Analytical approximations to the solution of the Thomas-Fermi and Thomas-Fermi-Dirac-Weizs\"acker equation for neutral systems are presented. The authors demonstrate in detail the quality of the solutions for one-center boundary conditions and provide an extension for two-center systems. Finally, the construction of effective single-particle potentials for diatomic systems based on the solutions obtained is discussed.
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Gross et al. (1979) studied this question.
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