Abstract
An approach to the calculation of the total energy of atoms and atomic ions as a function of atomic number Z and number of electrons N, based on the solution of secondorder differential equations together with auxiliary conditions, is presented. Some applications of the equations to the description of real atoms are also shown. Physical consequences of the approach are indicated. Attention is paid to the methodological aspects of the approach, which give the analytical form of the results and are very convenient for further treatment.
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Ptak, W.S., Giemza, J. & Tkacz, K. Differential equations for total energy of atoms and atomic ions within thomas-fermi approximation. J Math Chem 8, 161–168 (1991). https://doi.org/10.1007/BF01166932
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DOI: https://doi.org/10.1007/BF01166932