The improved Thomas-Fermi model : chemical and ionization potentials in atoms

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Abstract
Analytical expressions for non-relativistic values of the chemical μ( N, Z) and ionization I(N, Z) potentials are derived from the TF model including corrections for the exchange and inhomogeneity of electron density. These expressions reproduce well the smoothed ionization potential of an atom. It is shown that I(N, Z) and μ(N, Z) in a weak ionization limit are determined mainly by quantum contributions due to the exchange and correlation and may be written as A + B (Z - N). The relationship between μ and I for atoms with a small ionization degree, m = Z - N, is found μm+1 ≃ - (2 m + 1) (2 m + 2)-1 Im+1 which should be valid for atoms with s- and p-valence electrons. It is proved that the simple TF model gives an asymptotically exact value I(N, Z) within N/Z → 0 and the oscillation correction has a relative order N-1/3