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

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  • Jablonski, Aleksander

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.

Suggested Citation

  • Jablonski, Aleksander, 1992. "Approximation of the Thomas-Fermi-Dirac potential for neutral atoms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 183(3), pages 361-377.
    • Handle: RePEc:eee:phsmap:v:183:y:1992:i:3:p:361-377
    DOI: 10.1016/0378-4371(92)90151-F
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    1. Elstrand, Eivind, 1963. "Economics Of Large-Scale Milk Production In Norway And Other Countries With Special Emphasis On Cow Pools," Graduate Research Master's Degree Plan B Papers 11062, Michigan State University, Department of Agricultural, Food, and Resource Economics.
    2. Shimizu, Yoshinori, 1980. "“The Chicago Tradition” and the Empirical Relevance of the Modern Quantity Theory of Money," Hitotsubashi Journal of commerce and management, Hitotsubashi University, vol. 15(1), pages 28-35, October.
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