Abstract
The approximate solution of the nonlinear Thomas–Fermi (TF) equation for ions is found by the Fermi method. The solution is based on the new asymptotic representation of the TF ion size valid for any ionization degree. The two universal functions and their derivatives, introduced by Fermi, are calculated by recent effective algorithms for the Emden–Fowler type equations with the accuracy sufficient for majority of applications. The comparison of our results with those obtained previously shows high accuracy and validity for arbitrary values of ionization degree. This study could potentially be of interest for the statistical TF method applications in physics and chemistry.
Subject
Condensed Matter Physics,Nuclear and High Energy Physics,Atomic and Molecular Physics, and Optics
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