Thomas-Fermi model: The leading correction

Abstract

The correct treatment of strongly bound electrons is grafted smoothly onto the Thomas-Fermi computation of the total binding energy of neutral atoms. This provides a clearcut demonstration of the leading correction of relative order ${Z}^{\ensuremath{-}\frac{1}{3}}$ which, with effects of relative order ${Z}^{\ensuremath{-}\frac{2}{3}}$, gives an accurate account of the binding energy over a wide range of $Z$ values. There is a brief discussion of relativistic corrections, with results that are somewhat at variance with previous numerical estimates.