Approximation of the Thomas-Fermi-Dirac potential for neutral atoms

Aleksander Jablonski

Physica A: Statistical Mechanics and its Applications, 1992, vol. 183, issue 3, 361-377

Abstract: The frequently used analytical expression of Bonham and Strand approximating the Thomas-Fermi-Dirac (TFD) potential is closely analyzed. This expression does not satisfy the boundary conditions of the TFD differential equation, in particular, does not comprise the finite radius of the TFD potential. A modification of the analytical expression is proposed to adjust it to the boundary conditions. A new fit is made on the basis of the variational formulation of the TFD problem. An attempt is also made in the present work to develop a new numerical procedure providing very accurate solutions of this problem. Such solutions form a reference to check the quality of analytical approximations. Exemplary calculations of the elastic scattering cross sections are made for different expressions approximating the TFD potential to visualize the influence of the inaccuracies of the fit. It seems that the elastic scattering calculations should be based on extensive tables with the accurate values of the TFD screening function rather than on fitted analytical expressions.

Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:183:y:1992:i:3:p:361-377

DOI: 10.1016/0378-4371(92)90151-F

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