Key points are not available for this paper at this time.
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^-1{3} which, with effects of relative order Z^-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.
Julian Schwinger (Sat,) studied this question.