case, in addition to the Coulomb field of the nucleus, an important contribution to the energy is connected with the interaction between the electrons. This interaction is taken into account approximately by perturbation theory in the framework of the Thomas - Fermi statistical model. Using the Taytz approximation for the mean potential the analytical expressions for the energies of s-states are obtained with principal quantum numbers n = 1, 2, 3, 4. The energies are calculated for the nuclear charges in the interval 1 < Z ≤ 100. A good agreement with the experimental values of the energies was obtained. |
| format | Article |
| id | doaj-art-2457ea62c3114e86b8880f5cb06f09d8 |
| institution | OA Journals |
| issn | 1818-331X 2074-0565 |
| language | English |
| publishDate | 2017-12-01 |
| publisher | Institute for Nuclear Research, National Academy of Sciences of Ukraine |
| record_format | Article |
| series | Ядерна фізика та енергетика |
| spelling | doaj-art-2457ea62c3114e86b8880f5cb06f09d82025-08-20T01:58:52ZengInstitute for Nuclear Research, National Academy of Sciences of UkraineЯдерна фізика та енергетика1818-331X2074-05652017-12-01183215221Calculation of the atomic states energies in the Thomas - Fermi approximationS. N. Fedotkin0Institute for Nuclear Research, National Academy of Sciences of Ukraine, Kyiv, Ukraine A method for calculating the energies of levels for many-electron neutral atoms is proposed. In this case, in addition to the Coulomb field of the nucleus, an important contribution to the energy is connected with the interaction between the electrons. This interaction is taken into account approximately by perturbation theory in the framework of the Thomas - Fermi statistical model. Using the Taytz approximation for the mean potential the analytical expressions for the energies of s-states are obtained with principal quantum numbers n = 1, 2, 3, 4. The energies are calculated for the nuclear charges in the interval 1 < Z ≤ 100. A good agreement with the experimental values of the energies was obtained.http://jnpae.kinr.kiev.ua/18.3/html/18.3.0215.htmlenergies of atomic levelsThomas - Fermi modelperturbation theory |
| spellingShingle | S. N. Fedotkin Calculation of the atomic states energies in the Thomas - Fermi approximation Ядерна фізика та енергетика energies of atomic levels Thomas - Fermi model perturbation theory |
| title | Calculation of the atomic states energies in the Thomas - Fermi approximation |
| title_full | Calculation of the atomic states energies in the Thomas - Fermi approximation |
| title_fullStr | Calculation of the atomic states energies in the Thomas - Fermi approximation |
| title_full_unstemmed | Calculation of the atomic states energies in the Thomas - Fermi approximation |
| title_short | Calculation of the atomic states energies in the Thomas - Fermi approximation |
| title_sort | calculation of the atomic states energies in the thomas fermi approximation |
| topic | energies of atomic levels Thomas - Fermi model perturbation theory |
| url | http://jnpae.kinr.kiev.ua/18.3/html/18.3.0215.html |
| work_keys_str_mv | AT snfedotkin calculationoftheatomicstatesenergiesinthethomasfermiapproximation |