Thermodynamic Functions in the Thomas–Fermi Atom Model

Abstract

In applications, the important energy associated with the Thomas–Fermi atom model is the difference u of the total energy from that corresponding to an infinite atom. That part u′ of the energy u that depends on the difference of the initial slope of the Thomas–Fermi function from its value for an infinite atom limits the accuracy possible in energies on the model, over the intermediate range of atom radius xb. Values of the difference in initial slope accurate to four significant figures for xb up to 16 and accurate to three figures for xb up to 50 have been computed, essentially by integrating the pressure. These data have been fitted by an analytic function showing the proper limiting forms through the two leading terms in each case as xb approaches zero and as xb approaches infinity. The accuracy of the fit is 0.1%, in general. In conjunction with a fitted function given by Gilvarry and March, the present results yield thermodynamic functions accurate to a few parts in a thousand as analytic functions of the radius, over essentially the entire span of this variable.