The Thomas-Fermi model approximates electron density n(r) around an atom by balancing kinetic energy (local Fermi gas) against nuclear attraction. The total energy is a functional E[n].
Thomas-Fermi screening: φ(r)=(Z/r)·χ(r/a_TF), a_TF=0.8853·Z^(-1/3). Electron density n(r)=(1/3π²)(2φ(r))^(3/2). Visualised in dimensionless Thomas-Fermi units.