Computational analysis reveals a unified single-parameter master solution for impurity atoms in matrix metals, highlighting the accuracy limits of standard screened Coulomb potentials.
The scale transformation keeping invariant the TF equation for an impurity atom dissolved with infinite dilution in a matrix metal of very large size was established. It enabled us to reduce the double sequence of solutions of the TF equation specified by two parameters to a single sequence of master solutions specified by one parameter only. Starting from the asymptotic expansion of solution derived here anew the inward numerical integration of the TF equation was carried out. The screened Coulomb potential was compared with our numerical solutions to measure its degree of approximation.
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Umeda et al. (1958) studied this question.
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