On the atomic binding energy in the Thomas-Fermi model

The empirical binding energy −16Z7/3eV of heavy atoms is computed herein by a Hartree-type correction to a linearized version of the Thomas-Fermi model; the computations are carried out by means of a variational approach. Corrections to the exchange energy are also estimated. The Thomas-Fermi model is based on the quasi-classical description and the statistical character of the electronic single-particle states in heavy atoms, i.e. in atoms with large atomic numbers Z (Z 1).[1] The electrons are assumed to form an inhomogeneous gas of fermions, and the Fermi wavevector kF is determined by a self-consistent field potential ϕ, according to h̄2k2F/2m − eϕ = 0; (1) here, the notations are the usual ones, i.e. h ̄ is Planck’s constant, m is the electron mass, and −e is the electron charge. The electric potential ϕ is determined by Poisson’s equation ∆ϕ = −4piZeδ(r) + 4pine, (2) where the electron density is given by n = k3F/3pi 2, as for a Fermi gas. As it is well known, th