https://oldena.lpnu.ua/handle/ntb/46150| Title: | The shell model of electron structure of negative hydrogen ion |
| Other Titles: | Оболонкова модель електронної структури негативного іона водню |
| Authors: | Ваврух, М. Дзіковський, Д. Стельмах, О. Vavrukh, M. Dzikovskyi, D. Stelmakh, O. |
| Affiliation: | Львівський національний університет імені Івана Франка Ivan Franko National University of Lviv |
| Bibliographic description (Ukraine): | Vavrukh M. The shell model of electron structure of negative hydrogen ion / M. Vavrukh, D. Dzikovskyi, O. Stelmakh // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2019. — Vol 6. — No 1. — P. 144–151. |
| Bibliographic description (International): | Vavrukh M. The shell model of electron structure of negative hydrogen ion / M. Vavrukh, D. Dzikovskyi, O. Stelmakh // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2019. — Vol 6. — No 1. — P. 144–151. |
| Is part of: | Mathematical Modeling and Computing, 1 (6), 2019 |
| Issue: | 1 |
| Issue Date: | 26-Feb-2019 |
| Publisher: | Lviv Politechnic Publishing House |
| Place of the edition/event: | Львів Lviv |
| UDC: | 523.9 523.9-7 523.9-47 |
| Keywords: | негативний іон водню базисний підхід варіаційний підхід енергія іонізації negative hydrogen ion reference system approach variation method energy of ionization |
| Number of pages: | 8 |
| Page range: | 144-151 |
| Start page: | 144 |
| End page: | 151 |
| Abstract: | У межах нерелятивістського наближення одержано компактний наближений
розв’язок рівняння Шредингера для іона H− у вигляді розкладу за поліномами Лежандра
і варіаційними функціями типу Шулля–Льовдіна. Точність розрахунку енергії іона
відповідає результатам, одержаним за допомогою багатопараметричних функцій Гіллєраса і Пекеріса. In the frame of non-relativistic approximation, a compact approximate solution of the Schr¨odinger equation for the ion of H− has been obtained in the form of product for Legendre polynomials and variational functions of the Schull–L¨owdin type. The accuracy of calculation of ion energy is of the same order that the results obtained using the multiparametric functions of Hylleraas and Pekeris. |
| URI: | https://ena.lpnu.ua/handle/ntb/46150 |
| Copyright owner: | CMM IAPMM NAS © 2019 Lviv Polytechnic National University |
| References (Ukraine): | 1. WildtR. The Continuous Spectrum of Stellar Atmospheres Consisting Only of Atoms and Negative Ions of Hydrogen. Astrophys. Journ. 93, 47–51 (1941). 2. Chandrasekhar S., Breen F.H. On the Continuous Absorption Coefficient of the Negative Hydrogen Ion. III. Astrophys. Journ. 104, 430–445 (1946). 3. Geltman S. The Bound-Free Absorption Coefficient of the Hydrogen Negative Ion. Astrophys. Journ. 136, 935–945 (1962). 4. WishartA.W. The Bound-Free Photodetachment Cross Section of H−. J. Phys. B: Atom. Molec. Phys. 12 (21), 3511–3519, (1979). 5. VavrukhМ.V., Vasil’eva I.Е., StelmakhО.М., TyshkoN. L. Continuous Absorption and Depression in the Solar Spectrum at Wavelengths from 650 to 820 nm. Kinematics and Physics of Celestial Bodies. 32 (3), 129–144 (2016). 6. Hylleraas E.A. Die Elektronenaffinit¨at des Wasserstoffatoms nach der Wellenmechanik. Zeitschrift f¨ur Physik. 60, 624–630 (1930). 7. PekerisC. L. 11S, 21S and 23S States of H− and of He. Phys. Rev. 126, 1470–1476 (1962). 8. MasseyH. S.W. Negative Ions. Cambridge University Press (1976). 9. SchullH., L¨owdinP.-O. Correlation Splitting in Helium-Like Ions. J. Chem. Phys. 25, 1035–1040 (1956). 10. KinoshitaT. Ground State of the Helium Atom. Phys. Rev. 105, 1490–1502 (1957). 11. Hart J. F., HerzbergG. Twenty-Parameter Eigenfunctions and Energy Values of the Ground States of He and He-Like Ions. Phys. Rev. 106, 79–82 (1957). 12. TweedR. J. Correlated wavefunctions for helium-like atomic systems. J. Phys. B: Atom. Molec. Phys. 5, 810–819 (1972). |
| References (International): | 1. WildtR. The Continuous Spectrum of Stellar Atmospheres Consisting Only of Atoms and Negative Ions of Hydrogen. Astrophys. Journ. 93, 47–51 (1941). 2. Chandrasekhar S., Breen F.H. On the Continuous Absorption Coefficient of the Negative Hydrogen Ion. III. Astrophys. Journ. 104, 430–445 (1946). 3. Geltman S. The Bound-Free Absorption Coefficient of the Hydrogen Negative Ion. Astrophys. Journ. 136, 935–945 (1962). 4. WishartA.W. The Bound-Free Photodetachment Cross Section of H−. J. Phys. B: Atom. Molec. Phys. 12 (21), 3511–3519, (1979). 5. VavrukhM.V., Vasil’eva I.E., StelmakhO.M., TyshkoN. L. Continuous Absorption and Depression in the Solar Spectrum at Wavelengths from 650 to 820 nm. Kinematics and Physics of Celestial Bodies. 32 (3), 129–144 (2016). 6. Hylleraas E.A. Die Elektronenaffinit¨at des Wasserstoffatoms nach der Wellenmechanik. Zeitschrift f¨ur Physik. 60, 624–630 (1930). 7. PekerisC. L. 11S, 21S and 23S States of H− and of He. Phys. Rev. 126, 1470–1476 (1962). 8. MasseyH. S.W. Negative Ions. Cambridge University Press (1976). 9. SchullH., L¨owdinP.-O. Correlation Splitting in Helium-Like Ions. J. Chem. Phys. 25, 1035–1040 (1956). 10. KinoshitaT. Ground State of the Helium Atom. Phys. Rev. 105, 1490–1502 (1957). 11. Hart J. F., HerzbergG. Twenty-Parameter Eigenfunctions and Energy Values of the Ground States of He and He-Like Ions. Phys. Rev. 106, 79–82 (1957). 12. TweedR. J. Correlated wavefunctions for helium-like atomic systems. J. Phys. B: Atom. Molec. Phys. 5, 810–819 (1972). |
| Content type: | Article |
| Appears in Collections: | Mathematical Modeling And Computing. – 2019. – Vol. 6, No. 1 |
| File | Description | Size | Format | |
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| 2019v6n1_Vavrukh_M-The_shell_model_of_electron_144-151.pdf | 928.54 kB | Adobe PDF | View/Open | |
| 2019v6n1_Vavrukh_M-The_shell_model_of_electron_144-151__COVER.png | 375.88 kB | image/png | View/Open |
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