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We use an iterative process to get an analytical solution for a screened Thomas-Fermi (Yukawa) potential. The analytical solution is not exact, but the result agrees with the best variational and numerical integration results. The critical Thomas-Fermi wave vector qc above which there is no bound state is obtained within 0.03% accuracy. We also show that the critical effective charge vanishes.
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Garavelli et al. (1991) studied this question.
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